systematic working through marked up printout of whole thesis as is
This commit is contained in:
Robin
parent
9fce93fdce
commit
2469683b5d
17
burner/Makefile
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17
burner/Makefile
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@ -0,0 +1,17 @@
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#
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# Make the propositional logic diagram a paper
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#
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paper: paper.tex burner_paper.tex
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#latex paper.tex
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#dvipdf paper pdflatex cannot use eps ffs
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pdflatex paper.tex
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okular paper.pdf
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# Remove the need for referncing graphics in subdirectories
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#
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burner_paper.tex: burner.tex
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cat burner.tex | sed 's/burner\///' > paper.tex
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63
burner/burner.tex
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63
burner/burner.tex
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%
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% Make the revision and doc number macro's then they are defined in one place
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\begin{abstract}
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things can get very abstract
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\end{abstract}
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\section{Overview of A Burner Controller : Safety Perspective}
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\section{Background to the Industrial Burner Safety Analysis Problem}
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An industrial burner is a good example of a safety critical system.
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It has the potential for devistating explosions due to boiler overpressure, low water, or
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ignition of an explosive mixture, and, because of the large amounts of fuel used,
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is also a fire hazard. Industrial boilers are often left running unattended
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for long periods of time (typically days).
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To add to these problems
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Operators are often under pressure to keep them running. A boiler supplying
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heat to a large greenhouse complex could ruin crops
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should it go off-line. Similarly a production line relying on heat or steam
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can be very expensive in production down-time should it fail.
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This places extra responsibility on the burner controller.
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These are common place and account for a very large proportion of the enery usage
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in the world today (find and ref stats)
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Industrial burners are common enough to have different specific standards
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written for the fuel types they use \ref{EN298} \ref{EN230} \ref{EN12067}.
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A modern industrial burner has mechanical, electronic and software
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elements, that are all safety critical. That is to say
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unhandled failures could create dangerous faults.
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A more detailed description of industrial burner controllers
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is dealt with in chapter~\ref{burnercontroller}.
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Systems such as industrial burners have been partially automated for some time.
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A mechanical cam arrangement controls the flow of air and fuel for the range of
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firing rate (output of the boiler).
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These mechanical systems could suffer failures (such as a mechanical linkage beoming
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detached) and could then operate in a potentially dangerous state.
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More modern burner controllers use a safety critical computer controlling
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motors to operate the fuel and air mixture and to control the safety
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valves.
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In working in the industrial burner industry and submitting product for
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North American and European safety approval, it was apparent that
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formal techniques could be applied to aspects of the ciruit design.
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Some safety critical circuitry would be subjected to thought experiments, where
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the actions of one or more components failing would be examined.
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As a simple example a milli-volt input could become disconnected.
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A milli-volt input is typically amplified so that its range matches that
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of the A->D converter that you are reading. were this signal source to become disconnected
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the systems would see a floating, amplified signal.
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A high impedance safety resistor can be added to the circuit,
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to pull the signal high (or out of nornal range) upon disconnection.
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The system then knows that a fault has occurred and will not use
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that sensor reading (see \ref{fig:millivolt}).
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9
burner/burner.tex~
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9
burner/burner.tex~
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%
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% Make the revision and doc number macro's then they are defined in one place
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\begin{abstract}
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\end{abstract}
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\section{Overview of A Burner Controller : Safety Perspective}
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404
burner/mybib.bib
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404
burner/mybib.bib
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%
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%
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% $Id: mybib.bib,v 1.5 2008/12/18 17:05:23 robin Exp $
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%
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%
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@TechReport{db,
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author = {R Clark, D Legge},
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title = {ETC6000 Daughterboard Design notes},
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institution = {ETC HR221850},
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year = {2004},
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key = {},
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|
OPTtype = {},
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OPTnumber = {},
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|
OPTaddress = {},
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|
OPTmonth = {},
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OPTnote = {},
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OPTannote = {},
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OPTurl = {},
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OPTdoi = {},
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issn = {HR221850},
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OPTlocalfile = {},
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OPTabstract = {},
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}
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@TechReport{mil1991,
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author = {U.S. Department of Defence},
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title = {Reliability Prediction of Electronic Equipment},
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|
institution = {DOD},
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year = {1991},
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|
key = {MIL-HDBK-217F},
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|
OPTtype = {},
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|
OPTnumber = {},
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|
OPTaddress = {},
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|
OPTmonth = {},
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OPTnote = {},
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OPTannote = {},
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OPTurl = {},
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OPTdoi = {},
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OPTissn = {},
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OPTlocalfile = {},
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OPTabstract = {},
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}
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@Manual{tlp181,
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title = {TLP 181 Datasheet},
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key = {TOSHIBA Photocoupler GaAs Ired & Photo−Transistor},
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author = {Toshiba inc.},
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OPTorganization = {},
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%address = {http://www.toshiba.com/taec/components2/Datasheet\_Sync//206/4191.pdf},
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|
OPTedition = {},
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|
OPTmonth = {},
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year = {2009},
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|
OPTnote = {},
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||||||
|
OPTannote = {},
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|
OPTurl = {},
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OPTdoi = {},
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OPTissn = {},
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OPTlocalfile = {},
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OPTabstract = {},
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}
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@Manual{pic18f2523,
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title = {PIC18F2523 Datasheet},
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OPTkey = {},
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||||||
|
author = {Microchip inc},
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|
OPTorganization = {},
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||||||
|
address = {http://ww1.microchip.com/downloads/en/DeviceDoc/39755c.pdf},
|
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|
OPTedition = {},
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||||||
|
OPTmonth = {},
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||||||
|
year = {2009},
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||||||
|
OPTnote = {},
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||||||
|
OPTannote = {},
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|
OPTurl = {},
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|
OPTdoi = {},
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OPTissn = {},
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OPTlocalfile = {},
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|
OPTabstract = {},
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}
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|
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@Book{wt,
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|
title = {Water Treatment Essentials for Boiler Plant Operation},
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publisher = {Mc Graw Hill ISBN 0-07-048291-5},
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|
year = {1997},
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|
author = {Robert G Nunn},
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|
ALTALTeditor = {},
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|
OPTkey = {},
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||||||
|
OPTvolume = {},
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||||||
|
OPTnumber = {},
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||||||
|
OPTseries = {},
|
||||||
|
OPTaddress = {},
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||||||
|
OPTedition = {},
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||||||
|
OPTmonth = {},
|
||||||
|
OPTnote = {},
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||||||
|
OPTannote = {},
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|
OPTurl = {},
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|
OPTdoi = {},
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|
OPTissn = {ISBN 0-07-048291-5},
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|
OPTlocalfile = {},
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||||||
|
OPTabstracts = {},
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|
}
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@TechReport{pcbAI222562,
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|
author = {C Talmay},
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title = {Circuit Schematic TDS Daughterboard AI222562},
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|
institution = {ETC},
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year = {2010},
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|
OPTkey = {},
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|
OPTtype = {},
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|
OPTnumber = {AI222562},
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|
OPTaddress = {},
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|
OPTmonth = {},
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|
OPTnote = {},
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OPTannote = {},
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OPTurl = {},
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OPTdoi = {},
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OPTissn = {},
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OPTlocalfile = {},
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OPTabstract = {},
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||||||
|
}
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@TechReport{spiraxsarco,
|
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|
author = {Spirax Sarco},
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|
title = {http://www.spiraxsarco.com/resources/steam-engineering-tutorials.asp},
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|
institution = {Spirax Sarco},
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|
year = {2010},
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|
OPTkey = {},
|
||||||
|
OPTtype = {},
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||||||
|
OPTnumber = {},
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||||||
|
OPTaddress = {},
|
||||||
|
OPTmonth = {},
|
||||||
|
OPTnote = {},
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|
OPTannote = {},
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|
OPTurl = {},
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|
OPTdoi = {},
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|
OPTissn = {},
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|
OPTlocalfile = {},
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|
OPTabstract = {},
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||||||
|
}
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|
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|
@Book{aoe,
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|
title = {The Art of Electronics},
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|
publisher = {Cambridge},
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|
year = {1989},
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|
author = {Paul Horowitz, Winfield Hill},
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|
%author = {},
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|
OPTkey = {},
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|
OPTvolume = {},
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|
OPTnumber = {},
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|
OPTseries = {},
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|
OPTaddress = {},
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|
OPTedition = {2nd},
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|
OPTmonth = {},
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|
OPTnote = {},
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||||||
|
OPTannote = {},
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||||||
|
OPTurl = {},
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|
OPTdoi = {},
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||||||
|
OPTissn = {ISBN 0-521-37095-7},
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||||||
|
OPTlocalfile = {},
|
||||||
|
OPTabstracts = {},
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||||||
|
}
|
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|
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|
@TechReport{eurothermtables,
|
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|
author = {},
|
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|
title = {Thermocouple Emf TABLES and PLATINUM 100 RESISTANCE THERMOMETER TABLES},
|
||||||
|
institution = {Eurotherm},
|
||||||
|
year = {1973},
|
||||||
|
OPTkey = {},
|
||||||
|
OPTtype = {},
|
||||||
|
OPTnumber = {},
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||||||
|
OPTaddress = {},
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||||||
|
OPTmonth = {June},
|
||||||
|
OPTnote = {Bulletin TT-1},
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||||||
|
OPTannote = {},
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|
OPTurl = {},
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||||||
|
OPTdoi = {},
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||||||
|
OPTissn = {},
|
||||||
|
OPTlocalfile = {},
|
||||||
|
OPTabstract = {},
|
||||||
|
}
|
||||||
|
|
||||||
|
@MISC{iso639-1,
|
||||||
|
title = "ISO 639-1: Code for the Representation of Names of Languages",
|
||||||
|
author = "International Standardization Organization",
|
||||||
|
howpublished = "http://www.loc.gov/standards/iso639-2/criteria1.html"
|
||||||
|
year = "1998"
|
||||||
|
}
|
||||||
|
|
||||||
|
@MISC{nano-x,
|
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|
title = "The nano-X windowing system",
|
||||||
|
author = "Greg Haerr",
|
||||||
|
howpublished = "http://www.microwindows.org/"
|
||||||
|
year = "2003"
|
||||||
|
}
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||||||
|
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|
||||||
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|
|
||||||
|
@MISC{X11,
|
||||||
|
title = "The XFree86 Project, Inc",
|
||||||
|
author = "Open Source",
|
||||||
|
howpublished = "http://www.xfree86.org/"
|
||||||
|
year = "1992"
|
||||||
|
}
|
||||||
|
|
||||||
|
|
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|
http://www.xfree86.org/
|
||||||
|
|
||||||
|
@MISC{iso639-2,
|
||||||
|
title = "ISO 639-2: Code for the Representation of Names of Languages",
|
||||||
|
author = "International Standardization Organization",
|
||||||
|
howpublished = "http://www.loc.gov/standards/iso639-2/criteria1.html"
|
||||||
|
year = "1998"
|
||||||
|
}
|
||||||
|
|
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|
|
||||||
|
@misc{ touchscreenprod,
|
||||||
|
author = "M. Thirsk",
|
||||||
|
title = "Touchscreen Production Procedure : HR~222165",
|
||||||
|
howpublished = "Internal ETC Document",
|
||||||
|
year = "2008" };
|
||||||
|
|
||||||
|
|
||||||
|
@misc{ touchscreensoftware,
|
||||||
|
author = "ETC Software Dept.",
|
||||||
|
title = "Touchscreen Software released to Production : HR~222162",
|
||||||
|
howpublished = "Internal ETC Software (medium: 2 MMC cards)",
|
||||||
|
year = "2008" };
|
||||||
|
|
||||||
|
@misc{ touchscreengui,
|
||||||
|
author = "D.J. Legge, R.P.Clark",
|
||||||
|
title = "Touchscreen GUI Design Document : HR~222163",
|
||||||
|
howpublished = "Internal ETC Document",
|
||||||
|
year = "2008" };
|
||||||
|
|
||||||
|
|
||||||
|
@misc{ gumstix,
|
||||||
|
author = "Gumstix Inc",
|
||||||
|
title = "Gumstix Home Page",
|
||||||
|
howpublished = "WEB http://www.gumstix.com/",
|
||||||
|
year = "2008" };
|
||||||
|
|
||||||
|
|
||||||
|
@misc{ fltk,
|
||||||
|
author = "FLTK open Source Developers",
|
||||||
|
title = "Fast Light Toolkit",
|
||||||
|
howpublished = "WEB http://www.fltk.org/",
|
||||||
|
year = "2008" };
|
||||||
|
|
||||||
|
|
||||||
|
@Book{ldd,
|
||||||
|
author = {Jonathon Corbet},
|
||||||
|
ALTeditor = {Alessandro Rubini},
|
||||||
|
ALTeditor = {Greg Kroah-Hartman},
|
||||||
|
title = {Linux Device Drivers},
|
||||||
|
publisher = {O'Reilly ISBN 0-596-00590-3},
|
||||||
|
year = {1998},
|
||||||
|
OPTkey = {ISBN 0-596-00590-3},
|
||||||
|
OPTvolume = {},
|
||||||
|
OPTnumber = {},
|
||||||
|
OPTseries = {linux},
|
||||||
|
OPTaddress = {},
|
||||||
|
OPTedition = {3rd},
|
||||||
|
OPTmonth = {},
|
||||||
|
OPTnote = {},
|
||||||
|
OPTannote = {},
|
||||||
|
OPTurl = {www.oreilly.com},
|
||||||
|
OPTdoi = {},
|
||||||
|
OPTissn = {},
|
||||||
|
OPTlocalfile = {},
|
||||||
|
OPTabstract = {}
|
||||||
|
};
|
||||||
|
|
||||||
|
|
||||||
|
@Book{bash,
|
||||||
|
author = {Carl Albing},
|
||||||
|
title = {Bash Cookbook},
|
||||||
|
publisher = {O'Reilly ISBN 0-596-52678-4},
|
||||||
|
year = {2007},
|
||||||
|
OPTkey = {ISBN 0-596-52678-4},
|
||||||
|
OPTvolume = {},
|
||||||
|
OPTnumber = {},
|
||||||
|
OPTseries = {unix/linux},
|
||||||
|
OPTaddress = {},
|
||||||
|
OPTedition = {},
|
||||||
|
OPTmonth = {},
|
||||||
|
OPTnote = {},
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||||||
|
OPTannote = {},
|
||||||
|
OPTurl = {www.oreilly.com},
|
||||||
|
OPTdoi = {},
|
||||||
|
OPTissn = {},
|
||||||
|
OPTlocalfile = {},
|
||||||
|
OPTabstract = {}
|
||||||
|
};
|
||||||
|
|
||||||
|
@Book{sedawk,
|
||||||
|
author = {Dale Dougherty, Arnold Robbins},
|
||||||
|
title = {Sed and Awk},
|
||||||
|
publisher = {O'Reilly ISBN 1-56592-225-5},
|
||||||
|
year = {1997},
|
||||||
|
OPTkey = {ISBN 1-56592-225-5},
|
||||||
|
OPTvolume = {},
|
||||||
|
OPTnumber = {},
|
||||||
|
OPTseries = {unix/linux},
|
||||||
|
OPTaddress = {},
|
||||||
|
OPTedition = {},
|
||||||
|
OPTmonth = {},
|
||||||
|
OPTnote = {},
|
||||||
|
OPTannote = {},
|
||||||
|
OPTurl = {www.oreilly.com},
|
||||||
|
OPTdoi = {},
|
||||||
|
OPTissn = {},
|
||||||
|
OPTlocalfile = {},
|
||||||
|
OPTabstract = {}
|
||||||
|
};
|
||||||
|
|
||||||
|
@Book{bels,
|
||||||
|
author = {Karim Yaghmour},
|
||||||
|
title = {Building Embedded LINUX systems},
|
||||||
|
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|
||||||
|
year = {2003},
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
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|
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|
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|
||||||
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|
||||||
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|
||||||
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|
||||||
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|
||||||
|
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|
||||||
|
|
||||||
|
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|
||||||
|
author = {Olaf Pfeiffer},
|
||||||
|
ALTeditor = {Andrew Ayre},
|
||||||
|
ALTeditor = {Christian Keydel},
|
||||||
|
title = {Embedded networking with CAN and CANopen},
|
||||||
|
publisher = {RTC ISBN 0-929392-78-7},
|
||||||
|
year = {2003},
|
||||||
|
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|
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|
||||||
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|
||||||
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|
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|
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|
||||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||||
|
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|
||||||
|
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|
||||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||||
|
|
||||||
|
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|
||||||
|
author = {Micheal Owens},
|
||||||
|
title = {The definitive guide to SQLite},
|
||||||
|
publisher = {Apres ISBN 1-59059-673-0},
|
||||||
|
year = {2006},
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||||
|
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|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {1}Overview of PT100 four wire circuit}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Accuracy despite variable \\ resistance in cables}{1}}
|
||||||
|
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|
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|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Calculating Temperature from \\ the sense line voltages}{2}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {2}Safety case for 4 wire circuit}{2}}
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Single Fault FMEA Analysis \\ of PT100 Four wire circuit}{3}}
|
||||||
|
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|
||||||
|
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|
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|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {3}Single Fault FMEA Analysis \\ of PT100 Four wire circuit}{4}}
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
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|
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|
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|
||||||
|
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Proof of Out of Range \\ Values for Failures}{5}}
|
||||||
|
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|
||||||
|
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|
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|
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|
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|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Summary of Analysis}{6}}
|
||||||
|
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces PT100 Component Failure Modes}}{7}}
|
||||||
|
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|
||||||
|
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces PT100 Circuit Failure Modes : From Single Faults Analysis}}{7}}
|
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|
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|
||||||
|
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|
||||||
|
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Mean Time to Failure}{8}}
|
||||||
|
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces PT100 FMEA Single // Fault Statistics}}{8}}
|
||||||
|
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|
||||||
|
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Probablistic Fault Tree : PT100 Single Faults}}{9}}
|
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|
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|
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|
||||||
|
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|
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|
\@writefile{toc}{\contentsline {section}{\numberline {4} PT100 Double Simultaneous \\ Fault Analysis}{10}}
|
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|
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|
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burner/paper.pdf
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|
|||||||
|
|
||||||
|
\documentclass[a4paper,10pt]{article}
|
||||||
|
\usepackage{graphicx}
|
||||||
|
\usepackage{fancyhdr}
|
||||||
|
\usepackage{tikz}
|
||||||
|
\usepackage{amsfonts,amsmath,amsthm}
|
||||||
|
\input{../style}
|
||||||
|
|
||||||
|
%\newtheorem{definition}{Definition:}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
\pagestyle{fancy}
|
||||||
|
|
||||||
|
\outerhead{{\small\bf PT100 FMMD analysis}}
|
||||||
|
%\innerfoot{{\small\bf R.P. Clark } }
|
||||||
|
% numbers at outer edges
|
||||||
|
\pagenumbering{arabic} % Arabic page numbers hereafter
|
||||||
|
\author{R.P.Clark}
|
||||||
|
\title{PT100 FMMD analysis}
|
||||||
|
\maketitle
|
||||||
|
\input{pt100_paper}
|
||||||
|
|
||||||
|
\bibliographystyle{plain}
|
||||||
|
\bibliography{vmgbibliography,mybib}
|
||||||
|
|
||||||
|
\today
|
||||||
|
\end{document}
|
||||||
BIN
burner/pt100.dia~
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|
|||||||
|
%
|
||||||
|
% Make the revision and doc number macro's then they are defined in one place
|
||||||
|
|
||||||
|
\begin{abstract}
|
||||||
|
The PT100, or platinum wire \ohms{100} sensor is
|
||||||
|
a wisely used industrial temperature sensor that is
|
||||||
|
are slowly replacing the use of thermocouples in many
|
||||||
|
industrial applications below 600\oc, due to high accuracy\cite{aoe}.
|
||||||
|
|
||||||
|
This chapter looks at the most common configuration, the
|
||||||
|
four wire circuit, and analyses it from an FMEA perspective twice.
|
||||||
|
Once considering single faults (cardinality constrained powerset of 1) and then again, considering the
|
||||||
|
possibility of double simultaneous faults (cardinality constrained powerset of 2).
|
||||||
|
|
||||||
|
The analysis is performed using Propositional Logic
|
||||||
|
diagrasms to assist the reasoning process.
|
||||||
|
This chapter describes taking
|
||||||
|
the failure modes of the components, analysing the circuit using FMEA
|
||||||
|
and producing a failure mode model for the circuit as a whole.
|
||||||
|
Thus after the analysis the PT100 temperature sensing circuit, may be veiwed
|
||||||
|
from an FMEA persepective as a component itsself, with a set of know failure modes.
|
||||||
|
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./pt100/pt100.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 four wire circuit}
|
||||||
|
\label{fig:pt100}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
\section{Overview of PT100 four wire circuit}
|
||||||
|
|
||||||
|
The PT100 four wire circuit consists of two resistors supplying
|
||||||
|
a current to a third, the thermistor or PT100. By measuring volatges
|
||||||
|
from sections of this circuit forming potential dividers, we can determine the
|
||||||
|
current resistance of the platinum wire sensor. The resistance
|
||||||
|
of this is directly related to temperature, and may be determined by
|
||||||
|
look-up tables or a suitable polynomial expression.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt100/vrange.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 expected voltage ranges}
|
||||||
|
\label{fig:pt100vrange}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
The voltage ranges we expect from from this three stage potential divider
|
||||||
|
are shown in figure \ref{fig:pt100vrange}. Note that there is
|
||||||
|
an expected range for each reading for a given temperature span.
|
||||||
|
Note that the low reading goes down as temperature increases, and the higher reading goes up.
|
||||||
|
For this reason the low reading will be reffered to as {\em sense-}
|
||||||
|
and the higher as {\em sense+}.
|
||||||
|
|
||||||
|
\subsection{Accuracy despite variable resistance in cables}
|
||||||
|
|
||||||
|
For electronic and accuracy reasons a four wire circuit is preffered
|
||||||
|
because of resistance in the cables. Resitance from the supply
|
||||||
|
causes a slight voltage
|
||||||
|
drop in the supply to the PT100. As no significant current
|
||||||
|
is carried by the two `sense' lines the resistance back to the ADC
|
||||||
|
causes only a negligible voltage drop, and thus the four wire
|
||||||
|
configuration is more accurate.
|
||||||
|
|
||||||
|
\subsection{Calculating Temperature from the sense line voltages}
|
||||||
|
|
||||||
|
The current flowing though the
|
||||||
|
whole circuit can be measured on the PCB by reading a third
|
||||||
|
sense voltage from one of the load resistors. Knowing the current flowing
|
||||||
|
through the circuit
|
||||||
|
and knowing the voltage drop over the PT100, we can calculate its
|
||||||
|
resistance by ohms law $V=I.R$, $R=\frac{I}{V}$.
|
||||||
|
Thus a little loss of supply current due to resistance in the cables
|
||||||
|
does not impinge on accuracy.
|
||||||
|
The resistance to temperature conversion is achieved
|
||||||
|
through the published PT100 tables\cite{eurothermtables}.
|
||||||
|
|
||||||
|
\section{Safety case for 4 wire circuit}
|
||||||
|
|
||||||
|
This sub-section looks at the behaviour of the PT100 four wire circuit
|
||||||
|
for the effects of component failures.
|
||||||
|
All components have a set of known `failure modes'.
|
||||||
|
In other words we know that a given component can fail in several distict ways.
|
||||||
|
Studies have been published which list common component types
|
||||||
|
and their sets of failure modes, often with MTTF statistics \cite{mil1991}.
|
||||||
|
Thus for each component, an analysis is made for each of it failure modes,
|
||||||
|
with respect to its effect on the
|
||||||
|
circuit. Each one of these scenarios is termed a `test case'.
|
||||||
|
The resultant circuit behaviour for each of these test cases is noted.
|
||||||
|
The worst case for this type of
|
||||||
|
analysis would be a fault that we cannot detect.
|
||||||
|
Where this occurs a circuit re-design is probably the only sensible course of action.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\label{fmea}
|
||||||
|
This circuit simply consists of three resistors.
|
||||||
|
Resistors according to the DOD Electronic component fault handbook
|
||||||
|
1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
|
||||||
|
%Should wires become disconnected these will have the same effect as
|
||||||
|
%given resistors going open.
|
||||||
|
For the purpose of his analyis;
|
||||||
|
$R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
|
||||||
|
$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
|
||||||
|
|
||||||
|
We can define the terms `High Fault' and `Low Fault' here, with reference to figure
|
||||||
|
\ref{fig:pt100vrange}. Should we get a reading outside the safe green zone
|
||||||
|
in the diagram we can consider this a fault.
|
||||||
|
Should the reading be above its expected range this is a `High Fault'
|
||||||
|
and if below a `Low Fault'.
|
||||||
|
|
||||||
|
The Table \ref{ptfmea} plays through the scenarios of each of the resistors failing
|
||||||
|
in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings.
|
||||||
|
The range 0\oc to 300\oc will be analysed using potential divider equations to
|
||||||
|
determine out of range voltage limits in section \ref{ptbounds}.
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 FMEA Single Faults} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
$R_1$ SHORT & High Fault & - & Value Out of Range Value \\ \hline
|
||||||
|
$R_1$ OPEN & Low Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_3$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
$R_3$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_2$ SHORT & - & Low Fault & Value Out of Range Value \\
|
||||||
|
$R_2$ OPEN & High Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptfmea}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
From table \ref{ptfmea} it can be seen that any component failure in the circuit
|
||||||
|
should cause a common symptom, that of one or more of the values being `out of range'.
|
||||||
|
Temperature range calculations and detailed calculations
|
||||||
|
on the effects of each test case are found in section \ref{pt100range}
|
||||||
|
and \ref{pt100temp}.
|
||||||
|
|
||||||
|
|
||||||
|
\pagebreak
|
||||||
|
% \subsection{Single Fault Modes as PLD}
|
||||||
|
%
|
||||||
|
% The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
% on a PLD diagram. Each test case, or analysis into the effects of the component failure
|
||||||
|
% caused by the component~failure is represented by an labelled asterisk.
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% \begin{figure}[h]
|
||||||
|
% \centering
|
||||||
|
% \includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg}
|
||||||
|
% % pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
% \caption{PT100 Component Failure Modes}
|
||||||
|
% \label{fig:pt100_tc}
|
||||||
|
% \end{figure}
|
||||||
|
%
|
||||||
|
% This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
% To establish the valid voltage ranges for these, and knowing our
|
||||||
|
% valid tempperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
% valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
% for the circuit shown in figure \ref{fig:vd}.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./pt100/voltage_divider.png}
|
||||||
|
% voltage_divider.png: 183x170 pixel, 72dpi, 6.46x6.00 cm, bb=0 0 183 170
|
||||||
|
\caption{Voltage Divider}
|
||||||
|
\label{fig:vd}
|
||||||
|
\end{figure}
|
||||||
|
%The looking at figure \ref{fig:vd} the standard voltage divider formula (equation \ref{eqn:vd}) is used.
|
||||||
|
|
||||||
|
\begin{equation}
|
||||||
|
\label{eqn:vd}
|
||||||
|
V_{out} = V_{in}.\frac{Z2}{Z2+Z1}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Range and PT100 Calculations}
|
||||||
|
\label{pt100temp}
|
||||||
|
PT100 resistors are designed to
|
||||||
|
have a resistance of ohms{100} at 0 \oc \cite{eurothermtables}.
|
||||||
|
A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc}
|
||||||
|
for a given application.
|
||||||
|
According to the Eurotherm PT100
|
||||||
|
tables \cite{eurothermtables}, this corresponded to the resistances \ohms{60.28}
|
||||||
|
and \ohms{212.02} respectively. From this the potential divider circuit can be
|
||||||
|
analysed and the maximum and minimum acceptable voltages determined.
|
||||||
|
These can be used as bounds results to apply the findings from the
|
||||||
|
PT100 FMEA analysis in section \ref{fmea}.
|
||||||
|
|
||||||
|
As the PT100 forms a potential divider with the \ohms{2k2} load resistors,
|
||||||
|
the upper and lower readings can be calculated thus:
|
||||||
|
|
||||||
|
|
||||||
|
$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
So by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
To convert these to twelve bit ADC (\adctw) counts:
|
||||||
|
|
||||||
|
$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 Maximum and Minimum Values} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||c|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Temperature} & \textbf{PT100 resistance} &
|
||||||
|
\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
||||||
|
\hline
|
||||||
|
% {-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
||||||
|
% & & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
||||||
|
{0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Boundary of \\
|
||||||
|
& & 2002\adctw & 2094\adctw & out of range LOW \\ \hline
|
||||||
|
{+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
||||||
|
& & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptbounds}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
|
||||||
|
for any single error (short or opening of any resistor) this bounds check
|
||||||
|
will detect it.
|
||||||
|
|
||||||
|
%\vbox{
|
||||||
|
%\subsubsection{Calculating Bounds: High Value : HP48 RPL}
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%HP RPL calculator program to take pt100 resistance
|
||||||
|
%and convert to voltage and {\adctw} values.
|
||||||
|
%
|
||||||
|
%\begin{verbatim}
|
||||||
|
%<< -> p
|
||||||
|
% <<
|
||||||
|
% p 2200 + 2200 2200 + p + / 5 * DUP 5
|
||||||
|
% / 4096 *
|
||||||
|
% >>
|
||||||
|
%>>
|
||||||
|
%\end{verbatim}
|
||||||
|
%}
|
||||||
|
%
|
||||||
|
%\vbox{
|
||||||
|
%\subsubsection{Calculating Bounds: LOW Value : HP48 RPL}
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%HP RPL calculator program to take pt100 resistance
|
||||||
|
%and convert to voltage and {\adctw} values.
|
||||||
|
%
|
||||||
|
%\begin{verbatim}
|
||||||
|
%<< -> p
|
||||||
|
% <<
|
||||||
|
% p 2200 2200 p 2200 + + / 5 * DUP 5
|
||||||
|
% / 4096 *
|
||||||
|
% >>
|
||||||
|
%>>
|
||||||
|
%\end{verbatim}
|
||||||
|
%}
|
||||||
|
%
|
||||||
|
%\subsection{Implementation of Four Wire Circuit}
|
||||||
|
%
|
||||||
|
%A standard 4 wire PT100\cite[pp 992]{aoe} circuit is read by
|
||||||
|
%ports on the 12 bit ADC of the PIC18F2523\cite{pic18f2523}.
|
||||||
|
%Three readings are taken. A reading to confirm the voltage level
|
||||||
|
%over $R_2$ is taken,
|
||||||
|
%from which the current can be determined.
|
||||||
|
%The two sense lines then give the vo
|
||||||
|
|
||||||
|
\section{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\subsection{Single Fault Modes as PLD}
|
||||||
|
|
||||||
|
The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
on a PLD diagram. Each test case, or analysis into the effects of the component failure
|
||||||
|
caused by the component~failure is represented by an labelled asterisk.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
To establish the valid voltage ranges for these, and knowing our
|
||||||
|
valid tempperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
for the circuit shown in .
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Proof of Out of Range Values for Failures}
|
||||||
|
\label{pt110range}
|
||||||
|
Using the temperature ranges defined above we can compare the voltages
|
||||||
|
we would get from the resistor failures to prove that they are
|
||||||
|
`out of range'. There are six test cases and each will be examined in turn.
|
||||||
|
|
||||||
|
\subsubsection{ TC1 : Voltages $R_1$ SHORT }
|
||||||
|
With pt100 at 0\oc
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
Since the highreading or sense+ is directly connected to the 5V rail,
|
||||||
|
both temperature readings will be 5V..
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+68\Omega} = 4.85V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
|
||||||
|
|
||||||
|
Thus with $R_1$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC2 : Voltages $R_1$ OPEN }
|
||||||
|
|
||||||
|
In this case the 5V rail is disconnected. All voltages read are 0V, and
|
||||||
|
therefore both readings are outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 4 : Voltages $R_2$ SHORT }
|
||||||
|
|
||||||
|
With pt100 at -100\oc
|
||||||
|
$$ lowreading = 0V $$
|
||||||
|
Since the lowreading or sense- is directly connected to the 0V rail,
|
||||||
|
both temperature readings will be 0V.
|
||||||
|
$$ lowreading = 5V.\frac{68\Omega}{2k2+68\Omega} = 0.15V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
|
||||||
|
|
||||||
|
Thus with $R_2$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC : 5 Voltages $R_2$ OPEN }
|
||||||
|
Here there is no potential divider operating and both sense lines
|
||||||
|
will read 5V, outside of the proscibed range.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 5 : Voltages $R_3$ SHORT }
|
||||||
|
|
||||||
|
Here the potential divider is simply between
|
||||||
|
the two 2k2 load resistors. Thus it will read a nominal;
|
||||||
|
2.5V.
|
||||||
|
|
||||||
|
Assuming the load resistors are
|
||||||
|
precision components, and then taking an absolute worst case of 1\% either way.
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
|
||||||
|
|
||||||
|
These readings both lie outside the proscribed range.
|
||||||
|
Also the sense+ and sense- readings would have the same value.
|
||||||
|
|
||||||
|
\subsubsection{ TC 6 : Voltages $R_3$ OPEN }
|
||||||
|
|
||||||
|
Here the potential divider is broken. The sense- will read 0V and the sense+ will
|
||||||
|
read 5V. Both readings are outside the proscribed range.
|
||||||
|
|
||||||
|
\subsection{Summary of Analysis}
|
||||||
|
|
||||||
|
All six test cases have been analysed and the results agree with the hypothesis
|
||||||
|
put in Table \ref{ptfmea}. The PLD diagram, can now be used to collect the
|
||||||
|
symptoms. In this case there is a common and easily detected symptom for all these single
|
||||||
|
resistor faults : Voltage out of range.
|
||||||
|
|
||||||
|
A spider can be drawn on the PLD diagram to this effect.
|
||||||
|
|
||||||
|
In practical use, by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc_sp.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc_sp}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The PT100 circuit can now be treated as a component in its own right, and has one failure mode,
|
||||||
|
{\textbf OUT\_OF\_RANGE}. It can now be represnted as a PLD see figure \ref{fig:pt100_singlef}.
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./pt100/pt100_singlef.jpg}
|
||||||
|
% pt100_singlef.jpg: 167x194 pixel, 72dpi, 5.89x6.84 cm, bb=0 0 167 194
|
||||||
|
\caption{PT100 Circuit Failure Modes : From Single Faults Analysis}
|
||||||
|
\label{fig:pt100_singlef}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
%Interestingly we can calculate the failure statistics for this circuit now.
|
||||||
|
%Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for pt100) ???
|
||||||
|
|
||||||
|
The PT100 analysis presents a simple result for single faults.
|
||||||
|
|
||||||
|
% OK we can look at stats here.
|
||||||
|
% the probabilities of the faults occurring in failures per billion hours
|
||||||
|
% of operation.
|
||||||
|
\subsection{Statistical MTTF for the PT100 circuit}
|
||||||
|
|
||||||
|
Mil1991\cite{mil1991} gives a mean time to failure for a fixed film resistor
|
||||||
|
at up to 60oC at a low stress (current) level as
|
||||||
|
$$0.00092 . 1.0 . 15 . 1.0 . 1000$$
|
||||||
|
|
||||||
|
13.8 failure per billion hours of operation.
|
||||||
|
|
||||||
|
|
||||||
|
RAC \cite{rac} states that a resistor will fail 9/10 OPEN and 1/10 SHORT.
|
||||||
|
So 13.8 - 1.38 OPEN
|
||||||
|
1.38 SHORT
|
||||||
|
|
||||||
|
MILL 1991 gives Thermisitors, bead $$0.21 15 1.0 1000$$
|
||||||
|
3150 failures per billion hours of operation.
|
||||||
|
|
||||||
|
Again we can apply the RAC division of resistor errors.
|
||||||
|
|
||||||
|
We can now see the six error types and see a statistical
|
||||||
|
prediction of which will occur. We can also
|
||||||
|
determine the reliability of the circuit as a whole.
|
||||||
|
|
||||||
|
The next analysis phase looks at how the circuit will behave under double simultaneous failure
|
||||||
|
conditions.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% typeset in {\Huge \LaTeX} \today
|
||||||
|
|
||||||
|
%
|
||||||
|
%\begin{table}[ht]
|
||||||
|
%\caption{PT100 Maximum and Minimum Values} % title of Table
|
||||||
|
%\centering % used for centering table
|
||||||
|
%\begin{tabular}{||c|c|c|l|l||}
|
||||||
|
%\hline \hline
|
||||||
|
% \textbf{Temperature} & \textbf{PT100 resistance} &
|
||||||
|
%\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
||||||
|
%\hline
|
||||||
|
%% {-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
||||||
|
%% & & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
||||||
|
% {0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Boundary of \\
|
||||||
|
% & & 2002\adctw & 2094\adctw & out of range LOW \\ \hline
|
||||||
|
% {+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
||||||
|
% & & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
||||||
|
%\hline
|
||||||
|
%\end{tabular}
|
||||||
|
%\label{ptbounds}
|
||||||
|
%\end{table}
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 FMEA Single Fault Statistics} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|c||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
$R_1$ SHORT & High Fault & - & 12.42 \\ \hline
|
||||||
|
$R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline
|
||||||
|
$R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_2$ SHORT & - & Low Fault & 12.42 \\
|
||||||
|
$R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{pt100_single_stats}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
|
||||||
|
The ciruit overall has a MTTF of (13.8*2 + 3150) 3177.6
|
||||||
|
Failure in Time FIT\footnote{FIT values are measured as failures per billion ($10^9$) hours of operation}.
|
||||||
|
This gives an individual pt100 circuit of this type an MTTF of around 39 years.
|
||||||
|
|
||||||
|
Interestingly though we can now look at the results of our analysis
|
||||||
|
as a probablistic tree see figure \ref{fig:stat_single}. We can see the overall
|
||||||
|
reliability of the circuit
|
||||||
|
and we can see the most likely fault (the thermisitor going OPEN circuit).
|
||||||
|
The circuit is 8 times more likely to fail in this way than in any other.
|
||||||
|
Were we to need a more reliable temperature sensor this would probably
|
||||||
|
be the component area we would scrutinise first.
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 856 328,keepaspectratio=true]{./stat_single.jpg}
|
||||||
|
% stat_single.jpg: 856x328 pixel, 72dpi, 30.20x11.57 cm, bb=0 0 856 328
|
||||||
|
\caption{Probablistic Tree}
|
||||||
|
\label{fig:stat_single}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\clearpage
|
||||||
|
|
||||||
|
\section{ PT100 Double Simultaneous Fault Analysis}
|
||||||
412
burner/pt100.tex.backup
Normal file
412
burner/pt100.tex.backup
Normal file
@ -0,0 +1,412 @@
|
|||||||
|
%
|
||||||
|
% Make the revision and doc number macro's then they are defined in one place
|
||||||
|
|
||||||
|
\begin{abstract}
|
||||||
|
The PT100, or platinum wire \ohms{100} sensor is
|
||||||
|
a wisely used industrial temperature sensor that is
|
||||||
|
are slowly replacing the use of thermocouples in many
|
||||||
|
industrial applications below 600\oc, due to high accuracy\cite{aoe}.
|
||||||
|
|
||||||
|
This chapter looks at the most common configuration, the
|
||||||
|
four wire circuit, and analyses it from an FMEA perspective twice.
|
||||||
|
Once considering single faults (cardinality constrained powerset of 1) and then again, considering the
|
||||||
|
possibility of double simultaneous faults (cardinality constrained powerset of 2).
|
||||||
|
|
||||||
|
The analysis is performed using Propositional Logic
|
||||||
|
diagrasms to assist the reasoning process.
|
||||||
|
This chapter describes taking
|
||||||
|
the failure modes of the components, analysing the circuit using FMEA
|
||||||
|
and producing a failure mode model for the circuit as a whole.
|
||||||
|
Thus after the analysis the PT100 temperature sensing circuit, may be veiwed
|
||||||
|
from an FMEA persepective as a component itsself, with a set of know failure modes.
|
||||||
|
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./pt100/pt100.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 four wire circuit}
|
||||||
|
\label{fig:pt100}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
\section{Overview of PT100 four wire circuit}
|
||||||
|
|
||||||
|
The PT100 four wire circuit consists of two resistors supplying
|
||||||
|
a current to a third, the thermistor or PT100. By measuring volatges
|
||||||
|
from sections of this circuit forming potential dividers, we can determine the
|
||||||
|
current resistance of the platinum wire sensor. The resistance
|
||||||
|
of this is directly related to temperature, and may be determined by
|
||||||
|
look-up tables or a suitable polynomial expression.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt100/vrange.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 expected voltage ranges}
|
||||||
|
\label{fig:pt100vrange}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
The voltage ranges we expect from from this three stage potential divider
|
||||||
|
are shown in figure \ref{fig:pt100vrange}. Note that there is
|
||||||
|
an expected range for each reading for a given temperature span.
|
||||||
|
Note that the low reading goes down as temperature increases, and the higher reading goes up.
|
||||||
|
For this reason the low reading will be reffered to as {\em sense-}
|
||||||
|
and the higher as {\em sense+}.
|
||||||
|
|
||||||
|
\subsection{Accuracy despite variable resistance in cables}
|
||||||
|
|
||||||
|
For electronic and accuracy reasons a four wire circuit is preffered
|
||||||
|
because of resistance in the cables. Resitance from the supply
|
||||||
|
causes a slight voltage
|
||||||
|
drop in the supply to the PT100. As no significant current
|
||||||
|
is carried by the two `sense' lines the resistance back to the ADC
|
||||||
|
causes only a negligible voltage drop, and thus the four wire
|
||||||
|
configuration is more accurate.
|
||||||
|
|
||||||
|
\subsection{Calculating Temperature from the sense line voltages}
|
||||||
|
|
||||||
|
The current flowing though the
|
||||||
|
whole circuit can be measured on the PCB by reading a third
|
||||||
|
sense voltage from one of the load resistors. Knowing the current flowing
|
||||||
|
through the circuit
|
||||||
|
and knowing the voltage drop over the PT100, we can calculate its
|
||||||
|
resistance by ohms law $V=I.R$, $R=\frac{I}{V}$.
|
||||||
|
Thus a little loss of supply current due to resistance in the cables
|
||||||
|
does not impinge on accuracy.
|
||||||
|
The resistance to temperature conversion is achieved
|
||||||
|
through the published PT100 tables\cite{eurothermtables}.
|
||||||
|
|
||||||
|
\section{Safety case for 4 wire circuit}
|
||||||
|
|
||||||
|
This sub-section looks at the behaviour of the PT100 four wire circuit
|
||||||
|
for the effects of component failures.
|
||||||
|
All components have a set of known `failure modes'.
|
||||||
|
In other words we know that a given component can fail in several distict ways.
|
||||||
|
Studies have been published which list common component types
|
||||||
|
and their sets of failure modes, often with MTTF statistics \cite{mil1991}.
|
||||||
|
Thus for each component, an analysis is made for each of it failure modes,
|
||||||
|
with respect to its effect on the
|
||||||
|
circuit. Each one of these scenarios is termed a `test case'.
|
||||||
|
The resultant circuit behaviour for each of these test cases is noted.
|
||||||
|
The worst case for this type of
|
||||||
|
analysis would be a fault that we cannot detect.
|
||||||
|
Where this occurs a circuit re-design is probably the only sensible course of action.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\label{fmea}
|
||||||
|
This circuit simply consists of three resistors.
|
||||||
|
Resistors according to the DOD Electronic component fault handbook
|
||||||
|
1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
|
||||||
|
%Should wires become disconnected these will have the same effect as
|
||||||
|
%given resistors going open.
|
||||||
|
For the purpose of his analyis;
|
||||||
|
$R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
|
||||||
|
$R_p$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
|
||||||
|
|
||||||
|
We can define the terms `High Fault' and `Low Fault' here, with reference to figure
|
||||||
|
\ref{fig:pt100vrange}. Should we get a reading outside the safe green zone
|
||||||
|
in the diagram we can consider this a fault.
|
||||||
|
Should the reading be above its expected range this is a `High Fault'
|
||||||
|
and if below a `Low Fault'.
|
||||||
|
|
||||||
|
The Table \ref{ptfmea} plays through the scenarios of each of the resistors failing
|
||||||
|
in both SHORT and OPEN failure modes, and predicts an error condition in the readings.
|
||||||
|
The range 0\oc to 300\oc will be analysed using potential divider equations to
|
||||||
|
to the out of range voltage limits in section \ref{ptbounds}.
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 FMEA Single Faults} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
$R_1$ SHORT & High Fault & - & Value Out of Range Value \\ \hline
|
||||||
|
$R_1$ OPEN & Low Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_p$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
$R_p$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_2$ SHORT & - & Low Fault & Value Out of Range Value \\
|
||||||
|
$R_2$ OPEN & High Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptfmea}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
From table \ref{ptfmea} it can be seen that any component failure in the circuit
|
||||||
|
will cause a common symptom, that of one or more of the values being `out of range'.
|
||||||
|
Temperature range calculations and detailed calculations
|
||||||
|
on the effects of each test case are found in section \ref{pt100range}
|
||||||
|
and \ref{pt100temp}.
|
||||||
|
|
||||||
|
So by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
\pagebreak
|
||||||
|
\subsection{Single Fault Modes as PLD}
|
||||||
|
|
||||||
|
The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
on a PLD diagram. Each test case, or analysis into the effects of the component failure
|
||||||
|
caused by the component~failure is represented by an labelled asterisk.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
To establish the valid voltage ranges for these, and knowing our
|
||||||
|
valid tempperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
for the circuit shown in figure \ref{fig:vd}.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./pt100/voltage_divider.png}
|
||||||
|
% voltage_divider.png: 183x170 pixel, 72dpi, 6.46x6.00 cm, bb=0 0 183 170
|
||||||
|
\caption{Voltage Divider}
|
||||||
|
\label{fig:vd}
|
||||||
|
\end{figure}
|
||||||
|
%The looking at figure \ref{fig:vd} the standard voltage divider formula (equation \ref{eqn:vd}) is used.
|
||||||
|
|
||||||
|
\begin{equation}
|
||||||
|
\label{eqn:vd}
|
||||||
|
V_{out} = V_{in}.\frac{Z2}{Z2+Z1}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Range and PT100 Calculations}
|
||||||
|
\label{pt100temp}
|
||||||
|
PT100 resistors are designed to
|
||||||
|
have a resistance of ohms{100} at 0 \oc \cite{eurothermtables}.
|
||||||
|
A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc}
|
||||||
|
for a given application.
|
||||||
|
According to the Eurotherm PT100
|
||||||
|
tables \cite{eurothermtables}, this corresponded to the resistances \ohms{60.28}
|
||||||
|
and \ohms{212.02} respectively. From this the potential divider circuit can be
|
||||||
|
analysed and the maximum and minimum acceptable voltages determined.
|
||||||
|
These can be used as bounds results to apply the findings from the
|
||||||
|
PT100 FMEA analysis in section \ref{fmea}.
|
||||||
|
|
||||||
|
As the PT100 forms a potential divider with the \ohms{2k2} load resistors,
|
||||||
|
the upper and lower readings can be calculated thus:
|
||||||
|
|
||||||
|
|
||||||
|
$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
|
||||||
|
To convert these to twelve bit ADC (\adctw) counts:
|
||||||
|
|
||||||
|
$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 Maximum and Minimum Values} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||c|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Temperature} & \textbf{PT100 resistance} &
|
||||||
|
\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
||||||
|
\hline
|
||||||
|
% {-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
||||||
|
% & & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
||||||
|
{0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Boundary of \\
|
||||||
|
& & 2002\adctw & 2094\adctw & out of range LOW \\ \hline
|
||||||
|
{+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
||||||
|
& & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptbounds}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
|
||||||
|
for any single error (short or opening of any resistor) this bounds check
|
||||||
|
will detect it.
|
||||||
|
|
||||||
|
%\vbox{
|
||||||
|
%\subsubsection{Calculating Bounds: High Value : HP48 RPL}
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%HP RPL calculator program to take pt100 resistance
|
||||||
|
%and convert to voltage and {\adctw} values.
|
||||||
|
%
|
||||||
|
%\begin{verbatim}
|
||||||
|
%<< -> p
|
||||||
|
% <<
|
||||||
|
% p 2200 + 2200 2200 + p + / 5 * DUP 5
|
||||||
|
% / 4096 *
|
||||||
|
% >>
|
||||||
|
%>>
|
||||||
|
%\end{verbatim}
|
||||||
|
%}
|
||||||
|
%
|
||||||
|
%\vbox{
|
||||||
|
%\subsubsection{Calculating Bounds: LOW Value : HP48 RPL}
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%HP RPL calculator program to take pt100 resistance
|
||||||
|
%and convert to voltage and {\adctw} values.
|
||||||
|
%
|
||||||
|
%\begin{verbatim}
|
||||||
|
%<< -> p
|
||||||
|
% <<
|
||||||
|
% p 2200 2200 p 2200 + + / 5 * DUP 5
|
||||||
|
% / 4096 *
|
||||||
|
% >>
|
||||||
|
%>>
|
||||||
|
%\end{verbatim}
|
||||||
|
%}
|
||||||
|
%
|
||||||
|
%\subsection{Implementation of Four Wire Circuit}
|
||||||
|
%
|
||||||
|
%A standard 4 wire PT100\cite[pp 992]{aoe} circuit is read by
|
||||||
|
%ports on the 12 bit ADC of the PIC18F2523\cite{pic18f2523}.
|
||||||
|
%Three readings are taken. A reading to confirm the voltage level
|
||||||
|
%over $R_2$ is taken,
|
||||||
|
%from which the current can be determined.
|
||||||
|
%The two sense lines then give the vo
|
||||||
|
|
||||||
|
\section{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\subsection{Single Fault Modes as PLD}
|
||||||
|
|
||||||
|
The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
on a PLD diagram. Each test case, or analysis into the effects of the component failure
|
||||||
|
caused by the component~failure is represented by an labelled asterisk.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
To establish the valid voltage ranges for these, and knowing our
|
||||||
|
valid tempperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
for the circuit shown in .
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Proof of Out of Range Values for Failures}
|
||||||
|
\label{pt110range}
|
||||||
|
Using the temperature ranges defined above we can compare the voltages
|
||||||
|
we would get from the resistor failures to prove that they are
|
||||||
|
`out of range'. There are six test cases and each will be examined in turn.
|
||||||
|
|
||||||
|
\subsubsection{ TC1 : Voltages $R_1$ SHORT }
|
||||||
|
With pt100 at 0\oc
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
Since the highreading or sense+ is directly connected to the 5V rail,
|
||||||
|
both temperature readings will be 5V..
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+68\Omega} = 4.85V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
|
||||||
|
|
||||||
|
Thus with $R_1$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC2 : Voltages $R_1$ OPEN }
|
||||||
|
|
||||||
|
In this case the 5V rail is disconnected. All voltages read are 0V, and
|
||||||
|
therefore both readings are outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 4 : Voltages $R_2$ SHORT }
|
||||||
|
|
||||||
|
With pt100 at -100\oc
|
||||||
|
$$ lowreading = 0V $$
|
||||||
|
Since the lowreading or sense- is directly connected to the 0V rail,
|
||||||
|
both temperature readings will be 0V.
|
||||||
|
$$ lowreading = 5V.\frac{68\Omega}{2k2+68\Omega} = 0.15V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
|
||||||
|
|
||||||
|
Thus with $R_2$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC : 5 Voltages $R_2$ OPEN }
|
||||||
|
Here there is no potential divider operating and both sense lines
|
||||||
|
will read 5V, outside of the proscibed range.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 5 : Voltages $R_3$ SHORT }
|
||||||
|
|
||||||
|
Here the potential divider is simply between
|
||||||
|
the two 2k2 load resistors. Thus it will read a nominal;
|
||||||
|
2.5V.
|
||||||
|
|
||||||
|
Assuming the load resistors are
|
||||||
|
precision components, and then taking an absolute worst case of 1\% either way.
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
|
||||||
|
|
||||||
|
These readings both lie outside the proscribed range.
|
||||||
|
Also the sense+ and sense- readings would have the same value.
|
||||||
|
|
||||||
|
\subsubsection{ TC 6 : Voltages $R_3$ OPEN }
|
||||||
|
|
||||||
|
Here the potential divider is broken. The sense- will read 0V and the sense+ will
|
||||||
|
read 5V. Both readings are outside the proscribed range.
|
||||||
|
|
||||||
|
\subsection{Summary of Analysis}
|
||||||
|
|
||||||
|
All six test cases have been analysed and the results agree with the hypothesis
|
||||||
|
put in Table \ref{ptfmea}. The PLD diagram, can now be used to collect the
|
||||||
|
symptoms. In this case there is a common and easily detected symptom for all these single
|
||||||
|
resistor faults : Voltage out of range.
|
||||||
|
|
||||||
|
A spider can be drawn on the PLD diagram to this effect.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc_sp.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc_sp}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
%Interestingly we can calculate the failure statistics for this circuit now.
|
||||||
|
%Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for pt100) ???
|
||||||
|
|
||||||
|
The PT100 analysis presents a simple result for single faults.
|
||||||
|
The next analysis phase looks at how the circuit will behave under double simultaneous failure
|
||||||
|
conditions.
|
||||||
|
|
||||||
|
|
||||||
|
\section{ PT100 Double Simultaneous Fault Analysis}
|
||||||
|
|
||||||
|
% typeset in {\Huge \LaTeX} \today
|
||||||
|
|
||||||
516
burner/pt100.tex~
Normal file
516
burner/pt100.tex~
Normal file
@ -0,0 +1,516 @@
|
|||||||
|
%
|
||||||
|
% Make the revision and doc number macro's then they are defined in one place
|
||||||
|
|
||||||
|
\begin{abstract}
|
||||||
|
The PT100, or platinum wire \ohms{100} sensor is
|
||||||
|
a wisely used industrial temperature sensor that is
|
||||||
|
are slowly replacing the use of thermocouples in many
|
||||||
|
industrial applications below 600\oc, due to high accuracy\cite{aoe}.
|
||||||
|
|
||||||
|
This chapter looks at the most common configuration, the
|
||||||
|
four wire circuit, and analyses it from an FMEA perspective twice.
|
||||||
|
Once considering single faults (cardinality constrained powerset of 1) and then again, considering the
|
||||||
|
possibility of double simultaneous faults (cardinality constrained powerset of 2).
|
||||||
|
|
||||||
|
The analysis is performed using Propositional Logic
|
||||||
|
diagrasms to assist the reasoning process.
|
||||||
|
This chapter describes taking
|
||||||
|
the failure modes of the components, analysing the circuit using FMEA
|
||||||
|
and producing a failure mode model for the circuit as a whole.
|
||||||
|
Thus after the analysis the PT100 temperature sensing circuit, may be veiwed
|
||||||
|
from an FMEA persepective as a component itsself, with a set of know failure modes.
|
||||||
|
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./pt100/pt100.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 four wire circuit}
|
||||||
|
\label{fig:pt100}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
\section{Overview of PT100 four wire circuit}
|
||||||
|
|
||||||
|
The PT100 four wire circuit consists of two resistors supplying
|
||||||
|
a current to a third, the thermistor or PT100. By measuring volatges
|
||||||
|
from sections of this circuit forming potential dividers, we can determine the
|
||||||
|
current resistance of the platinum wire sensor. The resistance
|
||||||
|
of this is directly related to temperature, and may be determined by
|
||||||
|
look-up tables or a suitable polynomial expression.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt100/vrange.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 expected voltage ranges}
|
||||||
|
\label{fig:pt100vrange}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
The voltage ranges we expect from from this three stage potential divider
|
||||||
|
are shown in figure \ref{fig:pt100vrange}. Note that there is
|
||||||
|
an expected range for each reading for a given temperature span.
|
||||||
|
Note that the low reading goes down as temperature increases, and the higher reading goes up.
|
||||||
|
For this reason the low reading will be reffered to as {\em sense-}
|
||||||
|
and the higher as {\em sense+}.
|
||||||
|
|
||||||
|
\subsection{Accuracy despite variable resistance in cables}
|
||||||
|
|
||||||
|
For electronic and accuracy reasons a four wire circuit is preffered
|
||||||
|
because of resistance in the cables. Resitance from the supply
|
||||||
|
causes a slight voltage
|
||||||
|
drop in the supply to the PT100. As no significant current
|
||||||
|
is carried by the two `sense' lines the resistance back to the ADC
|
||||||
|
causes only a negligible voltage drop, and thus the four wire
|
||||||
|
configuration is more accurate.
|
||||||
|
|
||||||
|
\subsection{Calculating Temperature from the sense line voltages}
|
||||||
|
|
||||||
|
The current flowing though the
|
||||||
|
whole circuit can be measured on the PCB by reading a third
|
||||||
|
sense voltage from one of the load resistors. Knowing the current flowing
|
||||||
|
through the circuit
|
||||||
|
and knowing the voltage drop over the PT100, we can calculate its
|
||||||
|
resistance by ohms law $V=I.R$, $R=\frac{I}{V}$.
|
||||||
|
Thus a little loss of supply current due to resistance in the cables
|
||||||
|
does not impinge on accuracy.
|
||||||
|
The resistance to temperature conversion is achieved
|
||||||
|
through the published PT100 tables\cite{eurothermtables}.
|
||||||
|
|
||||||
|
\section{Safety case for 4 wire circuit}
|
||||||
|
|
||||||
|
This sub-section looks at the behaviour of the PT100 four wire circuit
|
||||||
|
for the effects of component failures.
|
||||||
|
All components have a set of known `failure modes'.
|
||||||
|
In other words we know that a given component can fail in several distict ways.
|
||||||
|
Studies have been published which list common component types
|
||||||
|
and their sets of failure modes, often with MTTF statistics \cite{mil1991}.
|
||||||
|
Thus for each component, an analysis is made for each of it failure modes,
|
||||||
|
with respect to its effect on the
|
||||||
|
circuit. Each one of these scenarios is termed a `test case'.
|
||||||
|
The resultant circuit behaviour for each of these test cases is noted.
|
||||||
|
The worst case for this type of
|
||||||
|
analysis would be a fault that we cannot detect.
|
||||||
|
Where this occurs a circuit re-design is probably the only sensible course of action.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\label{fmea}
|
||||||
|
This circuit simply consists of three resistors.
|
||||||
|
Resistors according to the DOD Electronic component fault handbook
|
||||||
|
1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
|
||||||
|
%Should wires become disconnected these will have the same effect as
|
||||||
|
%given resistors going open.
|
||||||
|
For the purpose of his analyis;
|
||||||
|
$R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
|
||||||
|
$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
|
||||||
|
|
||||||
|
We can define the terms `High Fault' and `Low Fault' here, with reference to figure
|
||||||
|
\ref{fig:pt100vrange}. Should we get a reading outside the safe green zone
|
||||||
|
in the diagram we can consider this a fault.
|
||||||
|
Should the reading be above its expected range this is a `High Fault'
|
||||||
|
and if below a `Low Fault'.
|
||||||
|
|
||||||
|
The Table \ref{ptfmea} plays through the scenarios of each of the resistors failing
|
||||||
|
in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings.
|
||||||
|
The range 0\oc to 300\oc will be analysed using potential divider equations to
|
||||||
|
determine out of range voltage limits in section \ref{ptbounds}.
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 FMEA Single Faults} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
$R_1$ SHORT & High Fault & - & Value Out of Range Value \\ \hline
|
||||||
|
$R_1$ OPEN & Low Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_3$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
$R_3$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_2$ SHORT & - & Low Fault & Value Out of Range Value \\
|
||||||
|
$R_2$ OPEN & High Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptfmea}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
From table \ref{ptfmea} it can be seen that any component failure in the circuit
|
||||||
|
should cause a common symptom, that of one or more of the values being `out of range'.
|
||||||
|
Temperature range calculations and detailed calculations
|
||||||
|
on the effects of each test case are found in section \ref{pt100range}
|
||||||
|
and \ref{pt100temp}.
|
||||||
|
|
||||||
|
|
||||||
|
\pagebreak
|
||||||
|
% \subsection{Single Fault Modes as PLD}
|
||||||
|
%
|
||||||
|
% The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
% on a PLD diagram. Each test case, or analysis into the effects of the component failure
|
||||||
|
% caused by the component~failure is represented by an labelled asterisk.
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% \begin{figure}[h]
|
||||||
|
% \centering
|
||||||
|
% \includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg}
|
||||||
|
% % pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
% \caption{PT100 Component Failure Modes}
|
||||||
|
% \label{fig:pt100_tc}
|
||||||
|
% \end{figure}
|
||||||
|
%
|
||||||
|
% This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
% To establish the valid voltage ranges for these, and knowing our
|
||||||
|
% valid tempperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
% valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
% for the circuit shown in figure \ref{fig:vd}.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./pt100/voltage_divider.png}
|
||||||
|
% voltage_divider.png: 183x170 pixel, 72dpi, 6.46x6.00 cm, bb=0 0 183 170
|
||||||
|
\caption{Voltage Divider}
|
||||||
|
\label{fig:vd}
|
||||||
|
\end{figure}
|
||||||
|
%The looking at figure \ref{fig:vd} the standard voltage divider formula (equation \ref{eqn:vd}) is used.
|
||||||
|
|
||||||
|
\begin{equation}
|
||||||
|
\label{eqn:vd}
|
||||||
|
V_{out} = V_{in}.\frac{Z2}{Z2+Z1}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Range and PT100 Calculations}
|
||||||
|
\label{pt100temp}
|
||||||
|
PT100 resistors are designed to
|
||||||
|
have a resistance of ohms{100} at 0 \oc \cite{eurothermtables}.
|
||||||
|
A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc}
|
||||||
|
for a given application.
|
||||||
|
According to the Eurotherm PT100
|
||||||
|
tables \cite{eurothermtables}, this corresponded to the resistances \ohms{60.28}
|
||||||
|
and \ohms{212.02} respectively. From this the potential divider circuit can be
|
||||||
|
analysed and the maximum and minimum acceptable voltages determined.
|
||||||
|
These can be used as bounds results to apply the findings from the
|
||||||
|
PT100 FMEA analysis in section \ref{fmea}.
|
||||||
|
|
||||||
|
As the PT100 forms a potential divider with the \ohms{2k2} load resistors,
|
||||||
|
the upper and lower readings can be calculated thus:
|
||||||
|
|
||||||
|
|
||||||
|
$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
So by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
To convert these to twelve bit ADC (\adctw) counts:
|
||||||
|
|
||||||
|
$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 Maximum and Minimum Values} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||c|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Temperature} & \textbf{PT100 resistance} &
|
||||||
|
\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
||||||
|
\hline
|
||||||
|
% {-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
||||||
|
% & & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
||||||
|
{0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Boundary of \\
|
||||||
|
& & 2002\adctw & 2094\adctw & out of range LOW \\ \hline
|
||||||
|
{+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
||||||
|
& & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptbounds}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
|
||||||
|
for any single error (short or opening of any resistor) this bounds check
|
||||||
|
will detect it.
|
||||||
|
|
||||||
|
%\vbox{
|
||||||
|
%\subsubsection{Calculating Bounds: High Value : HP48 RPL}
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%HP RPL calculator program to take pt100 resistance
|
||||||
|
%and convert to voltage and {\adctw} values.
|
||||||
|
%
|
||||||
|
%\begin{verbatim}
|
||||||
|
%<< -> p
|
||||||
|
% <<
|
||||||
|
% p 2200 + 2200 2200 + p + / 5 * DUP 5
|
||||||
|
% / 4096 *
|
||||||
|
% >>
|
||||||
|
%>>
|
||||||
|
%\end{verbatim}
|
||||||
|
%}
|
||||||
|
%
|
||||||
|
%\vbox{
|
||||||
|
%\subsubsection{Calculating Bounds: LOW Value : HP48 RPL}
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%HP RPL calculator program to take pt100 resistance
|
||||||
|
%and convert to voltage and {\adctw} values.
|
||||||
|
%
|
||||||
|
%\begin{verbatim}
|
||||||
|
%<< -> p
|
||||||
|
% <<
|
||||||
|
% p 2200 2200 p 2200 + + / 5 * DUP 5
|
||||||
|
% / 4096 *
|
||||||
|
% >>
|
||||||
|
%>>
|
||||||
|
%\end{verbatim}
|
||||||
|
%}
|
||||||
|
%
|
||||||
|
%\subsection{Implementation of Four Wire Circuit}
|
||||||
|
%
|
||||||
|
%A standard 4 wire PT100\cite[pp 992]{aoe} circuit is read by
|
||||||
|
%ports on the 12 bit ADC of the PIC18F2523\cite{pic18f2523}.
|
||||||
|
%Three readings are taken. A reading to confirm the voltage level
|
||||||
|
%over $R_2$ is taken,
|
||||||
|
%from which the current can be determined.
|
||||||
|
%The two sense lines then give the vo
|
||||||
|
|
||||||
|
\section{Single Fault FMEA Analysis of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\subsection{Single Fault Modes as PLD}
|
||||||
|
|
||||||
|
The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
on a PLD diagram. Each test case, or analysis into the effects of the component failure
|
||||||
|
caused by the component~failure is represented by an labelled asterisk.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
To establish the valid voltage ranges for these, and knowing our
|
||||||
|
valid tempperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
for the circuit shown in .
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Proof of Out of Range Values for Failures}
|
||||||
|
\label{pt110range}
|
||||||
|
Using the temperature ranges defined above we can compare the voltages
|
||||||
|
we would get from the resistor failures to prove that they are
|
||||||
|
`out of range'. There are six test cases and each will be examined in turn.
|
||||||
|
|
||||||
|
\subsubsection{ TC1 : Voltages $R_1$ SHORT }
|
||||||
|
With pt100 at 0\oc
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
Since the highreading or sense+ is directly connected to the 5V rail,
|
||||||
|
both temperature readings will be 5V..
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+68\Omega} = 4.85V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
|
||||||
|
|
||||||
|
Thus with $R_1$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC2 : Voltages $R_1$ OPEN }
|
||||||
|
|
||||||
|
In this case the 5V rail is disconnected. All voltages read are 0V, and
|
||||||
|
therefore both readings are outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 4 : Voltages $R_2$ SHORT }
|
||||||
|
|
||||||
|
With pt100 at -100\oc
|
||||||
|
$$ lowreading = 0V $$
|
||||||
|
Since the lowreading or sense- is directly connected to the 0V rail,
|
||||||
|
both temperature readings will be 0V.
|
||||||
|
$$ lowreading = 5V.\frac{68\Omega}{2k2+68\Omega} = 0.15V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
|
||||||
|
|
||||||
|
Thus with $R_2$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC : 5 Voltages $R_2$ OPEN }
|
||||||
|
Here there is no potential divider operating and both sense lines
|
||||||
|
will read 5V, outside of the proscibed range.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 5 : Voltages $R_3$ SHORT }
|
||||||
|
|
||||||
|
Here the potential divider is simply between
|
||||||
|
the two 2k2 load resistors. Thus it will read a nominal;
|
||||||
|
2.5V.
|
||||||
|
|
||||||
|
Assuming the load resistors are
|
||||||
|
precision components, and then taking an absolute worst case of 1\% either way.
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
|
||||||
|
|
||||||
|
These readings both lie outside the proscribed range.
|
||||||
|
Also the sense+ and sense- readings would have the same value.
|
||||||
|
|
||||||
|
\subsubsection{ TC 6 : Voltages $R_3$ OPEN }
|
||||||
|
|
||||||
|
Here the potential divider is broken. The sense- will read 0V and the sense+ will
|
||||||
|
read 5V. Both readings are outside the proscribed range.
|
||||||
|
|
||||||
|
\subsection{Summary of Analysis}
|
||||||
|
|
||||||
|
All six test cases have been analysed and the results agree with the hypothesis
|
||||||
|
put in Table \ref{ptfmea}. The PLD diagram, can now be used to collect the
|
||||||
|
symptoms. In this case there is a common and easily detected symptom for all these single
|
||||||
|
resistor faults : Voltage out of range.
|
||||||
|
|
||||||
|
A spider can be drawn on the PLD diagram to this effect.
|
||||||
|
|
||||||
|
In practical use, by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc_sp.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc_sp}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The PT100 circuit can now be treated as a component in its own right, and has one failure mode,
|
||||||
|
{\textbf OUT\_OF\_RANGE}. It can now be represnted as a PLD see figure \ref{fig:pt100_singlef}.
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./pt100/pt100_singlef.jpg}
|
||||||
|
% pt100_singlef.jpg: 167x194 pixel, 72dpi, 5.89x6.84 cm, bb=0 0 167 194
|
||||||
|
\caption{PT100 Circuit Failure Modes : From Single Faults Analysis}
|
||||||
|
\label{fig:pt100_singlef}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
%Interestingly we can calculate the failure statistics for this circuit now.
|
||||||
|
%Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for pt100) ???
|
||||||
|
|
||||||
|
The PT100 analysis presents a simple result for single faults.
|
||||||
|
|
||||||
|
% OK we can look at stats here.
|
||||||
|
% the probabilities of the faults occurring in failures per billion hours
|
||||||
|
% of operation.
|
||||||
|
\subsection{Statistical MTTF for the PT100 circuit}
|
||||||
|
|
||||||
|
Mil1991\cite{mil1991} gives a mean time to failure for a fixed film resistor
|
||||||
|
at up to 60oC at a low stress (current) level as
|
||||||
|
$$0.00092 . 1.0 . 15 . 1.0 . 1000$$
|
||||||
|
|
||||||
|
13.8 failure per billion hours of operation.
|
||||||
|
|
||||||
|
|
||||||
|
RAC \cite{rac} states that a resistor will fail 9/10 OPEN and 1/10 SHORT.
|
||||||
|
So 13.8 - 1.38 OPEN
|
||||||
|
1.38 SHORT
|
||||||
|
|
||||||
|
MILL 1991 gives Thermisitors, bead $$0.21 15 1.0 1000$$
|
||||||
|
3150 failures per billion hours of operation.
|
||||||
|
|
||||||
|
Again we can apply the RAC division of resistor errors.
|
||||||
|
|
||||||
|
We can now see the six error types and see a statistical
|
||||||
|
prediction of which will occur. We can also
|
||||||
|
determine the reliability of the circuit as a whole.
|
||||||
|
|
||||||
|
The next analysis phase looks at how the circuit will behave under double simultaneous failure
|
||||||
|
conditions.
|
||||||
|
|
||||||
|
|
||||||
|
\section{ PT100 Double Simultaneous Fault Analysis}
|
||||||
|
|
||||||
|
% typeset in {\Huge \LaTeX} \today
|
||||||
|
|
||||||
|
%
|
||||||
|
%\begin{table}[ht]
|
||||||
|
%\caption{PT100 Maximum and Minimum Values} % title of Table
|
||||||
|
%\centering % used for centering table
|
||||||
|
%\begin{tabular}{||c|c|c|l|l||}
|
||||||
|
%\hline \hline
|
||||||
|
% \textbf{Temperature} & \textbf{PT100 resistance} &
|
||||||
|
%\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
||||||
|
%\hline
|
||||||
|
%% {-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
||||||
|
%% & & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
||||||
|
% {0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Boundary of \\
|
||||||
|
% & & 2002\adctw & 2094\adctw & out of range LOW \\ \hline
|
||||||
|
% {+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
||||||
|
% & & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
||||||
|
%\hline
|
||||||
|
%\end{tabular}
|
||||||
|
%\label{ptbounds}
|
||||||
|
%\end{table}
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 FMEA Single Fault Statistics} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|c||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
$R_1$ SHORT & High Fault & - & 12.42 \\ \hline
|
||||||
|
$R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline
|
||||||
|
$R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_2$ SHORT & - & Low Fault & 12.42 \\
|
||||||
|
$R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{pt100_single_stats}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
|
||||||
|
The ciruit overall has a MTTF of (13.8*2 + 3150) 3177.6
|
||||||
|
per billion ($10^9$) hours of operation.
|
||||||
|
This gives an individual circuit a MTTF of around 39 years.
|
||||||
|
|
||||||
|
|
||||||
|
Interestingly though we can now look at the results of our analysis
|
||||||
|
as a probablistioc tree. We can see the overall reliability of the circuit
|
||||||
|
and we can see the most likely fault (the thermisitor going OPEN circuit).
|
||||||
|
The circuit is 8 times more likely to fail in this way than in any other.
|
||||||
|
Were we to need a more reliable temperature sensor this would probably
|
||||||
|
be the component area we would scrutinise first.
|
||||||
|
|
||||||
434
burner/pt100_paper.tex
Normal file
434
burner/pt100_paper.tex
Normal file
@ -0,0 +1,434 @@
|
|||||||
|
%
|
||||||
|
% Make the revision and doc number macro's then they are defined in one place
|
||||||
|
|
||||||
|
\begin{abstract}
|
||||||
|
The PT100, or platinum wire \ohms{100} sensor is
|
||||||
|
a widely used industrial temperature sensor that is
|
||||||
|
slowly replacing the use of thermocouples in many
|
||||||
|
industrial applications below 600\oc, due to high accuracy\cite{aoe}.
|
||||||
|
|
||||||
|
This chapter looks at the most common configuration, the
|
||||||
|
four wire circuit, and analyses it from an FMEA perspective twice.
|
||||||
|
Once considering single faults (cardinality constrained powerset of 1) and then again, considering the
|
||||||
|
possibility of double faults (cardinality constrained powerset of 2).
|
||||||
|
|
||||||
|
The analysis is performed using Propositional Logic
|
||||||
|
diagrams to assist the reasoning process.
|
||||||
|
This chapter describes taking
|
||||||
|
the failure modes of the components, analysing the circuit using FMEA
|
||||||
|
and producing a failure mode model for the circuit as a whole.
|
||||||
|
Thus after the analysis the PT100 temperature sensing circuit, may be veiwed
|
||||||
|
from an FMEA persepective as a component itself, with a set of known failure modes.
|
||||||
|
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./pt100.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 four wire circuit}
|
||||||
|
\label{fig:pt100}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
\section{Overview of PT100 four wire circuit}
|
||||||
|
|
||||||
|
The PT100 four wire circuit uses two wires to supply small electrical current,
|
||||||
|
and returns two sense volages by the other two.
|
||||||
|
By measuring volatges
|
||||||
|
from sections of this circuit forming potential dividers, we can determine the
|
||||||
|
resistance of the platinum wire sensor. The resistance
|
||||||
|
of this is directly related to temperature, and may be determined by
|
||||||
|
look-up tables or a suitable polynomial expression.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./vrange.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 expected voltage ranges}
|
||||||
|
\label{fig:pt100vrange}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The voltage ranges we expect from this three stage potential divider
|
||||||
|
are shown in figure \ref{fig:pt100vrange}. Note that there is
|
||||||
|
an expected range for each reading, for a given temperature span.
|
||||||
|
Note that the low reading goes down as temperature increases, and the higher reading goes up.
|
||||||
|
For this reason the low reading will be reffered to as {\em sense-}
|
||||||
|
and the higher as {\em sense+}.
|
||||||
|
|
||||||
|
\subsection{Accuracy despite variable \\ resistance in cables}
|
||||||
|
|
||||||
|
For electronic and accuracy reasons a four wire circuit is preffered
|
||||||
|
because of resistance in the cables. Resistance from the supply
|
||||||
|
causes a slight voltage
|
||||||
|
drop in the supply to the PT100. As no significant current
|
||||||
|
is carried by the two `sense' lines the resistance back to the ADC
|
||||||
|
causes only a negligible voltage drop, and thus the four wire
|
||||||
|
configuration is more accurate.
|
||||||
|
|
||||||
|
\subsection{Calculating Temperature from \\ the sense line voltages}
|
||||||
|
|
||||||
|
The current flowing though the
|
||||||
|
whole circuit can be measured on the PCB by reading a third
|
||||||
|
sense voltage from one of the load resistors. Knowing the current flowing
|
||||||
|
through the circuit
|
||||||
|
and knowing the voltage drop over the PT100, we can calculate its
|
||||||
|
resistance by ohms law $V=I.R$, $R=\frac{V}{I}$.
|
||||||
|
Thus a little loss of supply current due to resistance in the cables
|
||||||
|
does not impinge on accuracy.
|
||||||
|
The resistance to temperature conversion is achieved
|
||||||
|
through the published PT100 tables\cite{eurothermtables}.
|
||||||
|
|
||||||
|
\section{Safety case for 4 wire circuit}
|
||||||
|
|
||||||
|
This sub-section looks at the behaviour of the PT100 four wire circuit
|
||||||
|
for the effects of component failures.
|
||||||
|
All components have a set of known `failure modes'.
|
||||||
|
In other words we know that a given component can fail in several distinct ways.
|
||||||
|
Studies have been published which list common component types
|
||||||
|
and their sets of failure modes, often with MTTF statistics \cite{mil1991}.
|
||||||
|
Thus for each component, an analysis is made for each of it failure modes,
|
||||||
|
with respect to its effect on the
|
||||||
|
circuit. Each one of these scenarios is termed a `test case'.
|
||||||
|
The resultant circuit behaviour for each of these test cases is noted.
|
||||||
|
The worst case for this type of
|
||||||
|
analysis would be a fault that we cannot detect.
|
||||||
|
Where this occurs a circuit re-design is probably the only sensible course of action.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Single Fault FMEA Analysis \\ of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\label{fmea}
|
||||||
|
This circuit simply consists of three resistors.
|
||||||
|
Resistors according to the DOD Electronic component fault handbook
|
||||||
|
1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
|
||||||
|
%Should wires become disconnected these will have the same effect as
|
||||||
|
%given resistors going open.
|
||||||
|
For the purpose of this analyis;
|
||||||
|
$R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
|
||||||
|
$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
|
||||||
|
|
||||||
|
We can define the terms `High Fault' and `Low Fault' here, with reference to figure
|
||||||
|
\ref{fig:pt100vrange}. Should we get a reading outside the safe green zone
|
||||||
|
in the diagram we can consider this a fault.
|
||||||
|
Should the reading be above its expected range this is a `High Fault'
|
||||||
|
and if below a `Low Fault'.
|
||||||
|
|
||||||
|
Table \ref{ptfmea} plays through the scenarios of each of the resistors failing
|
||||||
|
in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings.
|
||||||
|
The range {0\oc} to {300\oc} will be analysed using potential divider equations to
|
||||||
|
determine out of range voltage limits in section \ref{ptbounds}.
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 FMEA Single Faults} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
$R_1$ SHORT & High Fault & - & Value Out of Range Value \\ \hline
|
||||||
|
$R_1$ OPEN & Low Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_3$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
$R_3$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_2$ SHORT & - & Low Fault & Value Out of Range Value \\
|
||||||
|
$R_2$ OPEN & High Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptfmea}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
From table \ref{ptfmea} it can be seen that any component failure in the circuit
|
||||||
|
should cause a common symptom, that of one or more of the values being `out of range'.
|
||||||
|
Temperature range calculations and detailed calculations
|
||||||
|
on the effects of each test case are found in section \ref{pt100range}
|
||||||
|
and \ref{pt100temp}.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Range and PT100 Calculations}
|
||||||
|
\label{pt100temp}
|
||||||
|
PT100 resistors are designed to
|
||||||
|
have a resistance of \ohms{100} at {0\oc} \cite{aoe},\cite{eurothermtables}.
|
||||||
|
A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc}
|
||||||
|
for a given application.
|
||||||
|
According to the Eurotherm PT100
|
||||||
|
tables \cite{eurothermtables}, this corresponded to the resistances \ohms{100}
|
||||||
|
and \ohms{212.02} respectively. From this the potential divider circuit can be
|
||||||
|
analysed and the maximum and minimum acceptable voltages determined.
|
||||||
|
These can be used as bounds results to apply the findings from the
|
||||||
|
PT100 FMEA analysis in section \ref{fmea}.
|
||||||
|
|
||||||
|
As the PT100 forms a potential divider with the \ohms{2k2} load resistors,
|
||||||
|
the upper and lower readings can be calculated thus:
|
||||||
|
|
||||||
|
|
||||||
|
$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
So by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
To convert these to twelve bit ADC (\adctw) counts:
|
||||||
|
|
||||||
|
$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 Maximum and Minimum Values} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||c|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Temperature} & \textbf{PT100 resistance} &
|
||||||
|
\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
||||||
|
\hline
|
||||||
|
% {-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
||||||
|
% & & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
||||||
|
{0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Boundary of \\
|
||||||
|
& & 2002\adctw & 2094\adctw & out of range LOW \\ \hline
|
||||||
|
{+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
||||||
|
& & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptbounds}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
|
||||||
|
for any single error (short or opening of any resistor) this bounds check
|
||||||
|
will detect it.
|
||||||
|
|
||||||
|
|
||||||
|
\section{Single Fault FMEA Analysis \\ of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\subsection{Single Fault Modes as PLD}
|
||||||
|
|
||||||
|
The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
on a PLD diagram.
|
||||||
|
Each test case, is defined by the contours that enclose
|
||||||
|
it. The test cases here deal with single faults only
|
||||||
|
and are thus enclosed by one contour each.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100_tc.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
To establish the valid voltage ranges for these, and knowing our
|
||||||
|
valid temperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
for the circuit shown in figure \ref{fig:vd}.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./voltage_divider.png}
|
||||||
|
% voltage_divider.png: 183x170 pixel, 72dpi, 6.46x6.00 cm, bb=0 0 183 170
|
||||||
|
\caption{Voltage Divider}
|
||||||
|
\label{fig:vd}
|
||||||
|
\end{figure}
|
||||||
|
%The looking at figure \ref{fig:vd} the standard voltage divider formula (equation \ref{eqn:vd}) is used.
|
||||||
|
|
||||||
|
\begin{equation}
|
||||||
|
\label{eqn:vd}
|
||||||
|
V_{out} = V_{in}.\frac{Z2}{Z2+Z1}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Proof of Out of Range \\ Values for Failures}
|
||||||
|
\label{pt110range}
|
||||||
|
Using the temperature ranges defined above we can compare the voltages
|
||||||
|
we would get from the resistor failures to prove that they are
|
||||||
|
`out of range'. There are six test cases and each will be examined in turn.
|
||||||
|
|
||||||
|
\subsubsection{ TC1 : Voltages $R_1$ SHORT }
|
||||||
|
With pt100 at 0\oc
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
Since the highreading or sense+ is directly connected to the 5V rail,
|
||||||
|
both temperature readings will be 5V..
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
|
||||||
|
|
||||||
|
Thus with $R_1$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC2 : Voltages $R_1$ OPEN }
|
||||||
|
|
||||||
|
In this case the 5V rail is disconnected. All voltages read are 0V, and
|
||||||
|
therefore both readings are outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 3 : Voltages $R_2$ SHORT }
|
||||||
|
|
||||||
|
With pt100 at 0\oc
|
||||||
|
$$ lowreading = 0V $$
|
||||||
|
Since the lowreading or sense- is directly connected to the 0V rail,
|
||||||
|
both temperature readings will be 0V.
|
||||||
|
$$ lowreading = 5V.\frac{100\Omega}{2k2+100\Omega} = 0.218V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
|
||||||
|
|
||||||
|
Thus with $R_2$ shorted both readings are outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC : 4 Voltages $R_2$ OPEN }
|
||||||
|
Here there is no potential divider operating and both sense lines
|
||||||
|
will read 5V, outside of the proscribed range.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 5 : Voltages $R_3$ SHORT }
|
||||||
|
|
||||||
|
Here the potential divider is simply between
|
||||||
|
the two 2k2 load resistors. Thus it will read a nominal;
|
||||||
|
2.5V.
|
||||||
|
|
||||||
|
Assuming the load resistors are
|
||||||
|
precision components, and then taking an absolute worst case of 1\% either way.
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
|
||||||
|
|
||||||
|
These readings both lie outside the proscribed range.
|
||||||
|
Also the sense+ and sense- readings would have the same value.
|
||||||
|
|
||||||
|
\subsubsection{ TC 6 : Voltages $R_3$ OPEN }
|
||||||
|
|
||||||
|
Here the potential divider is broken. The sense- will read 0V and the sense+ will
|
||||||
|
read 5V. Both readings are outside the proscribed range.
|
||||||
|
|
||||||
|
\subsection{Summary of Analysis}
|
||||||
|
|
||||||
|
All six test cases have been analysed and the results agree with the hypothesis
|
||||||
|
put in Table \ref{ptfmea}. The PLD diagram, can now be used to collect the
|
||||||
|
symptoms. In this case there is a common and easily detected symptom for all these single
|
||||||
|
resistor faults : Voltage out of range.
|
||||||
|
|
||||||
|
A spider can be drawn on the PLD diagram to this effect.
|
||||||
|
|
||||||
|
In practical use, by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100_tc_sp.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc_sp}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The PT100 circuit can now be treated as a component in its own right, and has one failure mode,
|
||||||
|
{\textbf OUT\_OF\_RANGE}. It can now be represnted as a PLD see figure \ref{fig:pt100_singlef}.
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./pt100_singlef.jpg}
|
||||||
|
% pt100_singlef.jpg: 167x194 pixel, 72dpi, 5.89x6.84 cm, bb=0 0 167 194
|
||||||
|
\caption{PT100 Circuit Failure Modes : From Single Faults Analysis}
|
||||||
|
\label{fig:pt100_singlef}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
%Interestingly we can calculate the failure statistics for this circuit now.
|
||||||
|
%Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for pt100) ???
|
||||||
|
\clearpage
|
||||||
|
\subsection{Mean Time to Failure}
|
||||||
|
|
||||||
|
Using the MIL1991\cite{mil1991} specifications for resistor and thermistor
|
||||||
|
failure statistics we calculate the reliability of this circuit.
|
||||||
|
MIL1991 gives MTTF for a wide range of common components.
|
||||||
|
It does not specify how the components will fail (in this case OPEN or SHORT). {Some standards, notably EN298 only consider resistors failing in OPEN mode}.
|
||||||
|
FMD-97 Gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. This example
|
||||||
|
compromises and uses a 90:10 ratio, for resistor failure.
|
||||||
|
Thus for this example resistors are expevcted to fail OPEN in 90\% of cases and SHORTED
|
||||||
|
in the other 10\%.
|
||||||
|
|
||||||
|
A standard fixed film resistor, for use in a benign environment, non military spec at
|
||||||
|
temperatures up to 60\oc is given a probability of 13.8 failures per billion ($10^9$)
|
||||||
|
hours of operation. This figure is referred to as a FIT\footnote{FIT values are measured as the number of failures per billion hours of operation, (roughly 1.1 Million years). The smaller the FIT number the more reliable the fault~mode}, Failure in time.
|
||||||
|
|
||||||
|
A thermistor, bead type, non military spec is given a FIT of 3150.
|
||||||
|
|
||||||
|
Using the RIAC finding we can draw up the following table (table \ref{tab:stat_single}),
|
||||||
|
showing the FIT values for all faults considered.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[h+]
|
||||||
|
\caption{PT100 FMEA Single // Fault Statistics} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
TC:1 $R_1$ SHORT & High Fault & - & 12.42 \\ \hline
|
||||||
|
TC:2 $R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
TC:3 $R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline
|
||||||
|
TC:4 $R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline
|
||||||
|
\hline
|
||||||
|
TC:5 $R_2$ SHORT & - & Low Fault & 12.42 \\
|
||||||
|
TC:6 $R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{tab:stat_single}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
The FIT for the circuit as a whole is the sum of MTTF values for all the
|
||||||
|
test cases. The PT100 circuit here has a FIT of 3177.6. This is a MTTF of
|
||||||
|
about 360 years per circuit.
|
||||||
|
|
||||||
|
A Probablistic tree can now be drawn, with a FIT value for the PT100
|
||||||
|
circuit and FIT values for all the component fault modes that it was calculated from.
|
||||||
|
We can see from this that that the most likely fault is the thermistor going OPEN.
|
||||||
|
This circuit is 8 times more likely to fail in this way than in any other.
|
||||||
|
Were we to need a more reliable temperature sensor this would probably
|
||||||
|
be the fault~mode we would scrutinise first.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h+]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 856 327,keepaspectratio=true]{./stat_single.jpg}
|
||||||
|
% stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327
|
||||||
|
\caption{Probablistic Fault Tree : PT100 Single Faults}
|
||||||
|
\label{fig:stat_single}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The PT100 analysis presents a simple result for single faults.
|
||||||
|
The next analysis phase looks at how the circuit will behave under double simultaneous failure
|
||||||
|
conditions.
|
||||||
|
|
||||||
|
\clearpage
|
||||||
|
\section{ PT100 Double Simultaneous \\ Fault Analysis}
|
||||||
|
|
||||||
|
% typeset in {\Huge \LaTeX} \today
|
||||||
|
|
||||||
BIN
burner/stat_single.dia~
Normal file
BIN
burner/stat_single.dia~
Normal file
Binary file not shown.
BIN
burner/vrange.dia~
Normal file
BIN
burner/vrange.dia~
Normal file
Binary file not shown.
@ -1,6 +1,6 @@
|
|||||||
|
|
||||||
\abstract{ This chapter defines what is meant by the terms
|
\abstract{ This chapter defines what is meant by the terms
|
||||||
components, component fault modess and `unitary~state' component fault modes.
|
components, component fault modes and `unitary~state' component fault modes.
|
||||||
Mathematical constraints and definitions are made using set theory.
|
Mathematical constraints and definitions are made using set theory.
|
||||||
}
|
}
|
||||||
|
|
||||||
@ -12,15 +12,28 @@ For most common electrical and mechanical components, the failure modes
|
|||||||
for a given type of part can be obtained from standard literature\cite{mil1991}
|
for a given type of part can be obtained from standard literature\cite{mil1991}
|
||||||
\cite{mech}. %The failure modes for a given component $K$ form a set $F$.
|
\cite{mech}. %The failure modes for a given component $K$ form a set $F$.
|
||||||
|
|
||||||
An important factor in defining a failure mode is that they
|
An important factor in defining a set of failure modes is that they
|
||||||
should be as clearly defined as possible.
|
should be as clearly defined as possible.
|
||||||
%
|
%
|
||||||
It should not be possible for instance for
|
It should not be possible for instance for
|
||||||
a component to have two or more failure modes active at once.
|
a component to have two or more failure modes active at once.
|
||||||
Should this be the case, the failure modes have not been clearly analysed.
|
|
||||||
The combination could be represented by a new failure mode, or
|
Having a set of failure modes where $N$ modes could be active simultaneously
|
||||||
the component should be re-analysed. A set of failure modes where only one fault mode
|
would mean having to consider $2^N$ failure mode scenarios.
|
||||||
|
%
|
||||||
|
Should a component be analysed and simultaneous failure mode cases exit,
|
||||||
|
the combinations could be represented by a new failure modes, or
|
||||||
|
the component should be considered from a fresh perspective,
|
||||||
|
perhaps considering it as several smaller components
|
||||||
|
within one package.
|
||||||
|
|
||||||
|
\begin{definition}
|
||||||
|
A set of failure modes where only one fault mode
|
||||||
can be active at a time is termed a `unitary~state' failure mode set.
|
can be active at a time is termed a `unitary~state' failure mode set.
|
||||||
|
This is termed the $U$ set thoughout this study.
|
||||||
|
This corresponds to the `mutually exclusive' definition in
|
||||||
|
probability theory\cite{probandstat}.
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
We can define a function $FM()$ to
|
We can define a function $FM()$ to
|
||||||
take a given component $K$ and return its set of failure modes $F$.
|
take a given component $K$ and return its set of failure modes $F$.
|
||||||
@ -38,61 +51,29 @@ A component with simple ``unitary~state'' failure modes is the electrical resist
|
|||||||
|
|
||||||
Electrical resistors can fail by going OPEN or SHORTED.
|
Electrical resistors can fail by going OPEN or SHORTED.
|
||||||
However they cannot fail with both conditions active. The conditions
|
However they cannot fail with both conditions active. The conditions
|
||||||
OPEN and SHORT are mutually exlusive.
|
OPEN and SHORT are mutually exclusive.
|
||||||
Because of this the failure mode set $F=FM(R)$ is `unitary~state'.
|
Because of this the failure mode set $F=FM(R)$ is `unitary~state'.
|
||||||
%A more complex component, say a micro controller could have several
|
|
||||||
%faults active. It could for instance have a broken I/O output
|
|
||||||
%and an unstable ADC input. Here the faults cannot be considered `unitary~state'.
|
|
||||||
|
|
||||||
% A set of failure modes, where only one or no failure modes
|
|
||||||
% are active is termed an `unitary~state' failure mode set. This
|
|
||||||
% will be donoted as set $A$.
|
|
||||||
%
|
|
||||||
To define `unitary~state' using set theory we can define a function
|
|
||||||
`active'.
|
|
||||||
The function $active(f)$ deontes that the failure mode $f$ (where $f$ is an element of $F$) is currently active.
|
|
||||||
|
|
||||||
Thus for the set $F$ to exist in $U$ the following condition must be true.
|
|
||||||
|
|
||||||
\begin{equation}
|
|
||||||
\label{unitarystate_def}
|
|
||||||
F \in U | f \in F \wedge active(f) \wedge f1 \in F \wedge f1 \neq f \wedge \neg active(f1)
|
|
||||||
\end{equation}
|
|
||||||
|
|
||||||
As an example the resistor $R$
|
|
||||||
has two failure modes $R_{open}$ and $R_{shorted}$.
|
|
||||||
|
|
||||||
$$ FM(R) = F = \{ R_{open}, R_{shorted} \} $$
|
|
||||||
|
|
||||||
Applying equation \ref{`unitarystate'_definition} to a resistor
|
|
||||||
for both fault modes
|
|
||||||
|
|
||||||
$$ active(R_{short}) | R_{short} \in F \wedge R_{open} \in F \wedge R_{open} \neq R_{short} \wedge \neg active(R_{open}) $$
|
|
||||||
$$ active(R_{open}) | R_{open} \in F \wedge R_{short} \in F \wedge R_{short} \neq R_{open} \wedge \neg active(R_{short}) $$
|
|
||||||
|
|
||||||
For the case of the resistor with only two failure modes the results above, being true,
|
|
||||||
show that the failure modes for a resistor of $ F = \{ R_{open}, R_{shorted} \} $ are `unitary~state'
|
|
||||||
component failure modes.
|
|
||||||
|
|
||||||
Thus
|
Thus
|
||||||
$$ FM(R) = \{ R_{open}, R_{shorted} \} \in U $$
|
|
||||||
|
$$ R_{SHORTED} \cap R_{OPEN} = \emptyset $$
|
||||||
|
|
||||||
|
|
||||||
A general case can be stated by taking equation \ref{unitary_state_def} and making it a function thus.
|
We can make this a general case by taking a set $C$ representing a collection
|
||||||
|
of component failure modes,
|
||||||
|
We can now state that
|
||||||
|
|
||||||
|
|
||||||
\begin{equation}
|
$$ c1 \cap c2 \neq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \not\in U $$
|
||||||
\label{`unitarystate'_def}
|
|
||||||
UnitaryState(F) = \forall f \in F | active(f) \wedge f1 \in F \wedge f1 \neq f \wedge \neg active(f1)
|
|
||||||
\end{equation}
|
|
||||||
|
|
||||||
%Which can be written
|
That is to say that if it is impossible that any pair of failure modes can be active at the same time
|
||||||
|
the failure mode set is not unitary~state and does not exist in the family of sets $U$
|
||||||
%$$ UnitaryState(FM(K)) $$
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
% should this be a paragraph in Symptom Abstraction ????
|
|
||||||
|
|
||||||
|
Note where that are more than two failure~modes, by banning pairs from happening at the same time
|
||||||
|
we have banned larger combinations as well
|
||||||
|
|
||||||
|
%$$ c1 \cap c2 \eq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \in U $$
|
||||||
|
|
||||||
|
%Thus if the failure~modes are pairwaise mutually exclusive they qualify for inclusion into the
|
||||||
|
%unitary~state set family.
|
||||||
|
|||||||
@ -21,12 +21,21 @@ This changed the target for the study slightly to encompass these domains in a c
|
|||||||
I completed an MSc in Software engineering in 2004 at Brighton university while working for
|
I completed an MSc in Software engineering in 2004 at Brighton university while working for
|
||||||
an Engineering firm as a software Engineer.
|
an Engineering firm as a software Engineer.
|
||||||
The firm make industrial burner controllers.
|
The firm make industrial burner controllers.
|
||||||
iIndustrial Burners are potentially very dangerous industrail plant.
|
Industrial Burners are potentially very dangerous industrial plant.
|
||||||
They are subject to stringent safety regulations and any product controlling them
|
They are generally left running unattended for long periods.
|
||||||
must conform to specific `EN' standards. This involved not only writing software and designing hardware in compliance,
|
They are subject to stringent safety regulations and
|
||||||
but also stages of formal certification testing. The certification testing had to be performed by
|
must conform to specific `EN' standards.
|
||||||
`competent body' recognised under European law. A significant part
|
|
||||||
of this process was `static testing'. This involved looking at the design of the products,
|
One cannot merely comply with the standards.
|
||||||
|
|
||||||
|
The product must be `certified' by an independent
|
||||||
|
and
|
||||||
|
`competent body' recognised under European law.
|
||||||
|
The cerification involved stress testing with repeated operation cycles,
|
||||||
|
within a range of temperatures. Electrical stress testing with high voltage interference, and
|
||||||
|
power supply voltage surges and dips. Electro static discharge testing, and
|
||||||
|
EMC (Electro Magnetic Compatibility). A significant part
|
||||||
|
of this process however, was `static testing'. This involved looking at the design of the products,
|
||||||
from the perspective of components failing, and the effect on safety this would have.
|
from the perspective of components failing, and the effect on safety this would have.
|
||||||
Some of the static testing involved checking that the germane `EN' standards had
|
Some of the static testing involved checking that the germane `EN' standards had
|
||||||
been complied with. Failure Mode Effects Analysis (FMEA) was also applied. This involved
|
been complied with. Failure Mode Effects Analysis (FMEA) was also applied. This involved
|
||||||
@ -36,10 +45,20 @@ answer was required, or a counter proposal to change the design to cope with
|
|||||||
the comonent failure eventuality. FMEA was time consuming, and being directed by
|
the comonent failure eventuality. FMEA was time consuming, and being directed by
|
||||||
experts undoubtly ironed out many potential safety faults before the product saw
|
experts undoubtly ironed out many potential safety faults before the product saw
|
||||||
light of day. However it was quickly apparent that only a small proportion
|
light of day. However it was quickly apparent that only a small proportion
|
||||||
of copmponent~failure modes was considered. Also there was no formaliswm.
|
of copmponent~failure modes was considered. Also there was no formalism.
|
||||||
The component~failure~modes investigated were not analysed within
|
The component~failure~modes investigated were not analysed within
|
||||||
any rigourous framework.
|
any rigourous framework.
|
||||||
|
|
||||||
|
\subsection{ Blanket Risk Reduction Approach }
|
||||||
|
|
||||||
|
The suite of tests applied for a certified product amount to a `blanket' approach.
|
||||||
|
That is to say that by applying Electrical, repeated operations, and environmental
|
||||||
|
stress testing it is hoped that the majority of latent faults are discovered.
|
||||||
|
The FMEA, or static sections, only look at the most obviously safety critical
|
||||||
|
aspects, and a small minority of the total component base for a product.
|
||||||
|
|
||||||
|
Systememic faults, or mistakes will often by-pass this testing.
|
||||||
|
|
||||||
\subsection{Possibility of applying mathematical techniques to FMEA}
|
\subsection{Possibility of applying mathematical techniques to FMEA}
|
||||||
|
|
||||||
My MSc project was a diagram editor for Constraint diagrams.
|
My MSc project was a diagram editor for Constraint diagrams.
|
||||||
@ -66,23 +85,25 @@ obviously impractical.
|
|||||||
\subsection{General description of a Safety Critical System}
|
\subsection{General description of a Safety Critical System}
|
||||||
|
|
||||||
A safety critical system is one in which lives may depend upon it or
|
A safety critical system is one in which lives may depend upon it or
|
||||||
it has the potential to become dangerous.
|
it has the potential to become dangerous\cite{sccs}.
|
||||||
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty)
|
%(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty)
|
||||||
|
|
||||||
An industrial burner is typical of plant that is potentially dangerous.
|
An industrial burner is typical of plant that is potentially dangerous.
|
||||||
An incorrect air/fuel mixture can be explosive.
|
An incorrect air/fuel mixture can be explosive.
|
||||||
Medical electronics for automatically dispensing drugs or maintaining
|
Medical electronics for automatically dispensing drugs or maintaining
|
||||||
life support are examples of systems that lives depend upon.
|
life support are examples of systems that lives depend upon.
|
||||||
|
|
||||||
\subsection{Two approaches : Probablistic, and Compnent fault tolerant}
|
\subsection{Two approaches : Probablistic, and Deterministic}
|
||||||
|
|
||||||
There are two main philosophies applied to safety critical systems certification.
|
There are two main philosophies applied to safety critical systems certification.
|
||||||
\paragraph{Statistical safety Measures}
|
\paragraph{Probablistic safety Measures}
|
||||||
One is a general number of acceptable failure per hour of operation.
|
One is a general number of acceptable failures per hour\footnote{The common metric is Failure in Time (FIT) values - failures per ${10}^{9}$
|
||||||
|
hours of operation} of operation or
|
||||||
|
a given statistical failure on demand.
|
||||||
This is the probablistic approach and is embodied in the european standard
|
This is the probablistic approach and is embodied in the european standard
|
||||||
EN61508 \cite{EN61508}.
|
EN61508 \cite{EN61508}.
|
||||||
|
|
||||||
\paragraph{Prescriptive safety Measures}
|
\paragraph{Deterministic safety Measures}
|
||||||
The second philosophy, applied to application specific standards, is to investigate
|
The second philosophy, applied to application specific standards, is to investigate
|
||||||
components ior sub-systems in the critical safety path and to look at component failure modes
|
components ior sub-systems in the critical safety path and to look at component failure modes
|
||||||
and ensure that they cannot cause dangerous faults.
|
and ensure that they cannot cause dangerous faults.
|
||||||
@ -114,67 +135,36 @@ reference chapter dealing speciifically with this but given a quick overview.
|
|||||||
\subsubsection{Overview of current testing and certification}
|
\subsubsection{Overview of current testing and certification}
|
||||||
ref chapter speciifically on this but give an overview now
|
ref chapter speciifically on this but give an overview now
|
||||||
|
|
||||||
\section{Background to the Industrial Burner Safety Analysis Problem}
|
|
||||||
|
|
||||||
An industrial burner is a good example of a safety critical system.
|
|
||||||
It has the potential for devistating explosions due to boiler overpressure, or
|
|
||||||
ignition of an explosive mixture, and, because of the large amounts of fuel used,
|
|
||||||
is also a fire hazard. Also Industrial boilers are often left running unattended
|
|
||||||
for long periods of time (typically days).
|
|
||||||
|
|
||||||
To add to these problems
|
|
||||||
Operators are often under pressure to keep them running. An boiler supplying
|
|
||||||
heat to a large greenhouse complex could ruin crops
|
|
||||||
should it go off-line. Similarly a production line relying on heat or steam
|
|
||||||
can be very expensive in production down-time should it fail.
|
|
||||||
This places extra responsibility on the burner controller.
|
|
||||||
|
|
||||||
|
|
||||||
These are common place and account for a very large proportion of the enery usage
|
|
||||||
in the world today (find and ref stats)
|
|
||||||
Industrial burners are common enough to have different specific standards
|
|
||||||
written for the fuel types they use \ref{EN298} \ref{EN230} \ref{EN12067}.
|
|
||||||
|
|
||||||
A modern industrial burner has mechanical, electronic and software
|
A modern industrial burner has mechanical, electronic and software
|
||||||
elements, that are all safety critical. That is to say
|
elements, that are all safety critical. That is to say
|
||||||
unhandled failures could create dangerous faults.
|
unhandled failures could create dangerous faults.
|
||||||
|
|
||||||
To add to these problems
|
%To add to these problems
|
||||||
Operators are often under pressure to keep them running. An boiler supplying
|
%Operators are often under pressure to keep them running. An boiler supplying
|
||||||
heat to a large greenhouse complex could ruin crops
|
%heat to a large greenhouse complex could ruin crops
|
||||||
should it go off-line. Similarly a production line relying on heat or steam
|
%should it go off-line. Similarly a production line relying on heat or steam
|
||||||
can be very expensive in production down-time should it fail.
|
%can be very expensive in production down-time should it fail.
|
||||||
This places extra responsibility on the burner controller.
|
%This places extra responsibility on the burner controller.
|
||||||
|
%
|
||||||
|
%
|
||||||
These are common place and account for a very large proportion of the enery usage
|
|
||||||
in the world today (find and ref stats)
|
|
||||||
Industrial burners are common enough to have different specific standards
|
|
||||||
written for the fuel types they usei \ref{EN298} \ref{EN230} \ref{EN12067}.
|
|
||||||
|
|
||||||
A modern industrial burner has mechanical, electronic and software
|
|
||||||
elements, that are all safety critical. That is to say
|
|
||||||
unhandled failures could create dangerous faults.
|
|
||||||
|
|
||||||
A more detailed description of industrial burner controllers
|
|
||||||
is dealt with in chapter~\ref{burnercontroller}.
|
|
||||||
|
|
||||||
\subsection{Mechanical components}
|
|
||||||
describe the mechanical parts - gas valves damper s
|
|
||||||
electronic and software
|
|
||||||
give a diagram of how it all fits A
|
|
||||||
together with a
|
|
||||||
\subsection{electronic Components}
|
|
||||||
|
|
||||||
\subsection{Software/Firmware Components}
|
|
||||||
|
|
||||||
|
|
||||||
\subsection{A high level Fault Hierarchy for an Industrial Burner}
|
|
||||||
|
|
||||||
This section shows the component level, leading up higher and higher in the abstraction level
|
|
||||||
to the software levels and finally a top level abstract level. If the system has been
|
|
||||||
designed correctly no `undetected faults' should be present here.
|
|
||||||
|
|
||||||
|
% This needs to become a chapter
|
||||||
|
%\subsection{Mechanical components}
|
||||||
|
%describe the mechanical parts - gas valves damper s
|
||||||
|
%electronic and software
|
||||||
|
%give a diagram of how it all fits A
|
||||||
|
%together with a
|
||||||
|
%\subsection{electronic Components}
|
||||||
|
%
|
||||||
|
%\subsection{Software/Firmware Components}
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%\subsection{A high level Fault Hierarchy for an Industrial Burner}
|
||||||
|
%
|
||||||
|
%This section shows the component level, leading up higher and higher in the abstraction level
|
||||||
|
%to the software levels and finally a top level abstract level. If the system has been
|
||||||
|
%designed correctly no `undetected faults' should be present here.
|
||||||
|
%
|
||||||
\section{An Outline of the FMMD Technique}
|
\section{An Outline of the FMMD Technique}
|
||||||
|
|
||||||
The methodology takes a bottom up approach to
|
The methodology takes a bottom up approach to
|
||||||
@ -182,8 +172,10 @@ the design of an integrated system.
|
|||||||
Each component is assigned a well defined set of failure modes.
|
Each component is assigned a well defined set of failure modes.
|
||||||
The components are formed into modules, or functional groups.
|
The components are formed into modules, or functional groups.
|
||||||
These functional groups are analysed with respect to the failure modes of the
|
These functional groups are analysed with respect to the failure modes of the
|
||||||
components. The `functional group' or module will have a set of derived
|
components. The `functional group' or module will, after analysis, have a set of derived
|
||||||
failure modes. The number of derived failure modes will be
|
failure modes. Thus we can now treat our `functional group' as a component in its own right,
|
||||||
|
with its own set of failure~modes.
|
||||||
|
The number of derived failure modes will be
|
||||||
less than or equal to the sum of the failure modes of all its components.
|
less than or equal to the sum of the failure modes of all its components.
|
||||||
A `derived' set of failure modes, is at a higher abstraction level.
|
A `derived' set of failure modes, is at a higher abstraction level.
|
||||||
derived modules may now be used as building blocks, to model the system at
|
derived modules may now be used as building blocks, to model the system at
|
||||||
@ -197,6 +189,7 @@ A formal description of this process is dealt with in Chapter \ref{fmmddefinitio
|
|||||||
%on simple control systems for maintaining temperature
|
%on simple control systems for maintaining temperature
|
||||||
%and for industrial burners. It is hoped that a general mathematical
|
%and for industrial burners. It is hoped that a general mathematical
|
||||||
%framework is created that can be applied to other fields of safety critical engineering.
|
%framework is created that can be applied to other fields of safety critical engineering.
|
||||||
|
\subsection{Automated Systems and Safety}
|
||||||
|
|
||||||
Automated systems, as opposed to manual ones are now the norm
|
Automated systems, as opposed to manual ones are now the norm
|
||||||
in the home and in industry.
|
in the home and in industry.
|
||||||
@ -238,30 +231,6 @@ corrections cannot be enough.
|
|||||||
It could also develop an internal fault, and must be able to cope with this.
|
It could also develop an internal fault, and must be able to cope with this.
|
||||||
|
|
||||||
|
|
||||||
Systems such as industrial burners have been partially automated for some time.
|
|
||||||
A mechanical cam arrangement controls the flow of air and fuel for the range of
|
|
||||||
firing rate (output of the boiler).
|
|
||||||
|
|
||||||
These mechanical systems could suffer failures (such as a mechanical linkage beoming
|
|
||||||
detached) and could then operate in a potentially dangerous state.
|
|
||||||
|
|
||||||
More modern burner controllers use a safety critical computer controlling
|
|
||||||
motors to operate the fuel and air mixture and to control the safety
|
|
||||||
valves.
|
|
||||||
|
|
||||||
In working in the industrial burner industry and submitting product for
|
|
||||||
North American and European safety approval, it was apparent that
|
|
||||||
formal techniques could be applied to aspects of the ciruit design.
|
|
||||||
Some safety critical circuitry would be subjected to thought experiments, where
|
|
||||||
the actions of one or more components failing would be examined.
|
|
||||||
As a simple example a milli-volt input could become disconnected.
|
|
||||||
A milli-volt input is typically amplified so that its range matches that
|
|
||||||
of the A->D converter that you are reading. were this signal source to become disconnected
|
|
||||||
the systems would see a floating, amplified signal.
|
|
||||||
A high impedance safety resistor can be added to the circuit,
|
|
||||||
to pull the signal high (or out of nornal range) upon disconnection.
|
|
||||||
The system then knows that a fault has occurred and will not use
|
|
||||||
that sensor reading (see \ref{fig:millivolt}).
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
@ -389,6 +358,12 @@ The problem lay in a seal that had an operating temperature range.
|
|||||||
On the day of the launch the temperature of this seal was out of range.
|
On the day of the launch the temperature of this seal was out of range.
|
||||||
A bottom up safety approach would have revealed this as a fault.
|
A bottom up safety approach would have revealed this as a fault.
|
||||||
|
|
||||||
|
The FTA in use by NASA and the US Nuclear regulatory commisssion
|
||||||
|
allows for enviromental considerations such as temperature\cite{NASA}\cite{NUK}.
|
||||||
|
But because of the top down nature of the FTA technique, the safety designer must be aware of
|
||||||
|
the environemtnal constraints of all component parts in order to use this correctly.
|
||||||
|
This element of FTA is discussed in \ref{surveysc}
|
||||||
|
|
||||||
\section{Problems with Natural Language}
|
\section{Problems with Natural Language}
|
||||||
|
|
||||||
Written natural language desciptions can not only be ambiguous or easy to misinterpret, it
|
Written natural language desciptions can not only be ambiguous or easy to misinterpret, it
|
||||||
@ -427,6 +402,7 @@ temperature being the most typical. Very often what happens to the system outsid
|
|||||||
\section{Project Goals}
|
\section{Project Goals}
|
||||||
|
|
||||||
\begin{itemize}
|
\begin{itemize}
|
||||||
|
\item To create a Bottom up FMEA technique that is modular and permits a linked hierarchy to be build representing the fault behaviour of a system.
|
||||||
\item To create a user friendly formal common visual notation to represent fault modes
|
\item To create a user friendly formal common visual notation to represent fault modes
|
||||||
in Software, Electronic and Mechanical sub-systems.
|
in Software, Electronic and Mechanical sub-systems.
|
||||||
\item To formally define this visual language.
|
\item To formally define this visual language.
|
||||||
|
|||||||
17
standards/Makefile
Normal file
17
standards/Makefile
Normal file
@ -0,0 +1,17 @@
|
|||||||
|
|
||||||
|
#
|
||||||
|
# Make the propositional logic diagram a paper
|
||||||
|
#
|
||||||
|
|
||||||
|
|
||||||
|
paper: paper.tex standards_paper.tex
|
||||||
|
#latex paper.tex
|
||||||
|
#dvipdf paper pdflatex cannot use eps ffs
|
||||||
|
pdflatex paper.tex
|
||||||
|
okular paper.pdf
|
||||||
|
|
||||||
|
|
||||||
|
# Remove the need for referncing graphics in subdirectories
|
||||||
|
#
|
||||||
|
standards_paper.tex: standards.tex
|
||||||
|
cat standards.tex | sed 's/standards\///' > standards_paper.tex
|
||||||
11
standards/paper.aux
Normal file
11
standards/paper.aux
Normal file
@ -0,0 +1,11 @@
|
|||||||
|
\relax
|
||||||
|
\bibstyle{plain}
|
||||||
|
\bibdata{vmgbibliography,mybib}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {2}European Safety Standards Legal Framework}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {3}North American Legal Framework}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {4}Cross Referencing}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {5}EN298}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {6}UL1998}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {7}EN230}{1}}
|
||||||
|
\@writefile{toc}{\contentsline {section}{\numberline {8}EN61508}{1}}
|
||||||
429
standards/paper.log
Normal file
429
standards/paper.log
Normal file
@ -0,0 +1,429 @@
|
|||||||
|
This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2010.2.1) 4 APR 2010 13:40
|
||||||
|
entering extended mode
|
||||||
|
%&-line parsing enabled.
|
||||||
|
**paper.tex
|
||||||
|
(./paper.tex
|
||||||
|
LaTeX2e <2005/12/01>
|
||||||
|
Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
|
||||||
|
yphenation, loaded.
|
||||||
|
(/usr/share/texmf-texlive/tex/latex/base/article.cls
|
||||||
|
Document Class: article 2005/09/16 v1.4f Standard LaTeX document class
|
||||||
|
(/usr/share/texmf-texlive/tex/latex/base/size10.clo
|
||||||
|
File: size10.clo 2005/09/16 v1.4f Standard LaTeX file (size option)
|
||||||
|
)
|
||||||
|
\c@part=\count79
|
||||||
|
\c@section=\count80
|
||||||
|
\c@subsection=\count81
|
||||||
|
\c@subsubsection=\count82
|
||||||
|
\c@paragraph=\count83
|
||||||
|
\c@subparagraph=\count84
|
||||||
|
\c@figure=\count85
|
||||||
|
\c@table=\count86
|
||||||
|
\abovecaptionskip=\skip41
|
||||||
|
\belowcaptionskip=\skip42
|
||||||
|
\bibindent=\dimen102
|
||||||
|
)
|
||||||
|
(/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty
|
||||||
|
Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
|
||||||
|
|
||||||
|
(/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty
|
||||||
|
Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
|
||||||
|
\KV@toks@=\toks14
|
||||||
|
)
|
||||||
|
(/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty
|
||||||
|
Package: graphics 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR)
|
||||||
|
|
||||||
|
(/usr/share/texmf-texlive/tex/latex/graphics/trig.sty
|
||||||
|
Package: trig 1999/03/16 v1.09 sin cos tan (DPC)
|
||||||
|
)
|
||||||
|
(/etc/texmf/tex/latex/config/graphics.cfg
|
||||||
|
File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive
|
||||||
|
)
|
||||||
|
Package graphics Info: Driver file: pdftex.def on input line 90.
|
||||||
|
|
||||||
|
(/usr/share/texmf-texlive/tex/latex/pdftex-def/pdftex.def
|
||||||
|
File: pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX
|
||||||
|
\Gread@gobject=\count87
|
||||||
|
))
|
||||||
|
\Gin@req@height=\dimen103
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\documentclass[a4paper,10pt]{article}
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\begin{document}
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\outerhead{{\small\bf Safety Critical Standards Review}}
|
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%\innerfoot{{\small\bf R.P. Clark } }
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% numbers at outer edges
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\pagenumbering{arabic} % Arabic page numbers hereafter
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\author{R.P.Clark}
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\title{Safety Critical Standards Review}
|
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\maketitle
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\input{standards_paper}
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\bibliographystyle{plain}
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\bibliography{vmgbibliography,mybib}
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\today
|
||||||
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\end{document}
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% Make the revision and doc number macro's then they are defined in one place
|
||||||
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|
||||||
|
\begin{abstract}
|
||||||
|
The PT100, or platinum wire \ohms{100} sensor is
|
||||||
|
a widely used industrial temperature sensor that is
|
||||||
|
slowly replacing the use of thermocouples in many
|
||||||
|
industrial applications below 600\oc, due to high accuracy\cite{aoe}.
|
||||||
|
|
||||||
|
This chapter looks at the most common configuration, the
|
||||||
|
four wire circuit, and analyses it from an FMEA perspective twice.
|
||||||
|
Once considering single faults (cardinality constrained powerset of 1) and then again, considering the
|
||||||
|
possibility of double faults (cardinality constrained powerset of 2).
|
||||||
|
|
||||||
|
The analysis is performed using Propositional Logic
|
||||||
|
diagrams to assist the reasoning process.
|
||||||
|
This chapter describes taking
|
||||||
|
the failure modes of the components, analysing the circuit using FMEA
|
||||||
|
and producing a failure mode model for the circuit as a whole.
|
||||||
|
Thus after the analysis the PT100 temperature sensing circuit, may be veiwed
|
||||||
|
from an FMEA persepective as a component itself, with a set of known failure modes.
|
||||||
|
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./pt100/pt100.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 four wire circuit}
|
||||||
|
\label{fig:pt100}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
\section{Overview of PT100 four wire circuit}
|
||||||
|
|
||||||
|
The PT100 four wire circuit uses two wires to supply small electrical current,
|
||||||
|
and returns two sense volages by the other two.
|
||||||
|
By measuring volatges
|
||||||
|
from sections of this circuit forming potential dividers, we can determine the
|
||||||
|
resistance of the platinum wire sensor. The resistance
|
||||||
|
of this is directly related to temperature, and may be determined by
|
||||||
|
look-up tables or a suitable polynomial expression.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=150pt,bb=0 0 273 483,keepaspectratio=true]{./pt100/vrange.jpg}
|
||||||
|
% pt100.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
|
||||||
|
\caption{PT100 expected voltage ranges}
|
||||||
|
\label{fig:pt100vrange}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The voltage ranges we expect from this three stage potential divider
|
||||||
|
are shown in figure \ref{fig:pt100vrange}. Note that there is
|
||||||
|
an expected range for each reading, for a given temperature span.
|
||||||
|
Note that the low reading goes down as temperature increases, and the higher reading goes up.
|
||||||
|
For this reason the low reading will be reffered to as {\em sense-}
|
||||||
|
and the higher as {\em sense+}.
|
||||||
|
|
||||||
|
\subsection{Accuracy despite variable \\ resistance in cables}
|
||||||
|
|
||||||
|
For electronic and accuracy reasons a four wire circuit is preffered
|
||||||
|
because of resistance in the cables. Resistance from the supply
|
||||||
|
causes a slight voltage
|
||||||
|
drop in the supply to the PT100. As no significant current
|
||||||
|
is carried by the two `sense' lines the resistance back to the ADC
|
||||||
|
causes only a negligible voltage drop, and thus the four wire
|
||||||
|
configuration is more accurate.
|
||||||
|
|
||||||
|
\subsection{Calculating Temperature from \\ the sense line voltages}
|
||||||
|
|
||||||
|
The current flowing though the
|
||||||
|
whole circuit can be measured on the PCB by reading a third
|
||||||
|
sense voltage from one of the load resistors. Knowing the current flowing
|
||||||
|
through the circuit
|
||||||
|
and knowing the voltage drop over the PT100, we can calculate its
|
||||||
|
resistance by ohms law $V=I.R$, $R=\frac{V}{I}$.
|
||||||
|
Thus a little loss of supply current due to resistance in the cables
|
||||||
|
does not impinge on accuracy.
|
||||||
|
The resistance to temperature conversion is achieved
|
||||||
|
through the published PT100 tables\cite{eurothermtables}.
|
||||||
|
|
||||||
|
\section{Safety case for 4 wire circuit}
|
||||||
|
|
||||||
|
This sub-section looks at the behaviour of the PT100 four wire circuit
|
||||||
|
for the effects of component failures.
|
||||||
|
All components have a set of known `failure modes'.
|
||||||
|
In other words we know that a given component can fail in several distinct ways.
|
||||||
|
Studies have been published which list common component types
|
||||||
|
and their sets of failure modes, often with MTTF statistics \cite{mil1991}.
|
||||||
|
Thus for each component, an analysis is made for each of it failure modes,
|
||||||
|
with respect to its effect on the
|
||||||
|
circuit. Each one of these scenarios is termed a `test case'.
|
||||||
|
The resultant circuit behaviour for each of these test cases is noted.
|
||||||
|
The worst case for this type of
|
||||||
|
analysis would be a fault that we cannot detect.
|
||||||
|
Where this occurs a circuit re-design is probably the only sensible course of action.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Single Fault FMEA Analysis \\ of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\label{fmea}
|
||||||
|
This circuit simply consists of three resistors.
|
||||||
|
Resistors according to the DOD Electronic component fault handbook
|
||||||
|
1991, fail by either going OPEN or SHORT circuit \cite{mil1991}.
|
||||||
|
%Should wires become disconnected these will have the same effect as
|
||||||
|
%given resistors going open.
|
||||||
|
For the purpose of this analyis;
|
||||||
|
$R_{1}$ is the \ohms{2k2} from 5V to the thermistor,
|
||||||
|
$R_3$ is the PT100 thermistor and $R_{2}$ connects the thermistor to ground.
|
||||||
|
|
||||||
|
We can define the terms `High Fault' and `Low Fault' here, with reference to figure
|
||||||
|
\ref{fig:pt100vrange}. Should we get a reading outside the safe green zone
|
||||||
|
in the diagram we can consider this a fault.
|
||||||
|
Should the reading be above its expected range this is a `High Fault'
|
||||||
|
and if below a `Low Fault'.
|
||||||
|
|
||||||
|
Table \ref{ptfmea} plays through the scenarios of each of the resistors failing
|
||||||
|
in both SHORT and OPEN failure modes, and hypothesises an error condition in the readings.
|
||||||
|
The range {0\oc} to {300\oc} will be analysed using potential divider equations to
|
||||||
|
determine out of range voltage limits in section \ref{ptbounds}.
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 FMEA Single Faults} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
$R_1$ SHORT & High Fault & - & Value Out of Range Value \\ \hline
|
||||||
|
$R_1$ OPEN & Low Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_3$ SHORT & Low Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
$R_3$ OPEN & High Fault & Low Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
$R_2$ SHORT & - & Low Fault & Value Out of Range Value \\
|
||||||
|
$R_2$ OPEN & High Fault & High Fault & Both values out of range \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptfmea}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
From table \ref{ptfmea} it can be seen that any component failure in the circuit
|
||||||
|
should cause a common symptom, that of one or more of the values being `out of range'.
|
||||||
|
Temperature range calculations and detailed calculations
|
||||||
|
on the effects of each test case are found in section \ref{pt100range}
|
||||||
|
and \ref{pt100temp}.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Range and PT100 Calculations}
|
||||||
|
\label{pt100temp}
|
||||||
|
PT100 resistors are designed to
|
||||||
|
have a resistance of \ohms{100} at {0\oc} \cite{aoe},\cite{eurothermtables}.
|
||||||
|
A suitable `wider than to be expected range' was considered to be {0\oc} to {300\oc}
|
||||||
|
for a given application.
|
||||||
|
According to the Eurotherm PT100
|
||||||
|
tables \cite{eurothermtables}, this corresponded to the resistances \ohms{100}
|
||||||
|
and \ohms{212.02} respectively. From this the potential divider circuit can be
|
||||||
|
analysed and the maximum and minimum acceptable voltages determined.
|
||||||
|
These can be used as bounds results to apply the findings from the
|
||||||
|
PT100 FMEA analysis in section \ref{fmea}.
|
||||||
|
|
||||||
|
As the PT100 forms a potential divider with the \ohms{2k2} load resistors,
|
||||||
|
the upper and lower readings can be calculated thus:
|
||||||
|
|
||||||
|
|
||||||
|
$$ highreading = 5V.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
So by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
To convert these to twelve bit ADC (\adctw) counts:
|
||||||
|
|
||||||
|
$$ highreading = 2^{12}.\frac{2k2+pt100}{2k2+2k2+pt100} $$
|
||||||
|
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+pt100} $$
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[ht]
|
||||||
|
\caption{PT100 Maximum and Minimum Values} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||c|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Temperature} & \textbf{PT100 resistance} &
|
||||||
|
\textbf{Lower} & \textbf{Higher} & \textbf{Description} \\
|
||||||
|
\hline
|
||||||
|
% {-100 \oc} & {\ohms{68.28}} & 2.46V & 2.53V & Boundary of \\
|
||||||
|
% & & 2017\adctw & 2079\adctw & out of range LOW \\ \hline
|
||||||
|
{0 \oc} & {\ohms{100}} & 2.44V & 2.56V & Boundary of \\
|
||||||
|
& & 2002\adctw & 2094\adctw & out of range LOW \\ \hline
|
||||||
|
{+300 \oc} & {\ohms{212.02}} & 2.38V & 2.62V & Boundary of \\
|
||||||
|
& & 1954\adctw & 2142\adctw & out of range HIGH \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{ptbounds}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that
|
||||||
|
for any single error (short or opening of any resistor) this bounds check
|
||||||
|
will detect it.
|
||||||
|
|
||||||
|
|
||||||
|
\section{Single Fault FMEA Analysis \\ of PT100 Four wire circuit}
|
||||||
|
|
||||||
|
\subsection{Single Fault Modes as PLD}
|
||||||
|
|
||||||
|
The component~failure~modes in table \ref{ptfmea} can be represented as contours
|
||||||
|
on a PLD diagram.
|
||||||
|
Each test case, is defined by the contours that enclose
|
||||||
|
it. The test cases here deal with single faults only
|
||||||
|
and are thus enclosed by one contour each.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
This circuit supplies two results, sense+ and sense- voltage readings.
|
||||||
|
To establish the valid voltage ranges for these, and knowing our
|
||||||
|
valid temperature range for this example ({0\oc} .. {300\oc}) we can calculate
|
||||||
|
valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
|
||||||
|
for the circuit shown in figure \ref{fig:vd}.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./pt100/voltage_divider.png}
|
||||||
|
% voltage_divider.png: 183x170 pixel, 72dpi, 6.46x6.00 cm, bb=0 0 183 170
|
||||||
|
\caption{Voltage Divider}
|
||||||
|
\label{fig:vd}
|
||||||
|
\end{figure}
|
||||||
|
%The looking at figure \ref{fig:vd} the standard voltage divider formula (equation \ref{eqn:vd}) is used.
|
||||||
|
|
||||||
|
\begin{equation}
|
||||||
|
\label{eqn:vd}
|
||||||
|
V_{out} = V_{in}.\frac{Z2}{Z2+Z1}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Proof of Out of Range \\ Values for Failures}
|
||||||
|
\label{pt110range}
|
||||||
|
Using the temperature ranges defined above we can compare the voltages
|
||||||
|
we would get from the resistor failures to prove that they are
|
||||||
|
`out of range'. There are six test cases and each will be examined in turn.
|
||||||
|
|
||||||
|
\subsubsection{ TC1 : Voltages $R_1$ SHORT }
|
||||||
|
With pt100 at 0\oc
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
Since the highreading or sense+ is directly connected to the 5V rail,
|
||||||
|
both temperature readings will be 5V..
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
|
||||||
|
|
||||||
|
Thus with $R_1$ shorted both readingare outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC2 : Voltages $R_1$ OPEN }
|
||||||
|
|
||||||
|
In this case the 5V rail is disconnected. All voltages read are 0V, and
|
||||||
|
therefore both readings are outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 3 : Voltages $R_2$ SHORT }
|
||||||
|
|
||||||
|
With pt100 at 0\oc
|
||||||
|
$$ lowreading = 0V $$
|
||||||
|
Since the lowreading or sense- is directly connected to the 0V rail,
|
||||||
|
both temperature readings will be 0V.
|
||||||
|
$$ lowreading = 5V.\frac{100\Omega}{2k2+100\Omega} = 0.218V$$
|
||||||
|
With pt100 at the high end of the temperature range 300\oc.
|
||||||
|
$$ highreading = 5V $$
|
||||||
|
$$ lowreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
|
||||||
|
|
||||||
|
Thus with $R_2$ shorted both readings are outside the
|
||||||
|
proscribed range in table \ref{ptbounds}.
|
||||||
|
|
||||||
|
\subsubsection{ TC : 4 Voltages $R_2$ OPEN }
|
||||||
|
Here there is no potential divider operating and both sense lines
|
||||||
|
will read 5V, outside of the proscribed range.
|
||||||
|
|
||||||
|
|
||||||
|
\subsubsection{ TC 5 : Voltages $R_3$ SHORT }
|
||||||
|
|
||||||
|
Here the potential divider is simply between
|
||||||
|
the two 2k2 load resistors. Thus it will read a nominal;
|
||||||
|
2.5V.
|
||||||
|
|
||||||
|
Assuming the load resistors are
|
||||||
|
precision components, and then taking an absolute worst case of 1\% either way.
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
|
||||||
|
|
||||||
|
$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
|
||||||
|
|
||||||
|
These readings both lie outside the proscribed range.
|
||||||
|
Also the sense+ and sense- readings would have the same value.
|
||||||
|
|
||||||
|
\subsubsection{ TC 6 : Voltages $R_3$ OPEN }
|
||||||
|
|
||||||
|
Here the potential divider is broken. The sense- will read 0V and the sense+ will
|
||||||
|
read 5V. Both readings are outside the proscribed range.
|
||||||
|
|
||||||
|
\subsection{Summary of Analysis}
|
||||||
|
|
||||||
|
All six test cases have been analysed and the results agree with the hypothesis
|
||||||
|
put in Table \ref{ptfmea}. The PLD diagram, can now be used to collect the
|
||||||
|
symptoms. In this case there is a common and easily detected symptom for all these single
|
||||||
|
resistor faults : Voltage out of range.
|
||||||
|
|
||||||
|
A spider can be drawn on the PLD diagram to this effect.
|
||||||
|
|
||||||
|
In practical use, by defining an acceptable measurement/temperature range,
|
||||||
|
and ensuring the
|
||||||
|
values are always within these bounds we can be confident that none of the
|
||||||
|
resistors in this circuit has failed.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 518 365,keepaspectratio=true]{./pt100/pt100_tc_sp.jpg}
|
||||||
|
% pt100_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
|
||||||
|
\caption{PT100 Component Failure Modes}
|
||||||
|
\label{fig:pt100_tc_sp}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The PT100 circuit can now be treated as a component in its own right, and has one failure mode,
|
||||||
|
{\textbf OUT\_OF\_RANGE}. It can now be represnted as a PLD see figure \ref{fig:pt100_singlef}.
|
||||||
|
|
||||||
|
\begin{figure}[h]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./pt100/pt100_singlef.jpg}
|
||||||
|
% pt100_singlef.jpg: 167x194 pixel, 72dpi, 5.89x6.84 cm, bb=0 0 167 194
|
||||||
|
\caption{PT100 Circuit Failure Modes : From Single Faults Analysis}
|
||||||
|
\label{fig:pt100_singlef}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
%Interestingly we can calculate the failure statistics for this circuit now.
|
||||||
|
%Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for pt100) ???
|
||||||
|
\clearpage
|
||||||
|
\subsection{Mean Time to Failure}
|
||||||
|
|
||||||
|
Using the MIL1991\cite{mil1991} specifications for resistor and thermistor
|
||||||
|
failure statistics we calculate the reliability of this circuit.
|
||||||
|
MIL1991 gives MTTF for a wide range of common components.
|
||||||
|
It does not specify how the components will fail (in this case OPEN or SHORT). {Some standards, notably EN298 only consider resistors failing in OPEN mode}.
|
||||||
|
FMD-97 Gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. This example
|
||||||
|
compromises and uses a 90:10 ratio, for resistor failure.
|
||||||
|
Thus for this example resistors are expevcted to fail OPEN in 90\% of cases and SHORTED
|
||||||
|
in the other 10\%.
|
||||||
|
|
||||||
|
A standard fixed film resistor, for use in a benign environment, non military spec at
|
||||||
|
temperatures up to 60\oc is given a probability of 13.8 failures per billion ($10^9$)
|
||||||
|
hours of operation. This figure is referred to as a FIT\footnote{FIT values are measured as the number of failures per billion hours of operation, (roughly 1.1 Million years). The smaller the FIT number the more reliable the fault~mode}, Failure in time.
|
||||||
|
|
||||||
|
A thermistor, bead type, non military spec is given a FIT of 3150.
|
||||||
|
|
||||||
|
Using the RIAC finding we can draw up the following table (table \ref{tab:stat_single}),
|
||||||
|
showing the FIT values for all faults considered.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[h+]
|
||||||
|
\caption{PT100 FMEA Single // Fault Statistics} % title of Table
|
||||||
|
\centering % used for centering table
|
||||||
|
\begin{tabular}{||l|c|c|l|l||}
|
||||||
|
\hline \hline
|
||||||
|
\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\
|
||||||
|
\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\
|
||||||
|
% R & wire & res + & res - & description
|
||||||
|
\hline
|
||||||
|
\hline
|
||||||
|
TC:1 $R_1$ SHORT & High Fault & - & 12.42 \\ \hline
|
||||||
|
TC:2 $R_1$ OPEN & Low Fault & Low Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
TC:3 $R_3$ SHORT & Low Fault & High Fault & 2835 \\ \hline
|
||||||
|
TC:4 $R_3$ OPEN & High Fault & Low Fault & 315 \\ \hline
|
||||||
|
\hline
|
||||||
|
TC:5 $R_2$ SHORT & - & Low Fault & 12.42 \\
|
||||||
|
TC:6 $R_2$ OPEN & High Fault & High Fault & 1.38 \\ \hline
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\label{tab:stat_single}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
The FIT for the circuit as a whole is the sum of MTTF values for all the
|
||||||
|
test cases. The PT100 circuit here has a FIT of 3177.6. This is a MTTF of
|
||||||
|
about 360 years per circuit.
|
||||||
|
|
||||||
|
A Probablistic tree can now be drawn, with a FIT value for the PT100
|
||||||
|
circuit and FIT values for all the component fault modes that it was calculated from.
|
||||||
|
We can see from this that that the most likely fault is the thermistor going OPEN.
|
||||||
|
This circuit is 8 times more likely to fail in this way than in any other.
|
||||||
|
Were we to need a more reliable temperature sensor this would probably
|
||||||
|
be the fault~mode we would scrutinise first.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}[h+]
|
||||||
|
\centering
|
||||||
|
\includegraphics[width=400pt,bb=0 0 856 327,keepaspectratio=true]{./pt100/stat_single.jpg}
|
||||||
|
% stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327
|
||||||
|
\caption{Probablistic Fault Tree : PT100 Single Faults}
|
||||||
|
\label{fig:stat_single}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
|
||||||
|
The PT100 analysis presents a simple result for single faults.
|
||||||
|
The next analysis phase looks at how the circuit will behave under double simultaneous failure
|
||||||
|
conditions.
|
||||||
|
|
||||||
|
\clearpage
|
||||||
|
\section{ PT100 Double Simultaneous \\ Fault Analysis}
|
||||||
|
|
||||||
|
% typeset in {\Huge \LaTeX} \today
|
||||||
|
|
||||||
30
standards/standards.tex
Normal file
30
standards/standards.tex
Normal file
@ -0,0 +1,30 @@
|
|||||||
|
%
|
||||||
|
% Make the revision and doc number macro's then they are defined in one place
|
||||||
|
|
||||||
|
\begin{abstract}
|
||||||
|
This chapter describes the legal frameworks and standards organisations
|
||||||
|
that exist in Europe and North America.
|
||||||
|
Some specific standards (that the author has experience with directly)
|
||||||
|
are reviewed.
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
|
||||||
|
\section{Introduction}
|
||||||
|
|
||||||
|
\section{European Safety Standards Legal Framework}
|
||||||
|
\section{North American Legal Framework}
|
||||||
|
|
||||||
|
Protection against being sued mainly ! UL - underwriters laboratories.... etc
|
||||||
|
|
||||||
|
\section{Cross Referencing}
|
||||||
|
|
||||||
|
Stabndards of ten reference other - i.e. EMC testing in EN298 refers toEN blah blah to level blah blah
|
||||||
|
|
||||||
|
|
||||||
|
\section{EN298}
|
||||||
|
|
||||||
|
\section{UL1998}
|
||||||
|
|
||||||
|
\section{EN230}
|
||||||
|
|
||||||
|
\section{EN61508}
|
||||||
30
standards/standards_paper.tex
Normal file
30
standards/standards_paper.tex
Normal file
@ -0,0 +1,30 @@
|
|||||||
|
%
|
||||||
|
% Make the revision and doc number macro's then they are defined in one place
|
||||||
|
|
||||||
|
\begin{abstract}
|
||||||
|
This chapter describes the legal frameworks and standards organisations
|
||||||
|
that exist in Europe and North America.
|
||||||
|
Some specific standards (that the author has experience with directly)
|
||||||
|
are reviewed.
|
||||||
|
\end{abstract}
|
||||||
|
|
||||||
|
|
||||||
|
\section{Introduction}
|
||||||
|
|
||||||
|
\section{European Safety Standards Legal Framework}
|
||||||
|
\section{North American Legal Framework}
|
||||||
|
|
||||||
|
Protection against being sued mainly ! UL - underwriters laboratories.... etc
|
||||||
|
|
||||||
|
\section{Cross Referencing}
|
||||||
|
|
||||||
|
Stabndards of ten reference other - i.e. EMC testing in EN298 refers toEN blah blah to level blah blah
|
||||||
|
|
||||||
|
|
||||||
|
\section{EN298}
|
||||||
|
|
||||||
|
\section{UL1998}
|
||||||
|
|
||||||
|
\section{EN230}
|
||||||
|
|
||||||
|
\section{EN61508}
|
||||||
@ -128,7 +128,7 @@ Software documentation for fmmd tool.
|
|||||||
\input{fzd/fzd}
|
\input{fzd/fzd}
|
||||||
|
|
||||||
\chapter{A detailed look at the safety systems required by industrial burner controller}
|
\chapter{A detailed look at the safety systems required by industrial burner controller}
|
||||||
%\input{indburner/indburner}
|
\input{burner/burner}
|
||||||
|
|
||||||
%\chapter{FMMD tool : Algorithms and Euler Diagram Parsing}
|
%\chapter{FMMD tool : Algorithms and Euler Diagram Parsing}
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user