robin/Robin_PHD
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

finish off detailed double analysis

Browse Source
This commit is contained in:
Robin 2010-06-13 18:26:02 +01:00
parent 05d6cdbb5d
commit 71b7f2ad21
2 changed files with 151 additions and 10 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

143
pt100/pt100.tex
View File

@ -24,7 +24,6 @@ from an FMEA persepective as a component itself, with a set of known failure mod
\end{abstract}
}
{
\section{Overview}
The PT100, or platinum wire \ohms{100} sensor is
a widely used industrial temperature sensor that is
@ -43,8 +42,6 @@ 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.
}
\begin{figure}[h]
@ -271,6 +268,7 @@ and are thus enclosed by one contour each.
\label{fig:pt100_tc}
\end{figure}
ating input Fault
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
@ -566,8 +564,143 @@ conditions.
\clearpage
\section{ PT100 Double Simultaneous \\ Fault Analysis}
In this section we examine the failure mode behaviour for all single
faults and double simultaneous faults.
This corresponds to the cardinality contstrained powerset of
the failure modes in the functional group.
All the single faults have already be proved in the last section.
For the next set of test cases, let us again hypothesise
the failure modes, and then examine each one in detail with
potential divider equation proofs.
Table \ref{tab:ptfmea2} lists all the combinations of double
faults and then hypothesises how the functional~group will react
under those conditions.
\begin{table}[ht]
\caption{PT100 FMEA Double Faults} % title of Table
\centering % used for centering table
\begin{tabular}{||l|l|c|c|l|l||}
\hline \hline
\textbf{TC} &\textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{General} \\
\textbf{number} &\textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{Symtom Description} \\
% R & wire & res + & res - & description
\hline
\hline
TC 7: & $R_1$ OPEN $R_2$ OPEN & Floating input Fault & Floating input Fault & Unknown value readings \\ \hline
TC 8: & $R_1$ OPEN $R_2$ SHORT & low & low & Both out of range \\ \hline
\hline
TC 9: & $R_1$ OPEN $R_3$ OPEN & high & low & Both out of Range \\ \hline
TC 10: & $R_1$ OPEN $R_3$ SHORT & low & low & Both out of range \\ \hline
\hline
TC 11: & $R_1$ SHORT $R_2$ OPEN & high & high & Both out of range \\ \hline
TC 12: & $R_1$ SHORT $R_2$ SHORT & high & low & Both out of range \\ \hline
\hline
TC 13: & $R_1$ SHORT $R_3$ OPEN & high & low & Both out of Range \\ \hline
TC 14: & $R_1$ SHORT $R_3$ SHORT & high & high & Both out of range \\ \hline
\hline
TC 15: & $R_2$ OPEN $R_3$ SHORT & high & Floating input Fault & sense+ out of range \\ \hline
TC 16: & $R_2$ OPEN $R_3$ SHORT & high & high & Both out of Range \\ \hline
TC 17: & $R_2$ SHORT $R_3$ OPEN & high & low & Both out of Range \\ \hline
TC 18: & $R_2$ SHORT $R_3$ SHORT & low & low & Both out of Range \\ \hline
\hline
\end{tabular}
\label{tab:ptfmea2}
\end{table}
\subsection{Verifying complete coverage for a \\ cardinality constrained powerset of 2}
It is important to check that we have covered all possible double fault combinations.
We can use the equation \ref{eqn:correctedccps2}, reproduced below to verify this.
DO THE DOUBLE
% typeset in {\Huge \LaTeX} \today
\begin{equation}
|{\mathcal{P}_{cc}SU}| = {\sum^{k}_{1..cc} \frac{|{SU}|!}{k!(|{SU}| - k)!}}
- \sum^{p}_{2..cc}{{\sum^{j}_{j \in J} \frac{|FM({C_j})|!}{p!(|FM({C_j})| - p)!}} }
\label{eqn:correctedccps2}
\end{equation}
$|FM(C_j)|$ is always 2 here, as all the components are resistors and have two failure modes.
%
% Factorial of zero is one ! You can only arrange an empty set one way !
Populating this equation with $|SU| = 6$ and $|FM(C_j)|$ is always 2 here as all the components are resistors and have two failure modes.
\begin{equation}
|{\mathcal{P}_{2}SU}| = {\sum^{k}_{1..2} \frac{6!}{k!(6 - k)!}}
- \sum^{p}_{2..2}{{\sum^{j}_{1..3} \frac{2!}{p!(2 - p)!}} }
\label{eqn:correctedccps2}
\end{equation}
$|{\mathcal{P}_{2}SU}|$ is the number of valid combinations of faults to check
under the conditions of unitary state failure modes for the components (a resistor cannot fail by being shorted and open at the same time).
Expanding the sumations
$$ NoOfTestCasesToCheck = \frac{6!}{1!(6-1)!} + \frac{6!}{2!(6-2)!} - \Big( \frac{2!}{2!(2 - 2)!} + \frac{2!}{2!(2 - 2)!} + \frac{2!}{2!(2 - 2)!} \Big) $$
$$ NoOfTestCasesToCheck = 6 + 15 - ( 1 + 1 + 1 ) = 18 $$
As the test case are all different and are of the correct cardinalities (6 single faults and (15-3) double)
we can be confident that we have looked at all combinations up to two, of the possible faults
in the pt100 circuit. The next task is to investigate
these test cases in more detail to prove the failure mode hypothese set out in table \ref{tab:ptfmea2}.
\subsection{Proof of Double Faults Hypothese }
\subsubsection{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN }
This double fault mode produces an interesting symptom.
Both sense lines are floating.
We cannot know what the {\adctw} readings on them will be.
In practise these would probably float to low values
but for the purpose of a safety critical analysis
all we can say is the values are `floating' and `unknown'.
This is an interesting case, because it is, at this stage an undetectable
fault that must be handled.
\subsubsection{ TC 8 : Voltages $R_1$ OPEN $R_2$ SHORT }
This cuts the supply from Vcc. Both sense lines will be at zero.
Thus both values will be out of range.
\subsubsection{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN }
Sense- will be floating.
Sense+ will be tied to Vcc and will thus be out of range.
\subsubsection{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT }
This shorts ground to the
both of the sense lines.
Both values thuis out of range.
\subsubsection{ TC 11 : Voltages $R_1$ SHORT $R_2$ OPEN }
This shorts both sense lines to Vcc.
Both values will be out of range.
\subsubsection{ TC 12 : Voltages $R_1$ SHORT $R_2$ SHORT }
This shorts the sense+ to Vcc and the sense- to ground.
Both values will be out of range.
typeset in {\Huge \LaTeX} \today

18
standards/standards.tex
View File

@ -4,29 +4,37 @@
\ifthenelse {\boolean{paper}}
{
\begin{abstract}
This chapter describes the legal frameworks and standards organisations
This paper 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}
}
{}
{
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.
}
\section{Introduction}
\subsection{Product Life Cycle}
i
difffernent areas
EN61508 REQ to SPEC to DESIGN
EN298
DESIGN TO PRODUCT
DESIGN TO
TESTING (EMC PRODUCT
FM
PRODUCT VERIFICATION MONITORING
NEW A PRODUCT LIFE CYCLE IMAGE WITH AN EULER DIAGRMA FOR THE DIFFERENT STANDARDS
Different agencies - approval is testing of new product
and verification to standard - manufacturing overwatch / supervision
word on tip of tounge -