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PT100 papaer now uses bib iles in thesis directory

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component_failure_modes_definition/component_failure_modes_definition.tex
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@ -188,7 +188,7 @@ We can represent this using a UML diagram in figure \ref{fig:cfg}.
Using the symbol $\bowtie$ to indicate the analysis process that takes a Using the symbol $\bowtie$ to indicate the analysis process that takes a
functional group and converts it into a new component. functional group and converts it into a new component.
$$ \bowtie ( FG ) \mapsto DerivedComponent $$ \[ \bowtie ( FG ) \mapsto DerivedComponent \]
\begin{figure}[h] \begin{figure}[h]

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introduction/introduction.tex
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@ -41,7 +41,7 @@ of this process however, is `static testing'. This involves looking at the desig
from the perspective of environmental stresses, natural input fault conditions\footnote{For instance in a burner controller, the gas supply pressure reducing}, from the perspective of environmental stresses, natural input fault conditions\footnote{For instance in a burner controller, the gas supply pressure reducing},
components failing, and the effects on safety this could have. components failing, and the effects on safety this could have.
Some static testing involves checking that the germane `EN' standards have Some static testing involves checking that the germane `EN' standards have
been complied with\footnore{for instance protection levels of enclosure, or down rating of electrical components}. been complied with\footnote{for instance protection levels of enclosure, or down rating of electrical components}.
Failure Mode Effects Analysis (FMEA) was also applied. This involved Failure Mode Effects Analysis (FMEA) was also applied. This involved
looking in detail at selected critical sections of the product and proposing looking in detail at selected critical sections of the product and proposing
component failure scenarios. component failure scenarios.

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millivoltamp/Makefile Normal file
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@ -0,0 +1,22 @@
#
# Make the propositional logic diagram a paper
#
paper: paper.tex millivoltamp_paper.tex
#latex paper.tex
#dvipdf paper pdflatex cannot use eps ffs
pdflatex paper.tex
mv paper.pdf millivoltamp_paper.pdf
okular millivoltamp_paper.pdf
# Remove the need for referncing graphics in subdirectories
#
millivoltamp_paper.tex: millivoltamp.tex
cat millivoltamp.tex | sed 's/millivoltamp\///' > millivoltamp_paper.tex
bib:
bibtex paper

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millivoltamp/millivoltamp.tex Normal file
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@ -0,0 +1,833 @@
%
% Make the revision and doc number macro's then they are defined in one place
\ifthenelse {\boolean{paper}}
{
\begin{abstract}
\paragraph{NOT WRITTEN YET USES PT100 DOC AS FRAME WORK: DO NOT READ}
This paper analyses the example ciruit with an added safety component, given in the introduction chapter.
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 Milli Volt Amplifier circuit, may be viewed
from an FMEA perspective as a component itself, with a set of known failure modes.
\end{abstract}
}
{
\section{Overview}
\paragraph{NOT WRITTEN YET USES PT100 DOC AS FRAME WORK: DO NOT READ}
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 Milli Volt Amplifier circuit, may be viewed
from an FMEA perspective as a component itself, with a set of known failure modes.
}
%\begin{figure}[h]
% \centering
% \includegraphics[width=400pt,bb=0 0 714 180,keepaspectratio=true]{./milli volt amplifier/milli volt amplifier.jpg}
% % milli volt amplifier.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
% \caption{Milli Volt Amplifier four wire circuit}
% \label{fig:milli volt amplifier}
%\end{figure}
%
\section{General Description of Milli Volt Amplifier four wire circuit}
The Milli Volt Amplifier four wire circuit uses two wires to supply small electrical current,
and returns two sense volages by the other two.
By measuring voltages
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]{./milli volt amplifier/vrange.jpg}
% % milli volt amplifier.jpg: 714x180 pixel, 72dpi, 25.19x6.35 cm, bb=0 0 714 180
% \caption{Milli Volt Amplifier expected voltage ranges}
% \label{fig:milli volt amplifiervrange}
%\end{figure}
%
The voltage ranges we expect from this three stage potential divider\footnote{
two stages are required for validation, a third stage is used to measure the current flowing
through the circuit to obtain accurate temperature readings}
are shown in figure \ref{fig:milli volt amplifiervrange}. 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 referred 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 preferred
because of resistance in the cables. Resistance from the supply
causes a slight voltage
drop in the supply to the Milli Volt Amplifier. 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\footnote{The increased accuracy is because the voltage measured, is the voltage across
the thermistor and not the voltage across the thermistor and current supply wire resistance.}.
\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 Milli Volt Amplifier, 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 Milli Volt Amplifier tables\cite{eurothermtables}.
The standard voltage divider equations (see figure \ref{fig:vd} and
equation \ref{eqn:vd}) can be used to calculate
expected voltages for failure mode and temperature reading purposes.
%\begin{figure}[h]
% \centering
% \includegraphics[width=100pt,bb=0 0 183 170,keepaspectratio=true]{./milli volt amplifier/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}
\section{Safety case for 4 wire circuit}
This sub-section looks at the behaviour of the Milli Volt Amplifier 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 its 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 Milli Volt Amplifier 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 Milli Volt Amplifier 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:milli volt amplifiervrange}. 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{Milli Volt Amplifier 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{milli volt amplifierrange}
and \ref{milli volt amplifiertemp}.
\subsection{Range and Amplifier Calculations}
\label{milli volt amplifiertemp}
Milli Volt Amplifier 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 Milli Volt Amplifier
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
Milli Volt Amplifier FMEA analysis in section \ref{fmea}.
As the Milli Volt Amplifier forms a potential divider with the \ohms{2k2} load resistors,
the upper and lower readings can be calculated thus:
$$ highreading = 5V.\frac{2k2+milli volt amplifier}{2k2+2k2+milli volt amplifier} $$
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+milli volt amplifier} $$
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:
$$ highreading = 2^{12}.\frac{2k2+milli volt amplifier}{2k2+2k2+milli volt amplifier} $$
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+milli volt amplifier} $$
\begin{table}[ht]
\caption{Milli Volt Amplifier Maximum and Minimum Values} % title of Table
\centering % used for centering table
\begin{tabular}{||c|c|c|l|l||}
\hline \hline
\textbf{Temperature} & \textbf{Milli Volt Amplifier 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 Milli Volt Amplifier 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]{./milli volt amplifier/milli volt amplifier_tc.jpg}
% % milli volt amplifier_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
% \caption{Milli Volt Amplifier Component Failure Modes}
% \label{fig:milli volt amplifier_tc}
%\end{figure}
%
%ating input Fault
This circuit supplies two results, the {\em sense+} and {\em 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]{./milli volt amplifier/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{ TC 1 : Voltages $R_1$ SHORT }
With milli volt amplifier 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 milli volt amplifier 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 readings are outside the
proscribed range in table \ref{ptbounds}.
\subsubsection{ TC 2 : 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 milli volt amplifier 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 milli volt amplifier at the high end of the temperature range 300\oc.
$$ highreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
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]{./milli volt amplifier/milli volt amplifier_tc_sp.jpg}
% % milli volt amplifier_tc.jpg: 518x365 pixel, 72dpi, 18.27x12.88 cm, bb=0 0 518 365
% \caption{Milli Volt Amplifier Component Failure Modes}
% \label{fig:milli volt amplifier_tc_sp}
%\end{figure}
%
\subsection{Derived Component : The Milli Volt Amplifier Circuit}
The Milli Volt Amplifier 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:milli volt amplifier_singlef}.
%\begin{figure}[h]
% \centering
% \includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./milli volt amplifier/milli volt amplifier_singlef.jpg}
% % milli volt amplifier_singlef.jpg: 167x194 pixel, 72dpi, 5.89x6.84 cm, bb=0 0 167 194
% \caption{Milli Volt Amplifier Circuit Failure Modes : From Single Faults Analysis}
% \label{fig:milli volt amplifier_singlef}
%\end{figure}
%
%From the single faults (cardinality constrained powerset of 1) analysis, we can now create
%a new derived component, the {\emmilli volt amplifiercircuit}. This has only \{ OUT\_OF\_RANGE \}
%as its single failure mode.
%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 milli volt amplifier) ???
\clearpage
\subsection{Mean Time to Failure}
Now that we have a model for the failure mode behaviour of the milli volt amplifier circuit
we can look at the statistics associated with each of the failure modes.
The DOD electronic reliability of components
document MIL-HDBK-217F\cite{mil1992} gives formulae for calculating
the
%$\frac{failures}{{10}^6}$
${failures}/{{10}^6}$ % looks better
in hours for a wide range of generic components
\footnote{These figures are based on components from the 1980's and MIL-HDBK-217F
can give conservative reliability figures when applied to
modern components}.
Using the MIL-HDBK-217F\cite{mil1992} specifications for resistor and thermistor
failure statistics we calculate the reliability of this circuit.
\subsubsection{Resistor FIT Calculations}
The formula for given in MIL-HDBK-217F\cite{mil1992}[9.2] for a generic fixed film non-power resistor
is reproduced in equation \ref{resistorfit}. The meanings
and values assigned to its co-efficients are described in table \ref{tab:resistor}.
\begin{equation}
% fixed comp resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E
resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E
\label{resistorfit}
\end{equation}
\begin{table}[ht]
\caption{Fixed film resistor Failure in time assessment} % title of Table
\centering % used for centering table
\begin{tabular}{||c|c|l||}
\hline \hline
\em{Parameter} & \em{Value} & \em{Comments} \\
& & \\ \hline \hline
${\lambda}_{b}$ & 0.00092 & stress/temp base failure rate $60^o$ C \\ \hline
%${\pi}_T$ & 4.2 & max temp of $60^o$ C\\ \hline
${\pi}_R$ & 1.0 & Resistance range $< 0.1M\Omega$\\ \hline
${\pi}_Q$ & 15.0 & Non-Mil spec component\\ \hline
${\pi}_E$ & 1.0 & benign ground environment\\ \hline
\hline \hline
\end{tabular}
\label{tab:resistor}
\end{table}
Applying equation \ref{resistorfit} with the parameters from table \ref{tab:resistor}
give the following failures in ${10}^6$ hours:
\begin{equation}
0.00092 \times 1.0 \times 15.0 \times 1.0 = 0.0138 \;{failures}/{{10}^{6} Hours}
\label{eqn:resistor}
\end{equation}
While MIL-HDBK-217F 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 expected 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 (see equation \ref{eqn:resistor}).
This figure is referred to as a FIT\footnote{FIT values are measured as the number of
failures per Billion (${10}^9$) hours of operation, (roughly 114,000 years). The smaller the
FIT number the more reliable the fault~mode} Failure in time.
The formula given for a thermistor in MIL-HDBK-217F\cite{mil1992}[9.8] is reproduced in
equation \ref{thermistorfit}. The variable meanings and values are described in table \ref{tab:thermistor}.
\begin{equation}
% fixed comp resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E
resistor{\lambda}_p = {\lambda}_{b}{\pi}_Q{\pi}_E
\label{thermistorfit}
\end{equation}
\begin{table}[ht]
\caption{Bead type Thermistor Failure in time assessment} % title of Table
\centering % used for centering table
\begin{tabular}{||c|c|l||}
\hline \hline
\em{Parameter} & \em{Value} & \em{Comments} \\
& & \\ \hline \hline
${\lambda}_{b}$ & 0.021 & stress/temp base failure rate bead thermistor \\ \hline
%${\pi}_T$ & 4.2 & max temp of $60^o$ C\\ \hline
%${\pi}_R$ & 1.0 & Resistance range $< 0.1M\Omega$\\ \hline
${\pi}_Q$ & 15.0 & Non-Mil spec component\\ \hline
${\pi}_E$ & 1.0 & benign ground environment\\ \hline
\hline \hline
\end{tabular}
\label{tab:thermistor}
\end{table}
\begin{equation}
0.021 \times 1.0 \times 15.0 \times 1.0 = 0.315 \; {failures}/{{10}^{6} Hours}
\label{eqn:thermistor}
\end{equation}
Thus thermistor, bead type, non military spec is given a FIT of 315.0
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{Milli Volt Amplifier 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 & - & 1.38 \\ \hline
TC:2 $R_1$ OPEN & Low Fault & Low Fault & 12.42\\ \hline
\hline
TC:3 $R_3$ SHORT & Low Fault & High Fault & 31.5 \\ \hline
TC:4 $R_3$ OPEN & High Fault & Low Fault & 283.5 \\ \hline
\hline
TC:5 $R_2$ SHORT & - & Low Fault & 1.38 \\
TC:6 $R_2$ OPEN & High Fault & High Fault & 12.42 \\ \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 Milli Volt Amplifier circuit here has a FIT of 342.6. This is a MTTF of
about 360 years per circuit.
A Probablistic tree can now be drawn, with a FIT value for the Milli Volt Amplifier
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 around 10 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]{./milli volt amplifier/stat_single.jpg}
% % stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327
% \caption{Probablistic Fault Tree : Milli Volt Amplifier Single Faults}
% \label{fig:stat_single}
%\end{figure}
The Milli Volt Amplifier 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{ Milli Volt Amplifier 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 constrained powerset of
the failure modes in the functional group.
All the single faults have already been 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{Milli Volt Amplifier 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}
\ifthenelse {\boolean{paper}}
{
from the definitions paper
\ref{pap:compdef}
,
reproduced below to verify this.
\indent{
where:
\begin{itemize}
\item The set $SU$ represents the components in the functional~group, where all components are guaranteed to have unitary state failure modes.
\item The indexed set $C_j$ represents all components in set $SU$.
\item The function $FM$ takes a component as an argument and returns its set of failure modes.
\item $cc$ is the cardinality constraint, here 2 as we are interested in double and single faults.
\end{itemize}
}
\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}
}
{
\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}
}
$|FM(C_j)|$ will always be 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 $|FM(C_j)|$ = 2.
%is always 2 for this circuit, 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 `double combinations', of the possible faults
in the milli volt amplifier circuit. The next task is to investigate
these test cases in more detail to prove the failure mode hypothesis set out in table \ref{tab:ptfmea2}.
\subsection{Proof of Double Faults Hypothesis }
\subsubsection{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN }
\label{milli volt amplifier:bothfloating}
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.
\subsubsection{ TC 13 : Voltages $R_1$ SHORT $R_3$ OPEN }
This shorts the sense+ to Vcc and the sense- to ground.
Both values will be out of range.
\subsubsection{ TC 14 : Voltages $R_1$ SHORT $R_3$ SHORT }
This shorts the sense+ and sense- to Vcc.
Both values will be out of range.
\subsubsection{ TC 15 : Voltages $R_2$ OPEN $R_3$ OPEN }
This shorts the sense+ to Vcc and causes sense- to float.
The sense+ value will be out of range.
\subsubsection{ TC 16 : Voltages $R_2$ OPEN $R_3$ SHORT }
This shorts the sense+ and sense- to Vcc.
Both values will be out of range.
\subsubsection{ TC 17 : Voltages $R_2$ SHORT $R_3$ OPEN }
This shorts the sense- to Ground.
The sense- value will be out of range.
\subsubsection{ TC 18 : Voltages $R_2$ SHORT $R_3$ SHORT }
This shorts the sense+ and sense- to Vcc.
Both values will be out of range.
\clearpage
\subsection{Double Faults Represented on a PLD Diagram}
We can show the test cases on a diagram with the double faults residing on regions
corresponding to overlapping contours see figure \ref{fig:plddouble}.
Thus $TC\_18$ will be enclosed by the $R2\_SHORT$ contour and the $R3\_SHORT$ contour.
%\begin{figure}[h]
% \centering
% \includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{milli volt amplifier/plddouble.jpg}
% % plddouble.jpg: 730x641 pixel, 72dpi, 25.75x22.61 cm, bb=0 0 730 641
% \caption{Milli Volt Amplifier Double Simultaneous Faults}
% \label{fig:plddouble}
%\end{figure}
The usefulnes of equation \ref{eqn:correctedccps2} is apparent. From the diagram it is easy to verify
the number of failure modes considered for each test case, but complete coverage for
a given cardinality constraint is not visually obvious.
\subsubsection{Symptom Extraction}
We can now examine the results of the test case analysis and apply symptom abstraction.
In all the test case results we have at least one an out of range value, except for
$TC\_7$
which has two unknown values/floating readings. We can collect all the faults, except $TC\_7$,
into the symptom $OUT\_OF\_RANGE$.
As a symptom $TC\_7$ could be described as $FLOATING$. We can thus draw a PLD diagram representing the
failure modes of this functional~group, the milli volt amplifier circuit from the perspective of double simultaneous failures,
in figure \ref{fig:dubsim}.
%\begin{figure}[h]
% \centering
% \includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{milli volt amplifier/plddoublesymptom.jpg}
% % plddouble.jpg: 730x641 pixel, 72dpi, 25.75x22.61 cm, bb=0 0 730 641
% \caption{Milli Volt Amplifier Double Simultaneous Faults}
% \label{fig:plddoublesymptom}
%\end{figure}
\clearpage
\subsection{Derived Component : The Milli Volt Amplifier Circuit}
The Milli Volt Amplifier circuit again, can now be treated as a component in its own right, and has two failure modes,
{\textbf{OUT\_OF\_RANGE}} and {\textbf{FLOATING}}.
It can now be represented as a PLD see figure \ref{fig:milli volt amplifier_doublef}.
%\begin{figure}[h]
% \centering
% \includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./milli volt amplifier/milli volt amplifier_doublef.jpg}
% % milli volt amplifier_singlef.jpg: 167x194 pixel, 72dpi, 5.89x6.84 cm, bb=0 0 167 194
% \caption{Milli Volt Amplifier Circuit Failure Modes : From Double Faults Analysis}
% \label{fig:milli volt amplifier_doublef}
%\end{figure}
\subsection{Statistics}
%%
%% Need to talk abou the `detection time'
%% or `Safety Relevant Validation Time' ref can book
%% EN61508 gives detection calculations to reduce
%% statistical impacts of failures.
%%
If we consider the failure modes to be statistically independent we can calculate
the FIT values for all the failures. The failure mode of concern, the undetectable {\textbf{FLOATING}} condition
requires that resistors $R_1$ and $R_2$ fail. We can multiply the MTTF
together and find an MTTF for both failing. The FIT value of 12.42 corresponds to
$12.42 \times {10}^{-9}$ failures per hour. Squaring this gives $ 154.3 \times {10}^{-18} $.
This is an astronomically small MTTF, and so small that it would
probably fall below a threshold to sensibly consider.
However, it is very interesting from a failure analysis perspective,
because here we have found a fault that we cannot detect at this
level. This means that should we wish to cope with
this fault, we need to devise a way of detecting this
condition in higher levels of the system.
\vspace{20pt}
%typeset in {\Huge \LaTeX} \today

34
millivoltamp/paper.tex Normal file
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@ -0,0 +1,34 @@
\documentclass[a4paper,10pt]{article}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{tikz}
\usepackage{amsfonts,amsmath,amsthm}
\usepackage{ifthen}
\newboolean{paper}
\setboolean{paper}{true} % boolvar=true or false
\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{Milli-Volt Amplifier FMMD analysis}
\maketitle
\input{millivoltamp_paper}
\bibliographystyle{plain}
\bibliography{../vmgbibliography,../mybib}
\today
\end{document}

274
mybib.bib
View File

@ -182,3 +182,277 @@
year = "2000" year = "2000"
} }
@Manual{tlp181,
title = {TLP 181 Datasheet},
key = {TOSHIBA Photocoupler GaAs Ired and Photo−Transistor},
author = {Toshiba inc.},
OPTorganization = {},
address = {http://www.toshiba.com/taec/components2/Datasheet\_Sync//206/4191.pdf},
OPTedition = {},
OPTmonth = {},
year = {2009},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {},
}
@Manual{pic18f2523,
title = {PIC18F2523 Datasheet},
OPTkey = {},
author = {Microchip inc},
OPTorganization = {},
address = {http://ww1.microchip.com/downloads/en/DeviceDoc/39755c.pdf},
OPTedition = {},
OPTmonth = {},
year = {2009},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {},
}
@Book{wt,
title = {Water Treatment Essentials for Boiler Plant Operation},
publisher = {Mc Graw Hill ISBN 0-07-048291-5},
year = {1997},
author = {Robert G Nunn},
ALTALTeditor = {},
OPTkey = {},
OPTvolume = {},
OPTnumber = {},
OPTseries = {},
OPTaddress = {},
OPTedition = {},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {ISBN 0-07-048291-5},
OPTlocalfile = {},
OPTabstracts = {},
}
@TechReport{spiraxsarco,
author = {Spirax Sarco},
title = {http://www.spiraxsarco.com/resources/steam-engineering-tutorials.asp},
institution = {Spirax Sarco},
year = {2010},
OPTkey = {},
OPTtype = {},
OPTnumber = {},
OPTaddress = {},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {},
}
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title = {The Art of Electronics},
publisher = {Cambridge},
year = {1989},
author = {Paul Horowitz, Winfield Hill},
OPTkey = {},
OPTvolume = {},
OPTnumber = {},
OPTseries = {},
OPTaddress = {},
OPTedition = {2nd},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {ISBN 0-521-37095-7},
OPTlocalfile = {},
OPTabstracts = {},
}
@TechReport{eurothermtables,
author = {Alan Brown},
title = {Thermocouple Emf TABLES and PLATINUM 100 RESISTANCE THERMOMETER TABLES},
institution = {Eurotherm, UK},
year = {1973},
OPTkey = {},
OPTtype = {},
OPTnumber = {},
OPTaddress = {},
OPTmonth = {June},
OPTnote = {Bulletin TT-1},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {},
}
@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 = {},
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},
publisher = {O'Reilly ISBN ISBN 0-596-00222-X},
year = {2003},
OPTkey = {ISBN 0-596-00222-X},
OPTvolume = {},
OPTnumber = {},
OPTseries = {linux},
OPTaddress = {},
OPTedition = {3rd},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {www.oreilly.com},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {}
};
@Book{can,
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},
OPTkey = { },
OPTvolume = {},
OPTnumber = {},
OPTseries = {Embedded Systems},
OPTaddress = {},
OPTedition = {1st},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {www.rtcbooks.com},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {}
};
@Article{article,
author = {dd},
title = {dd},
journal = {dd},
year = {2008},
OPTkey = {},
OPTvolume = {},
OPTnumber = {},
OPTpages = {1,2},
OPTmonth = {JAN},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {}
};
@Book{sqlite,
author = {Micheal Owens},
title = {The definitive guide to SQLite},
publisher = {Apres ISBN 1-59059-673-0},
year = {2006},
OPTkey = {},
OPTvolume = {},
OPTnumber = {},
OPTseries = {Databases/SQLite},
OPTaddress = {},
OPTedition = {},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {}
};

4
pt100/Makefile
View File

@ -16,3 +16,7 @@ paper: paper.tex pt100_paper.tex
# #
pt100_paper.tex: pt100.tex pt100_paper.tex: pt100.tex
cat pt100.tex | sed 's/pt100\///' > pt100_paper.tex cat pt100.tex | sed 's/pt100\///' > pt100_paper.tex
bib:
bibtex paper

68
pt100/mybib.bib
View File

@ -1,27 +1,3 @@
%
%
% $Id: mybib.bib,v 1.5 2008/12/18 17:05:23 robin Exp $
%
%
@TechReport{db,
author = {R Clark, D Legge},
title = {ETC6000 Daughterboard Design notes},
institution = {ETC HR221850},
year = {2004},
key = {},
OPTtype = {},
OPTnumber = {},
OPTaddress = {},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
issn = {HR221850},
OPTlocalfile = {},
OPTabstract = {},
}
@TechReport{mil1991, @TechReport{mil1991,
author = {U.S. Department of Defence}, author = {U.S. Department of Defence},
@ -104,24 +80,6 @@ OPTissn = {},
OPTabstracts = {}, OPTabstracts = {},
} }
@TechReport{pcbAI222562,
author = {C Talmay},
title = {Circuit Schematic TDS Daughterboard AI222562},
institution = {ETC},
year = {2010},
OPTkey = {},
OPTtype = {},
OPTnumber = {AI222562},
OPTaddress = {},
OPTmonth = {},
OPTnote = {},
OPTannote = {},
OPTurl = {},
OPTdoi = {},
OPTissn = {},
OPTlocalfile = {},
OPTabstract = {},
}
@TechReport{spiraxsarco, @TechReport{spiraxsarco,
author = {Spirax Sarco}, author = {Spirax Sarco},
@ -147,7 +105,6 @@ OPTissn = {},
publisher = {Cambridge}, publisher = {Cambridge},
year = {1989}, year = {1989},
author = {Paul Horowitz, Winfield Hill}, author = {Paul Horowitz, Winfield Hill},
%author = {},
OPTkey = {}, OPTkey = {},
OPTvolume = {}, OPTvolume = {},
OPTnumber = {}, OPTnumber = {},
@ -218,31 +175,6 @@ http://www.xfree86.org/
} }
@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, @misc{ fltk,

2
pt100/paper.tex
View File

@ -28,7 +28,7 @@
\input{pt100_paper} \input{pt100_paper}
\bibliographystyle{plain} \bibliographystyle{plain}
\bibliography{vmgbibliography,mybib} \bibliography{../vmgbibliography,../mybib}
\today \today
\end{document} \end{document}

8
pt100/pt100.tex
View File

@ -408,7 +408,7 @@ Now that we have a model for the failure mode behaviour of the pt100 circuit
we can look at the statistics associated with each of the failure modes. we can look at the statistics associated with each of the failure modes.
The DOD electronic reliability of components The DOD electronic reliability of components
document MIL-HDBK-217F\cite{mil1992} gives formulae for calculating document MIL-HDBK-217F\cite{mil1991} gives formulae for calculating
the the
%$\frac{failures}{{10}^6}$ %$\frac{failures}{{10}^6}$
${failures}/{{10}^6}$ % looks better ${failures}/{{10}^6}$ % looks better
@ -417,13 +417,13 @@ in hours for a wide range of generic components
can give conservative reliability figures when applied to can give conservative reliability figures when applied to
modern components}. modern components}.
Using the MIL-HDBK-217F\cite{mil1992} specifications for resistor and thermistor Using the MIL-HDBK-217F\cite{mil1991} specifications for resistor and thermistor
failure statistics we calculate the reliability of this circuit. failure statistics we calculate the reliability of this circuit.
\subsubsection{Resistor FIT Calculations} \subsubsection{Resistor FIT Calculations}
The formula for given in MIL-HDBK-217F\cite{mil1992}[9.2] for a generic fixed film non-power resistor The formula for given in MIL-HDBK-217F\cite{mil1991}[9.2] for a generic fixed film non-power resistor
is reproduced in equation \ref{resistorfit}. The meanings is reproduced in equation \ref{resistorfit}. The meanings
and values assigned to its co-efficients are described in table \ref{tab:resistor}. and values assigned to its co-efficients are described in table \ref{tab:resistor}.
@ -472,7 +472,7 @@ This figure is referred to as a FIT\footnote{FIT values are measured as the numb
failures per Billion (${10}^9$) hours of operation, (roughly 114,000 years). The smaller the failures per Billion (${10}^9$) hours of operation, (roughly 114,000 years). The smaller the
FIT number the more reliable the fault~mode} Failure in time. FIT number the more reliable the fault~mode} Failure in time.
The formula given for a thermistor in MIL-HDBK-217F\cite{mil1992}[9.8] is reproduced in The formula given for a thermistor in MIL-HDBK-217F\cite{mil1991}[9.8] is reproduced in
equation \ref{thermistorfit}. The variable meanings and values are described in table \ref{tab:thermistor}. equation \ref{thermistorfit}. The variable meanings and values are described in table \ref{tab:thermistor}.
\begin{equation} \begin{equation}

6
thesis.tex
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@ -10,8 +10,7 @@
\newboolean{paper} \newboolean{paper}
\setboolean{paper}{false} % boolvar=true or false \setboolean{paper}{false} % boolvar=true or false
\input{style} \input{style}
\usepackage{hyperref}
%\usepackage{hyperref}
\begin{document} \begin{document}
\pagestyle{fancy} \pagestyle{fancy}
@ -137,6 +136,9 @@ Software documentation for fmmd tool.
\chapter{Algorithms and Mathematical Relationships Discovered} \chapter{Algorithms and Mathematical Relationships Discovered}
\input{fzd/fzd} \input{fzd/fzd}
\chapter{Milli Volt Amp with Safety Resistor}
\input{millivoltamp/millivoltamp}
\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{burner/burner} \input{burner/burner}