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Massive tuesday taken as holiday edit.

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6
mybib.bib
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@ -1006,6 +1006,12 @@ ISSN={1530-2059},}
YEAR = "1988" YEAR = "1988"
} }
@BOOK{rdh,
AUTHOR = "F~Langford-Smith",
TITLE = "Radio designers Handbook: Fourth Edition",
PUBLISHER = "ILIFFE",
YEAR = "1953"
}
@BOOK{wdycwopt, @BOOK{wdycwopt,
AUTHOR = " Richard~P~Feynman", AUTHOR = " Richard~P~Feynman",

12
submission_thesis/CH1_introduction/copy.tex
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@ -44,7 +44,7 @@ are based on statistical thresholds for the frequency of dangerous failures.
We could state, for instance, that we can tolerate an `acceptable' maximum number of We could state, for instance, that we can tolerate an `acceptable' maximum number of
dangerous failures per billion hours of operation. dangerous failures per billion hours of operation.
% %
We can then broadly categorise ratings of failure rates into Safety Integrity Levels (SIL)~\cite{scsh}. We can then broadly categorise orders of failure rates into Safety Integrity Levels (SIL)~\cite{scsh}.
% %
So for a maximum of 10 potentially dangerous failures per billion hours of operation we assign a SIL level of 4, So for a maximum of 10 potentially dangerous failures per billion hours of operation we assign a SIL level of 4,
for 100 a SIL level of 3, and so on in powers of ten. for 100 a SIL level of 3, and so on in powers of ten.
@ -61,8 +61,8 @@ such as a nuclear power-station or air-liner,
with far greater consequences on dangerous failure with far greater consequences on dangerous failure
may require a SIL rating of 4. may require a SIL rating of 4.
% %
What we are saying is that while we may tolerate a low incidence of failure on a band-saw, That is while a low incidence of failure may be tolerable on a band-saw,
we will only tolerate extremely low incidences of failure in nuclear plant. extremely low incidences of failure would be tolerable in a nuclear plant.
SIL ratings provide another objective yardstick for the measurement of system safety. SIL ratings provide another objective yardstick for the measurement of system safety.
%governing failure conditions and determining risk levels associated with systems. %governing failure conditions and determining risk levels associated with systems.
@ -90,7 +90,7 @@ and using contract programmed software, allows the modelling of integrated
software/electrical systems. software/electrical systems.
% %
This is followed by two chapters showing examples of the new modular FMEA analysis technique (Failure Mode Modular De-Composition FMMD) This is followed by two chapters showing examples of the new modular FMEA analysis technique (Failure Mode Modular De-Composition FMMD)
firstly looking at common electronic circuits and then at electronic/software hybrid systems. firstly looking at a variety of common electronic circuits and then at electronic/software hybrid systems.
} }
\section{Motivation} \section{Motivation}
@ -134,8 +134,8 @@ Any of the components that could, in failing, create a dangerous state were alre
documented and approved using failure mode effects analysis (FMEA). documented and approved using failure mode effects analysis (FMEA).
% %
This new requirement This new requirement
effectively meant that all single and double component failures were effectively meant that single and double component failures were
now required to be analysed. now required to be analysed~\cite{en298}[9.1.5].
% %
This, from a state explosion problem alone, This, from a state explosion problem alone,
meant that it was going to be virtually impossible to perform. meant that it was going to be virtually impossible to perform.

321
submission_thesis/CH5_Examples/copy.tex
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@ -1,25 +1,6 @@
%\clearpage %\pagenumbering{arabic}
% %
% %% NEED TWO MORE EXAMPLES --- 02JUN2012
%
% * ENVIRONMENTAL CASE (perhaps temp on an opto-coupler
%
% * OPERATIONAL STATE (perhaps a self test on an ADC where it is set to output and driven high and low and read)
% to do: 23SEP2012
%
% 90_degrees is an incorrect failure mode in bubba and must be purged
%
% summing junction in sigma delta is not a valid fg, prob have to include
% the op-amp....
%
% very annoying to have to pull out the comparison complexity.
% makes the comparisons between approaches have less meaning.
% have to discuss this.
\label{sec:chap5} \label{sec:chap5}
%
This chapter demonstrates FMMD applied to This chapter demonstrates FMMD applied to
a variety of typical electronic circuits including analogue and digital a variety of typical electronic circuits including analogue and digital
%and electronics/software %and electronics/software
@ -68,21 +49,19 @@ by applying FMMD to a sigma delta ADC.
%analogue and digital signals. %analogue and digital signals.
\item Section~\ref{sec:Pt100} demonstrates FMMD being applied to a commonly used Pt100 \item Section~\ref{sec:Pt100} demonstrates FMMD being applied to a commonly used Pt100
safety critical temperature sensor circuit, this is analysed for single and then double failure modes. safety critical temperature sensor circuit, this is analysed for single and then double failure modes.
\end{itemize} \end{itemize}
%
%~\ref{sec:chap4} %~\ref{sec:chap4}
%can be re-used. %, but with provisos. %can be re-used. %, but with provisos.
% %
%The first %The first
%(see section~\ref{sec:diffamp}) %(see section~\ref{sec:diffamp})
% %
% %
% %
%
%
%
% %
% Moving Pt100 to metrics % Moving Pt100 to metrics
% %
@ -91,7 +70,7 @@ safety critical temperature sensor circuit, this is analysed for single and then
%and the analysis of double simultaneous failure modes. %and the analysis of double simultaneous failure modes.
% %
% Now in CHAPTER 6: Finally section~\ref{sec:elecsw} demonstrates FMMD analysis of a combined electronic and software system. % Now in CHAPTER 6: Finally section~\ref{sec:elecsw} demonstrates FMMD analysis of a combined electronic and software system.
%
% \section{Basic Concepts Of FMMD} % \section{Basic Concepts Of FMMD}
% %
% The %idea % The %idea
@ -149,16 +128,14 @@ safety critical temperature sensor circuit, this is analysed for single and then
% % \item {\dc} - a new component derived from an analysed {\fg} % % \item {\dc} - a new component derived from an analysed {\fg}
% % \end{itemize} % % \end{itemize}
% %
%
%%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX %%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
% %
% This section might fit in with the literature review.... Chris thinks its not relevant here % This section might fit in with the literature review.... Chris thinks its not relevant here
% and I agree 20OCT2012 % and I agree 20OCT2012
% %
%%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX %%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
%
% % \section{ FMMD overview} % % \section{ FMMD overview}
% % % %
% % In the next sections we apply FMMD to electronic circuits, analogue/digital and electronic/software hybrids. % % In the next sections we apply FMMD to electronic circuits, analogue/digital and electronic/software hybrids.
@ -244,12 +221,12 @@ safety critical temperature sensor circuit, this is analysed for single and then
% % % %
% % % %
% % % %
%
\clearpage \clearpage
\section{Example Analysis: Inverting OPAMP} \section{Example Analysis: Inverting OPAMP}
%
\label{sec:invamp} \label{sec:invamp}
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=200pt]{CH5_Examples/invamp.png} \includegraphics[width=200pt]{CH5_Examples/invamp.png}
@ -257,16 +234,16 @@ safety critical temperature sensor circuit, this is analysed for single and then
\caption{Inverting Amplifier Configuration} \caption{Inverting Amplifier Configuration}
\label{fig:invamp} \label{fig:invamp}
\end{figure} \end{figure}
%
%This configuration is interesting from methodology pers. %This configuration is interesting from methodology pers.
There are two obvious ways in which we can model this circuit. There are two obvious ways in which we can model this circuit.
One is to do this in two stages, by considering the gain resistors to be a potential divider One is to do this in two stages, by considering the gain resistors to be a potential divider
and then combining it with the OPAMP failure mode model. and then combining it with the OPAMP failure mode model.
The second is to place all three components in one {\fg}. The second is to place all three components in one {\fg}.
Both approaches are followed in the next two sub-sections. Both approaches are followed in the next two sub-sections.
%
\subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}} \subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}}
%
Ideally we would like to re-use {\dcs} from the $PD$ from section~\ref{subsec:potdiv}, which on initial inspection, %at first glance, Ideally we would like to re-use {\dcs} from the $PD$ from section~\ref{subsec:potdiv}, which on initial inspection, %at first glance,
looks a good candidate for this. looks a good candidate for this.
% %
@ -290,7 +267,7 @@ and analyse it as such; see table~\ref{tbl:pdneg}.
We assume a valid range for the output value of this circuit. We assume a valid range for the output value of this circuit.
Thus negative or low voltages can be considered as LOW Thus negative or low voltages can be considered as LOW
and voltages higher than this range considered as HIGH. and voltages higher than this range considered as HIGH.
%
\begin{table}[h+] \begin{table}[h+]
\caption{Inverted Potential divider: Single failure analysis} \caption{Inverted Potential divider: Single failure analysis}
\begin{tabular}{|| l | l | c | c | l ||} \hline \begin{tabular}{|| l | l | c | c | l ||} \hline
@ -304,7 +281,7 @@ and voltages higher than this range considered as HIGH.
\end{tabular} \end{tabular}
\label{tbl:pdneg} \label{tbl:pdneg}
\end{table} \end{table}
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -342,18 +319,18 @@ and voltages higher than this range considered as HIGH.
\path (R1SHORT) edge (PDHIGH); \path (R1SHORT) edge (PDHIGH);
\end{tikzpicture} \end{tikzpicture}
%
\caption{Failure symptoms of the `Inverted Potential Divider' $INVPD$} \caption{Failure symptoms of the `Inverted Potential Divider' $INVPD$}
\label{fig:pdneg} \label{fig:pdneg}
\end{figure} \end{figure}
%
%
We can form a {\dc} from the analysis results in table~\ref{tbl:pdneg} %this, We can form a {\dc} from the analysis results in table~\ref{tbl:pdneg} %this,
and call it an inverted potential divider $INVPD$. and call it an inverted potential divider $INVPD$.
%
We can now progress to the final stage of analysis for this amplifier, We can now progress to the final stage of analysis for this amplifier,
by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$. by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
%
\begin{table}[h+] \begin{table}[h+]
\caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}} \caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}}
\begin{tabular}{|| l | l | c | c | l ||} \hline \begin{tabular}{|| l | l | c | c | l ||} \hline
@ -376,11 +353,11 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
\end{tabular} \end{tabular}
\label{tbl:invamppd} \label{tbl:invamppd}
\end{table} \end{table}
%
%
%%This gives the same results as the analysis from figure~\ref{fig:invampanalysis}. %%This gives the same results as the analysis from figure~\ref{fig:invampanalysis}.
%
%
\begin{figure}[h+] \begin{figure}[h+]
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -475,8 +452,8 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
\caption{Full DAG representing failure modes and symptoms of the Inverting Op-amp Circuit} \caption{Full DAG representing failure modes and symptoms of the Inverting Op-amp Circuit}
\label{fig:invdag1} \label{fig:invdag1}
\end{figure} \end{figure}
%
%
%The differences are the root causes or component failure modes that %The differences are the root causes or component failure modes that
%lead to the symptoms (i.e. the symptoms are the same but causation tree will be different). %lead to the symptoms (i.e. the symptoms are the same but causation tree will be different).
We can now express the failure modes for the {\dc} $INVAMP$ thus; We can now express the failure modes for the {\dc} $INVAMP$ thus;
@ -486,9 +463,9 @@ We can draw a DAG representing the failure mode behaviour of
this amplifier (see figure~\ref{fig:invdag1}). Note that this allows us this amplifier (see figure~\ref{fig:invdag1}). Note that this allows us
to traverse from system level, or top failure modes to base component failure modes. to traverse from system level, or top failure modes to base component failure modes.
%%%%% 12DEC 2012 UP to here in notes from AF email. %%%%% 12DEC 2012 UP to here in notes from AF email.
%
\clearpage \clearpage
%
\subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}} \subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}}
\label{subsec:invamp2} \label{subsec:invamp2}
Here we analyse the same problem without using an intermediate $PD$ Here we analyse the same problem without using an intermediate $PD$
@ -504,10 +481,10 @@ This concern is re-visited in the differencing amplifier example in the next sec
%to symptoms) we cannot have a component failure mode that maps to two different symptoms (within a functional group). %to symptoms) we cannot have a component failure mode that maps to two different symptoms (within a functional group).
%Note that here we have a more general symptom $ OUT OF RANGE $ which could mean either %Note that here we have a more general symptom $ OUT OF RANGE $ which could mean either
%$HIGH$ or $LOW$ output. %$HIGH$ or $LOW$ output.
%
% 08feb2012 bugger considering -ve input. It complicates things. % 08feb2012 bugger considering -ve input. It complicates things.
% maybe do an ac amplifier later at some stage. % maybe do an ac amplifier later at some stage.
%
\begin{table}[h+] \begin{table}[h+]
\caption{Inverting Amplifier: Single failure analysis: 3 components} \caption{Inverting Amplifier: Single failure analysis: 3 components}
\begin{tabular}{|| l | l | c | c | l ||} \hline \begin{tabular}{|| l | l | c | c | l ||} \hline
@ -1919,6 +1896,7 @@ and is a well known safety critical circuit.
Applying FMMD lets us look at this circuit in a fresh light. Applying FMMD lets us look at this circuit in a fresh light.
We analyse this for both single and double failures, We analyse this for both single and double failures,
in addition it demonstrates FMMD coping with component parameter tolerances. in addition it demonstrates FMMD coping with component parameter tolerances.
%
The circuit is described traditionally and then analysed using the FMMD methodology. The circuit is described traditionally and then analysed using the FMMD methodology.
@ -1966,11 +1944,14 @@ industrial applications below 600\oc, due to high accuracy\cite{aoe}.
\label{Pt100range} \label{Pt100range}
The Pt100 four wire circuit uses two wires to supply a small electrical current, The Pt100 four wire circuit uses two wires to supply a small electrical current,
and returns two sense voltages by the other two. and returns two sense voltages by the other two.
%
By measuring voltages By measuring voltages
from sections of this circuit forming potential dividers, we can determine the from sections of this circuit forming potential dividers, we can determine the
resistance of the platinum wire sensor. The resistance resistance of the platinum wire sensor.
%
The resistance
of this is directly related to temperature, and may be determined by of this is directly related to temperature, and may be determined by
look-up tables or a suitable polynomial expression. look-up tables~\cite{eurothermtables} or a suitable polynomial expression.
% %
% %
\begin{figure}[h] \begin{figure}[h]
@ -2055,8 +2036,8 @@ Where this occurs a circuit re-design is probably the only sensible course of ac
\fmodegloss \fmodegloss
\paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit.} \paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit.}
\label{sec:singlePt100FMEA}
\label{fmea} %\label{fmea}
The Pt100 circuit consists of three resistors, two `current~supply' The Pt100 circuit consists of three resistors, two `current~supply'
wires and two `sensor' wires. wires and two `sensor' wires.
Resistors, are considered to fail by either going OPEN or SHORT (see section~\ref{sec:res_fms}). %circuit\footnote{EN298:2003~\cite{en298} also requires that components are downrated, Resistors, are considered to fail by either going OPEN or SHORT (see section~\ref{sec:res_fms}). %circuit\footnote{EN298:2003~\cite{en298} also requires that components are downrated,
@ -2144,25 +2125,25 @@ tables \cite{eurothermtables}, this corresponded to the resistances \ohms{100}
and \ohms{212.02} respectively. From this the potential divider circuit can be and \ohms{212.02} respectively. From this the potential divider circuit can be
analysed and the maximum and minimum acceptable voltages determined. analysed and the maximum and minimum acceptable voltages determined.
These can be used as bounds results to apply the findings from the These can be used as bounds results to apply the findings from the
Pt100 FMEA analysis in section \ref{fmea}. Pt100 FMEA analysis in section\ref{sec:Pt100floating}. %\ref{fmea}.
%
As the Pt100 forms a potential divider with the \ohms{2k2} load resistors, As the Pt100 forms a potential divider with the \ohms{2k2} load resistors,
the upper and lower readings can be calculated thus: the upper and lower readings can be calculated thus:
%
%
$$ highreading = 5V.\frac{2k2+Pt100}{2k2+2k2+pt100} $$ $$ highreading = 5V.\frac{2k2+Pt100}{2k2+2k2+pt100} $$
$$ lowreading = 5V.\frac{2k2}{2k2+2k2+Pt100} $$ $$ lowreading = 5V.\frac{2k2}{2k2+2k2+Pt100} $$
So by defining an acceptable measurement/temperature range, So by defining an acceptable measurement/temperature range,
and ensuring the and ensuring the
values are always within these bounds, we can be confident that none of the values are always within these bounds, we can be confident that none of the
resistors in this circuit has failed. resistors in this circuit has failed.
%
To convert these to twelve bit ADC (\adctw) counts: To convert these to twelve bit ADC (\adctw) counts:
%
$$ highreading = 2^{12}.\frac{2k2+Pt100}{2k2+2k2+pt100} $$ $$ highreading = 2^{12}.\frac{2k2+Pt100}{2k2+2k2+pt100} $$
$$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+Pt100} $$ $$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+Pt100} $$
%
%
\begin{table}[ht] \begin{table}[ht]
\caption{Pt100 Maximum and Minimum Values} % title of Table \caption{Pt100 Maximum and Minimum Values} % title of Table
\centering % used for centering table \centering % used for centering table
@ -2181,12 +2162,12 @@ $$ lowreading = 2^{12}.\frac{2k2}{2k2+2k2+Pt100} $$
\end{tabular} \end{tabular}
\label{ptbounds} \label{ptbounds}
\end{table} \end{table}
%
Table \ref{ptbounds} gives ranges that determine correct operation. In fact it can be shown that 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 for any single error (short or opening of any resistor) this bounds check
will detect it. will detect it.
%
%
% WAS a repeated paragraph % WAS a repeated paragraph
% \paragraph{Consideration of Resistor Tolerance.} % \paragraph{Consideration of Resistor Tolerance.}
% % % %
@ -2219,14 +2200,14 @@ will detect it.
% will be determined by the accuracy of $R_2$ and $R_{3}$. It is reasonable to % will be determined by the accuracy of $R_2$ and $R_{3}$. It is reasonable to
% take the mean square error of these accuracy figures~\cite{probstat}. % take the mean square error of these accuracy figures~\cite{probstat}.
% %
%
\paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit} \paragraph{Single Fault FMEA Analysis of $Pt100$ Four wire circuit}
%
%
\ifthenelse{\boolean{pld}} \ifthenelse{\boolean{pld}}
{ {
\paragraph{Single Fault Modes as PLD} \paragraph{Single Fault Modes as PLD}
%
The component~failure~modes in table \ref{ptfmea} can be represented as contours The component~failure~modes in table \ref{ptfmea} can be represented as contours
on a PLD diagram. on a PLD diagram.
Each test case, is defined by the contours that enclose Each test case, is defined by the contours that enclose
@ -2241,23 +2222,23 @@ and are thus enclosed by one contour each.
\label{fig:Pt100_tc} \label{fig:Pt100_tc}
\end{figure} \end{figure}
} % \ifthenelse {\boolean{pld}} } % \ifthenelse {\boolean{pld}}
%
%ating input Fault %ating input Fault
This circuit supplies two results, the {\em sense+} and {\em sense-} voltage readings. This circuit supplies two results, the {\em sense+} and {\em sense-} voltage readings.
To establish the valid voltage ranges for these, and knowing our 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 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} valid voltage reading ranges by using the standard voltage divider equation \ref{eqn:vd}
for the circuit shown in figure \ref{fig:vd}. for the circuit shown in figure \ref{fig:vd}.
%
%
%
%
\paragraph{Proof of Out of Range Values for Failures} \paragraph{Proof of Out of Range Values for Failures}
\label{pt110range} \label{pt110range}
Using the temperature ranges defined above we can compare the voltages Using the temperature ranges defined above we can compare the voltages
we would get from the resistor failures to prove that they are 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. `out~of~range'. There are six test cases and each will be examined in turn.
%
\subparagraph{ TC 1 : Voltages $R_1$ SHORT } \subparagraph{ TC 1 : Voltages $R_1$ SHORT }
With Pt100 at 0\oc With Pt100 at 0\oc
$$ highreading = 5V $$ $$ highreading = 5V $$
@ -2267,19 +2248,19 @@ $$ lowreading = 5V.\frac{2k2}{2k2+100\Omega} = 4.78V$$
With Pt100 at the high end of the temperature range 300\oc. With Pt100 at the high end of the temperature range 300\oc.
$$ highreading = 5V $$ $$ highreading = 5V $$
$$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$ $$ lowreading = 5V.\frac{2k2}{2k2+212.02\Omega} = 4.56V$$
%
Thus with $R_1$ shorted both readings are outside the Thus with $R_1$ shorted both readings are outside the
proscribed range in table \ref{ptbounds}. proscribed range in table \ref{ptbounds}.
%
\paragraph{ TC 2 : Voltages $R_1$ OPEN } \paragraph{ TC 2 : Voltages $R_1$ OPEN }
%
In this case the 5V rail is disconnected. All voltages read are 0V, and In this case the 5V rail is disconnected. All voltages read are 0V, and
therefore both readings are outside the therefore both readings are outside the
proscribed range in table \ref{ptbounds}. proscribed range in table \ref{ptbounds}.
%
%
\paragraph{ TC 3 : Voltages $R_2$ SHORT } \paragraph{ TC 3 : Voltages $R_2$ SHORT }
%
With Pt100 at 0\oc With Pt100 at 0\oc
$$ lowreading = 0V $$ $$ lowreading = 0V $$
Since the lowreading or sense- is directly connected to the 0V rail, Since the lowreading or sense- is directly connected to the 0V rail,
@ -2290,35 +2271,35 @@ $$ highreading = 5V.\frac{212.02\Omega}{2k2+212.02\Omega} = 0.44V$$
% %
Thus with $R_2$ shorted both readings are outside the Thus with $R_2$ shorted both readings are outside the
proscribed range in table \ref{ptbounds}. proscribed range in table \ref{ptbounds}.
%
\paragraph{ TC 4 : Voltages $R_2$ OPEN } \paragraph{ TC 4 : Voltages $R_2$ OPEN }
Here there is no potential divider operating and both sense lines Here there is no potential divider operating and both sense lines
will read 5V, outside of the proscribed range. will read 5V, outside of the proscribed range.
%
%
\paragraph{ TC 5 : Voltages $R_3$ SHORT } \paragraph{ TC 5 : Voltages $R_3$ SHORT }
%
Here the potential divider is simply between Here the potential divider is simply between
the two 2k2 load resistors. Thus it will read a nominal; the two 2k2 load resistors. Thus it will read a nominal;
2.5V. 2.5V.
%
Assuming the load resistors are Assuming the load resistors are
precision components, and then taking an absolute worst case of 1\% either way. precision components, and then taking an absolute worst case of 1\% either way.
%
$$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$ $$ 5V.\frac{2k2*0.99}{2k2*1.01+2k2*0.99} = 2.475V $$
%
$$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$ $$ 5V.\frac{2k2*1.01}{2k2*1.01+2k2*0.99} = 2.525V $$
%
These readings both lie outside the proscribed range. These readings both lie outside the proscribed range.
Also the sense+ and sense- readings would have the same value. Also the sense+ and sense- readings would have the same value.
%
\paragraph{ TC 6 : Voltages $R_3$ OPEN } \paragraph{ TC 6 : Voltages $R_3$ OPEN }
%
Here the potential divider is broken. The sense- will read 0V and the sense+ will Here the potential divider is broken. The sense- will read 0V and the sense+ will
read 5V. Both readings are outside the proscribed range. read 5V. Both readings are outside the proscribed range.
%
\subsection{Summary of Analysis} \subsection{Summary of Analysis}
%
All six test cases have been analysed and the results agree with the FMEA All six test cases have been analysed and the results agree with the FMEA
presented in table~\ref{ptfmea}. presented in table~\ref{ptfmea}.
%The PLD diagram, can now be used to collect the symptoms. %The PLD diagram, can now be used to collect the symptoms.
@ -2331,7 +2312,7 @@ In practical use, by defining an acceptable measurement/temperature range,
and ensuring the and ensuring the
values are always within these bounds, we can be confident that none of the values are always within these bounds, we can be confident that none of the
resistors in this circuit has failed. resistors in this circuit has failed.
%
\ifthenelse{\boolean{pld}} \ifthenelse{\boolean{pld}}
{ {
\begin{figure}[h] \begin{figure}[h]
@ -2342,8 +2323,8 @@ resistors in this circuit has failed.
\label{fig:Pt100_tc_sp} \label{fig:Pt100_tc_sp}
\end{figure} \end{figure}
} }
%
%
\subsection{Derived Component with one failure mode.} \subsection{Derived Component with one failure mode.}
The Pt100 circuit can now be treated as a component in its own right, and has one failure mode, The Pt100 circuit can now be treated as a component in its own right, and has one failure mode,
{\textbf OUT\_OF\_RANGE}. This is a single, detectable failure mode. The detectability of a {\textbf OUT\_OF\_RANGE}. This is a single, detectable failure mode. The detectability of a
@ -2353,7 +2334,7 @@ has been developed for safety critical temperature measurement.
\ifthenelse{\boolean{pld}} \ifthenelse{\boolean{pld}}
{ {
It can now be represented as a PLD see figure \ref{fig:Pt100_singlef}. It can now be represented as a PLD see figure \ref{fig:Pt100_singlef}.
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./CH5_Examples/Pt100_singlef.png} \includegraphics[width=100pt,bb=0 0 167 194,keepaspectratio=true]{./CH5_Examples/Pt100_singlef.png}
@ -2362,22 +2343,22 @@ It can now be represented as a PLD see figure \ref{fig:Pt100_singlef}.
\label{fig:Pt100_singlef} \label{fig:Pt100_singlef}
\end{figure} \end{figure}
} }
%
%From the single faults (cardinality constrained powerset of 1) analysis, we can now create %From the single faults (cardinality constrained powerset of 1) analysis, we can now create
%a new derived component, the {\emPt100circuit}. This has only \{ OUT\_OF\_RANGE \} %a new derived component, the {\emPt100circuit}. This has only \{ OUT\_OF\_RANGE \}
%as its single failure mode. %as its single failure mode.
%
%
%Interestingly we can calculate the failure statistics for this circuit now. %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) ??? %Mill 1991 gives resistor stats of ${10}^{11}$ times 6 (can we get special stats for Pt100) ???
%\clearpage %\clearpage
%
%
%
%\section{Double failure analysis} %\section{Double failure analysis}
%
%CITE PRICE MULTIPLE FAILURE PAPER. %CITE PRICE MULTIPLE FAILURE PAPER.
%
%\clearpage %\clearpage
\section{ Pt100 Double Simultaneous Fault Analysis} \section{ Pt100 Double Simultaneous Fault Analysis}
\label{sec:Pt100d} \label{sec:Pt100d}
@ -2398,7 +2379,7 @@ Table \ref{tab:ptfmea2} lists all the combinations of double
faults as FMMD test cases. faults as FMMD test cases.
%and then hypothesises how the functional~group will react %and then hypothesises how the functional~group will react
%under those conditions. %under those conditions.
%
\begin{table}[ht] \begin{table}[ht]
\caption{Pt100 FMEA Double Faults} % title of Table \caption{Pt100 FMEA Double Faults} % title of Table
\centering % used for centering table \centering % used for centering table
@ -2431,10 +2412,10 @@ TC 18: & $R_2$ SHORT $R_3$ SHORT & low & low & Both out of Rang
\end{tabular} \end{tabular}
\label{tab:ptfmea2} \label{tab:ptfmea2}
\end{table} \end{table}
%
%
%\paragraph{Proof of Double Faults Hypothesis} %\paragraph{Proof of Double Faults Hypothesis}
%
\paragraph{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN } \paragraph{ TC 7 : Voltages $R_1$ OPEN $R_2$ OPEN }
\label{Pt100:bothfloating} \label{Pt100:bothfloating}
This double fault mode produces an interesting symptom. This double fault mode produces an interesting symptom.
@ -2451,84 +2432,84 @@ fault.
% %
Undetectable faults are generally to be avoided in a safety critical environment~\cite{ACS:ACS1297,721666}. Undetectable faults are generally to be avoided in a safety critical environment~\cite{ACS:ACS1297,721666}.
%that must be handled. %that must be handled.
%
%
\paragraph{ TC 8 : Voltages $R_1$ OPEN $R_2$ SHORT } \paragraph{ TC 8 : Voltages $R_1$ OPEN $R_2$ SHORT }
%
This cuts the supply from Vcc. Both sense lines will be at zero. This cuts the supply from Vcc. Both sense lines will be at zero.
Thus both values will be out of range. Thus both values will be out of range.
%
%
\paragraph{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN } \paragraph{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN }
%
Sense- will be floating. Sense- will be floating.
Sense+ will be tied to Vcc and will thus be out of range. Sense+ will be tied to Vcc and will thus be out of range.
%
\paragraph{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT } \paragraph{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT }
%
This shorts ground to This shorts ground to
both of the sense lines. both of the sense lines.
Both values will be out of range. Both values will be out of range.
%
\paragraph{ TC 11 : Voltages $R_1$ SHORT $R_2$ OPEN } \paragraph{ TC 11 : Voltages $R_1$ SHORT $R_2$ OPEN }
%
This shorts both sense lines to Vcc. This shorts both sense lines to Vcc.
Both values will be out of range. Both values will be out of range.
%
%
\paragraph{ TC 12 : Voltages $R_1$ SHORT $R_2$ SHORT } \paragraph{ TC 12 : Voltages $R_1$ SHORT $R_2$ SHORT }
%
This shorts the sense+ to Vcc and the sense- to ground. This shorts the sense+ to Vcc and the sense- to ground.
Both values will be out of range. Both values will be out of range.
%
%
\paragraph{ TC 13 : Voltages $R_1$ SHORT $R_3$ OPEN } \paragraph{ TC 13 : Voltages $R_1$ SHORT $R_3$ OPEN }
%
This shorts the sense+ to Vcc and the sense- to ground. This shorts the sense+ to Vcc and the sense- to ground.
Both values will be out of range. Both values will be out of range.
%
\paragraph{ TC 14 : Voltages $R_1$ SHORT $R_3$ SHORT } \paragraph{ TC 14 : Voltages $R_1$ SHORT $R_3$ SHORT }
%
This shorts the sense+ and sense- to Vcc. This shorts the sense+ and sense- to Vcc.
Both values will be out of range. Both values will be out of range.
%
\paragraph{ TC 15 : Voltages $R_2$ OPEN $R_3$ OPEN } \paragraph{ TC 15 : Voltages $R_2$ OPEN $R_3$ OPEN }
%
This shorts the sense+ to Vcc and causes sense- to float. This shorts the sense+ to Vcc and causes sense- to float.
The sense+ value will be out of range. The sense+ value will be out of range.
%
%
\paragraph{ TC 16 : Voltages $R_2$ OPEN $R_3$ SHORT } \paragraph{ TC 16 : Voltages $R_2$ OPEN $R_3$ SHORT }
%
This shorts the sense+ and sense- to Vcc. This shorts the sense+ and sense- to Vcc.
Both values will be out of range. Both values will be out of range.
%
%
%
%
%
\paragraph{ TC 17 : Voltages $R_2$ SHORT $R_3$ OPEN } \paragraph{ TC 17 : Voltages $R_2$ SHORT $R_3$ OPEN }
%
This shorts the sense- to ground. This shorts the sense- to ground.
The sense- value will be out of range. The sense- value will be out of range.
%
%
\paragraph{ TC 18 : Voltages $R_2$ SHORT $R_3$ SHORT } \paragraph{ TC 18 : Voltages $R_2$ SHORT $R_3$ SHORT }
%
This shorts the sense+ and sense- to Vcc. This shorts the sense+ and sense- to Vcc.
Both values will be out of range. Both values will be out of range.
%
%\clearpage %\clearpage
%
\ifthenelse{\boolean{pld}} \ifthenelse{\boolean{pld}}
{ {
\subsection{Double Faults Represented on a PLD Diagram} \subsection{Double Faults Represented on a PLD Diagram}
%
We can show the test cases on a diagram with the double faults residing on regions 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}. 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. Thus $TC\_18$ will be enclosed by the $R2\_SHORT$ contour and the $R3\_SHORT$ contour.
%
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{./CH5_Examples/plddouble.png} \includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{./CH5_Examples/plddouble.png}
@ -2536,7 +2517,7 @@ Thus $TC\_18$ will be enclosed by the $R2\_SHORT$ contour and the $R3\_SHORT$ co
\caption{Pt100 Double Simultaneous Faults} \caption{Pt100 Double Simultaneous Faults}
\label{fig:plddouble} \label{fig:plddouble}
\end{figure} \end{figure}
%
We use equation \ref{eqn:correctedccps2} to verify complete coverage for We use equation \ref{eqn:correctedccps2} to verify complete coverage for
a given cardinality constraint is not visually obvious. a given cardinality constraint is not visually obvious.
% %
@ -2546,22 +2527,22 @@ not that all for a given cardinality constraint have been included.
} }
{ {
} }
%
\paragraph{Symptom Extraction} \paragraph{Symptom Extraction}
%
We can now examine the results of the test case analysis and apply symptom abstraction. 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 out of range value, except for In all the test case results we have at least one out of range value, except for
$TC\_7$ $TC\_7$
which has two unknown values/floating readings. We can collect all the faults, except $TC\_7$, which has two unknown values/floating readings. We can collect all the faults, except $TC\_7$,
into the symptom $OUT\_OF\_RANGE$. into the symptom $OUT\_OF\_RANGE$.
As a symptom $TC\_7$ could be described as $FLOATING$. As a symptom $TC\_7$ could be described as $FLOATING$.
%
\ifthenelse{\boolean{pld}} \ifthenelse{\boolean{pld}}
{ {
We can thus draw a PLD diagram representing the We can thus draw a PLD diagram representing the
failure modes of this functional~group, the Pt100 circuit from the perspective of double simultaneous failures, failure modes of this functional~group, the Pt100 circuit from the perspective of double simultaneous failures,
in figure \ref{fig:Pt100_doublef}. in figure \ref{fig:Pt100_doublef}.
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{./CH5_Examples/plddoublesymptom.png} \includegraphics[width=450pt,bb=0 0 730 641,keepaspectratio=true]{./CH5_Examples/plddoublesymptom.png}
@ -2572,12 +2553,13 @@ in figure \ref{fig:Pt100_doublef}.
} %% \ifthenelse {\boolean{pld}} } %% \ifthenelse {\boolean{pld}}
{ {
} }
%
%\clearpage %\clearpage
\subsection{Derived Component : The Pt100 Circuit} \subsection{Derived Component : The Pt100 Circuit}
\label{sec:Pt100floating}
The Pt100 circuit again, can now be treated as a component in its own right, and has two failure modes, The Pt100 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}}. {\textbf{OUT\_OF\_RANGE}} and {\textbf{FLOATING}}.
%
\ifthenelse{\boolean{pld}} \ifthenelse{\boolean{pld}}
{ {
It can now be represented as a PLD see figure \ref{fig:Pt100_doublef}. It can now be represented as a PLD see figure \ref{fig:Pt100_doublef}.
@ -2591,9 +2573,9 @@ It can now be represented as a PLD see figure \ref{fig:Pt100_doublef}.
} % \ifthenelse {\boolean{pld}} } % \ifthenelse {\boolean{pld}}
{ {
} }
%
%
%
% The resistors R1, R2 form a summing junction % The resistors R1, R2 form a summing junction
% to the negative input of IC1. % to the negative input of IC1.
% Using the earlier definition for resistor failure modes, % Using the earlier definition for resistor failure modes,
@ -2621,18 +2603,17 @@ It can now be represented as a PLD see figure \ref{fig:Pt100_doublef}.
% %
% This summing junction fails with two symptoms. We create a {\dc} called $SUMJUNCT$ and we can state, % This summing junction fails with two symptoms. We create a {\dc} called $SUMJUNCT$ and we can state,
% $$fm(SUMJUNCT) = \{ R1\_IN\_DOM, R2\_IN\_DOM \} $$. % $$fm(SUMJUNCT) = \{ R1\_IN\_DOM, R2\_IN\_DOM \} $$.
%
%
%The D type flip flop %The D type flip flop
%
%\subsection{FMMD Process applied to $\Sigma \Delta $ADC}. %\subsection{FMMD Process applied to $\Sigma \Delta $ADC}.
%
%T%he block diagram in figure~\ref{fig %T%he block diagram in figure~\ref{fig
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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submission_thesis/CH6_Software_Examples/software.tex
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submission_thesis/colophon/copy.tex
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@ -19,11 +19,11 @@ the University of Brighton, pushing me forward in clarity of self-expression,
precision through mathematics, critical assessment and carefully crafted English: precision through mathematics, critical assessment and carefully crafted English:
its members will always remain dear to me. its members will always remain dear to me.
% %
%%%% IS THIS BIT A BIT MAD???? %%%% IS THIS BIT A BIT MAD???? YES! 27AUG2013
Like an army recruits training Sergeant Major I found them % % % Like an army recruits training Sergeant Major I found them
hard task masters at first, and then, as with realising the rationale behind training and % % % hard task masters at first, and then, as with realising the rationale behind training and
{\em even} parade drill, respected and grew to like them. % % % {\em even} parade drill, respected and grew to like them.
% % % % %
% %
My first debt of gratitude must go to my supervisors, My first debt of gratitude must go to my supervisors,
Dr. A. Fish, Dr. A. Fish,

1
submission_thesis/style.tex
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@ -9,6 +9,7 @@
\newcommand{\ft}{\ensuremath{4\!\!\rightarrow\!\!20mA} } \newcommand{\ft}{\ensuremath{4\!\!\rightarrow\!\!20mA} }
\newcommand{\tenfifty}{\ensuremath{10\!\!\rightarrow\!\!50mA} }
\usepackage{graphicx} \usepackage{graphicx}
\usepackage{fancyhdr} \usepackage{fancyhdr}
\usepackage{tikz} \usepackage{tikz}