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3
submission_thesis/CH1_introduction/copy.tex
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@ -57,6 +57,7 @@ the higher SIL rating we can demand for it.
A band-saw with one operative may require a SIL rating of 1, A band-saw with one operative may require a SIL rating of 1,
a nuclear power-station, with far greater consequences on dangerous failure a nuclear power-station, 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, What we are saying is that while we may tolerate a low incidence of failure on a band-saw,
we will only tolerate extremely low incidences of failure in nuclear plant. we will only tolerate extremely low incidences of failure in nuclear plant.
SIL ratings give us another objective yardstick for the measurement of system safety. SIL ratings give us another objective yardstick for the measurement of system safety.
@ -128,7 +129,7 @@ effectively meant that all single and double component failures
now required to be analysed. This, from a state explosion problem alone, now required to be analysed. 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.
% %
To compound the problem %state explosion problem To compound the problem, %state explosion problem
FMEA has a deficiency of repeated work, as each component failure is typically represented FMEA has a deficiency of repeated work, as each component failure is typically represented
by one line or entry in a spreadsheet~\cite{bfmea}; analysis on repeated sections of by one line or entry in a spreadsheet~\cite{bfmea}; analysis on repeated sections of
circuitry (for instance repeated 4-20mA outputs on a PCB) meant that circuitry (for instance repeated 4-20mA outputs on a PCB) meant that

69
submission_thesis/CH5_Examples/copy.tex
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@ -57,7 +57,7 @@ loop topology---using a `Bubba' oscillator---demonstrating how FMMD differs from
Two analysis strategies are employed, one using Two analysis strategies are employed, one using
initially identified {\fgs} and the second using a more complex hierarchy of %{\fgs} and initially identified {\fgs} and the second using a more complex hierarchy of %{\fgs} and
{\dcs} showing {\dcs} showing
that a finer grained/more de-composed approach offers more re-use possibilities in future analysis tasks. that a finer grained/more decomposed approach offers more re-use possibilities in future analysis tasks.
% %
\item Section~\ref{sec:sigmadelta} demonstrates FMMD can be applied to mixed analogue and digital circuitry \item Section~\ref{sec:sigmadelta} demonstrates FMMD can be applied to mixed analogue and digital circuitry
by applying FMMD to a sigma delta ADC. by applying FMMD to a sigma delta ADC.
@ -570,7 +570,7 @@ inverting amplifier (i.e. the same failure modes for the {\dc} INVAMP).
All FMEA is performed in the context of the environment and functionality of the enitity All FMEA is performed in the context of the environment and functionality of the enitity
under analysis. under analysis.
This example shows that for the condition where the input voltage This example shows that for the condition where the input voltage
is constrained to being positive, we can apply two levels of de-composition. is constrained to being positive, we can apply two levels of decomposition.
For the unconstrained case, we have to consider all three components as one larger {\fg}. For the unconstrained case, we have to consider all three components as one larger {\fg}.
% METRICS The complexity comparison figures % METRICS The complexity comparison figures
@ -594,7 +594,7 @@ For the unconstrained case, we have to consider all three components as one larg
\label{sec:diffamp} \label{sec:diffamp}
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=370pt]{CH5_Examples/circuit1001.png} \includegraphics[width=400pt]{CH5_Examples/circuit1001.png}
% circuit1001.png: 420x300 pixel, 72dpi, 14.82x10.58 cm, bb=0 0 420 300 % circuit1001.png: 420x300 pixel, 72dpi, 14.82x10.58 cm, bb=0 0 420 300
\caption{Circuit 1} \caption{Circuit 1}
\label{fig:circuit1} \label{fig:circuit1}
@ -815,7 +815,7 @@ Here it is more intuitive to model the resistors not as a potential divider, but
& (impedance of IC1 vs +V2) & \\ \hline & (impedance of IC1 vs +V2) & \\ \hline
TC5: $R4\_open$ & High or Low output & AMPIncorrectOutput \\ TC5: $R4\_open$ & High or Low output & AMPIncorrectOutput \\
& +V2$>$+V1 $\mapsto$ High & \\ & +V2$>$+V1 $\mapsto$ High & \\
& +V1$>$+V2 $\mapsto$ Low & \\ & +V1$>$+V2 $\mapsto$ Low & \\ \hline
TC6: $R4\_short$ & +V2 follower & AMPIncorrectOutput \\ \hline TC6: $R4\_short$ & +V2 follower & AMPIncorrectOutput \\ \hline
%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
\hline \hline
@ -838,7 +838,7 @@ $$ fm(SEC\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} .$$
\pagebreak[4] \pagebreak[4]
\subsection{Final stage of the $DiffAmp$ Analysis} \subsection{Final stage of the $DiffAmp$ Analysis}
For the final stage we create a functional group consisting of For the final stage we create a {\fg} consisting of
two derived components of the type $NI\_AMP$ and $SEC\_AMP$. two derived components of the type $NI\_AMP$ and $SEC\_AMP$.
We apply FMMD analysis to this {\fg} in table~\ref{tbl:diffampfinal}. We apply FMMD analysis to this {\fg} in table~\ref{tbl:diffampfinal}.
% %
@ -888,7 +888,7 @@ re-construct an FTA diagram from the information in this graph.
We merely have to choose a top level event and work down using $XOR$ gates.}. We merely have to choose a top level event and work down using $XOR$ gates.}.
% %
This circuit performs poorly from a safety point of view. This circuit performs poorly from a safety point of view.
Its failure modes could be indistinguishable from valid readings (especially Its failure modes could be undetectable, i.e. indistinguishable from valid readings (especially
when it becomes a V2 follower). when it becomes a V2 follower).
\begin{figure}[h] \begin{figure}[h]
@ -916,6 +916,12 @@ This example shows a three stages hierarchy, and a graph tracing the base~compon
top level event. It also re-visits the decisions about membership of {\fgs}, due to the context top level event. It also re-visits the decisions about membership of {\fgs}, due to the context
of the circuit raised in section~\ref{subsec:invamp2}. of the circuit raised in section~\ref{subsec:invamp2}.
%16MAR2013 COULD Put an euler diagram here
\clearpage \clearpage
\section{Five Pole Low Pass Filter, using two Sallen~Key stages.} \section{Five Pole Low Pass Filter, using two Sallen~Key stages.}
\label{sec:fivepolelp} \label{sec:fivepolelp}
@ -969,7 +975,7 @@ read its output signal.
However, from a failure mode perspective we can analyse it in a very similar way However, from a failure mode perspective we can analyse it in a very similar way
to a potential divider (see section~\ref{subsec:potdiv}). to a potential divider (see section~\ref{subsec:potdiv}).
Capacitors generally fail OPEN but some types fail OPEN and SHORT. Capacitors generally fail OPEN but some types fail OPEN and SHORT.
We will consider the worst case two failure mode model for this analysis. We will consider the worst case: a two failure mode model for this analysis.
We analyse the first order low pass filter in table~\ref{tbl:firstorderlpass}.\\ We analyse the first order low pass filter in table~\ref{tbl:firstorderlpass}.\\
@ -1041,7 +1047,7 @@ We can create a derived component for it, lets call it $LP1$.
$$ fm(LP1) = \{ LP1High, LP1Low, LP1filterincorrect, LP1nosignal \} $$ $$ fm(LP1) = \{ LP1High, LP1Low, LP1filterincorrect, LP1nosignal \} $$
In terms of the circuit, we have modelled the functional groups $FirstOrderLP$, and In terms of the circuit, we have modelled the {\fgs} $FirstOrderLP$, and
$LP1$. We can represent these on the circuit diagram by drawing contours around the components $LP1$. We can represent these on the circuit diagram by drawing contours around the components
on the schematic as in figure~\ref{fig:circuit2002_LP1}. on the schematic as in figure~\ref{fig:circuit2002_LP1}.
@ -1049,7 +1055,7 @@ on the schematic as in figure~\ref{fig:circuit2002_LP1}.
\centering \centering
\includegraphics[width=200pt,keepaspectratio=true]{CH5_Examples/circuit2002_LP1.png} \includegraphics[width=200pt,keepaspectratio=true]{CH5_Examples/circuit2002_LP1.png}
% circuit2002_LP1.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331 % circuit2002_LP1.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{Circuit showing functional groups modelled so far.} \caption{Circuit showing {\fgs} modelled so far.}
\label{fig:circuit2002_LP1} \label{fig:circuit2002_LP1}
\end{figure} \end{figure}
@ -1120,7 +1126,7 @@ We can index the Sallen Key stages, and these are marked on the circuit schemati
\centering \centering
\includegraphics[width=200pt]{CH5_Examples/circuit2002_FIVEPOLE.png} \includegraphics[width=200pt]{CH5_Examples/circuit2002_FIVEPOLE.png}
% circuit2002_FIVEPOLE.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331 % circuit2002_FIVEPOLE.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331
\caption{Functional Groups in Five Pole Low Pass Filter: shown as an Euler diagram super-imposed onto the electrical schematic.} \caption{Functional Groupings in Five Pole Low Pass Filter: shown as an Euler diagram super-imposed onto the electrical schematic.}
\label{fig:circuit2002_FIVEPOLE} \label{fig:circuit2002_FIVEPOLE}
\end{figure} \end{figure}
@ -1196,7 +1202,7 @@ We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
We now can create a {\dc} to represent the circuit in figure~\ref{fig:circuit2}, we call this We now can create a {\dc} to represent the circuit in figure~\ref{fig:circuit2}, we call this
$FivePoleLP$: applying the $fm$ function (see table~\ref{tbl:fivepole}) $FivePoleLP$: applying the $fm$ function (see table~\ref{tbl:fivepole})
yields $fm(FivePoleLP) = \{ HIGH, LOW, FilterIncorrect, NO\_SIGNAL \}$. yields $$fm(FivePoleLP) = \{ HIGH, LOW, FilterIncorrect, NO\_SIGNAL \}.$$
%\pagebreak[4] %\pagebreak[4]
@ -1259,7 +1265,7 @@ However, this is not a problem for FMMD, as {\fgs} are readily identifiable.
% METRICS We now create FMMD models and compare the complexity of FMMD and FMEA. % METRICS We now create FMMD models and compare the complexity of FMMD and FMEA.
% %
%We start the FMMD process by determining {\fgs}. %We start the FMMD process by determining {\fgs}.
We initially identify three types of functional groups, an inverting amplifier (analysed in section~\ref{fig:invamp}), We initially identify three types of {\fgs}, an inverting amplifier (analysed in section~\ref{fig:invamp}),
a 45 degree phase shifter (a {$10k\Omega$} resistor and a $10nF$ capacitor) and a non-inverting buffer a 45 degree phase shifter (a {$10k\Omega$} resistor and a $10nF$ capacitor) and a non-inverting buffer
amplifier. We can name these $INVAMP$, $PHS45$ and $NIBUFF$ respectively. amplifier. We can name these $INVAMP$, $PHS45$ and $NIBUFF$ respectively.
We can use these {\fgs} to describe the circuit in block diagram form with arrows indicating the signal path, in figure~\ref{fig:bubbablock}. We can use these {\fgs} to describe the circuit in block diagram form with arrows indicating the signal path, in figure~\ref{fig:bubbablock}.
@ -1290,7 +1296,7 @@ This consists of a resistor and a capacitor. We already have failure mode models
we now need to see how these failure modes would affect the phase shifter. Note that the circuit here we now need to see how these failure modes would affect the phase shifter. Note that the circuit here
is identical to the low pass filter in circuit topology (see section~\ref{sec:lp}), but its intended use is different. is identical to the low pass filter in circuit topology (see section~\ref{sec:lp}), but its intended use is different.
We have to analyse this circuit from the perspective of it being a {\em phase~shifter} not a {\em low~pass~filter}. We have to analyse this circuit from the perspective of it being a {\em phase~shifter} not a {\em low~pass~filter}.
Our functional group for the phase shifter consists of a resistor and a capacitor, $G_0 = \{ R, C \}$ Our {\fg} for the phase shifter consists of a resistor and a capacitor, $G_0 = \{ R, C \}$
(FMMD analysis details at section~\ref{detail:PHS45}) (FMMD analysis details at section~\ref{detail:PHS45})
@ -1314,7 +1320,7 @@ $$ fm(NIBUFF) = fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} . $$
% describe what we are doing, a buffered 45 degree phase shift element % describe what we are doing, a buffered 45 degree phase shift element
\subsection{Bringing the functional Groups Together: FMMD model of the `Bubba' Oscillator.} \subsection{Bringing the {\fgs} Together: FMMD model of the `Bubba' Oscillator.}
We could at this point bring all the {\dcs} together into one large functional We could at this point bring all the {\dcs} together into one large functional
group (see figure~\ref{fig:bubbaeuler1}) %{fig:poss1finalbubba}) group (see figure~\ref{fig:bubbaeuler1}) %{fig:poss1finalbubba})
@ -1323,7 +1329,7 @@ Initially we use the first identified {\fgs} to create our model without further
\subsection{FMMD Analysis using initially identified functional groups} \subsection{FMMD Analysis using initially identified {\fgs}}
\label{sec:bubba1} \label{sec:bubba1}
Our {\fg} for this analysis can be expressed thus: Our {\fg} for this analysis can be expressed thus:
% %
@ -1367,7 +1373,7 @@ $$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$
%of $468$ failure modes to check against components. %of $468$ failure modes to check against components.
%However, %However,
The analysis here appears top-heavy; we should be able to refine the model more The analysis here appears top-heavy; we should be able to refine the model more
and break this down into smaller functional groups by allowing more stages of hierarchy. and break this down into smaller {\fgs} by allowing more stages of hierarchy.
%and hopefully %and hopefully
%this should lead a further reduction in the complexity comparison figure. %this should lead a further reduction in the complexity comparison figure.
By decreasing the size of the modules with further refinement, By decreasing the size of the modules with further refinement,
@ -1379,7 +1385,7 @@ we may also discover new derived components that may be of use for other analyse
\subsection{FMMD Analysis of Bubba Oscillator using a finer grained modular approach (i.e. more hierarchical stages)} \subsection{FMMD Analysis of Bubba Oscillator using a finer grained modular approach (i.e. more hierarchical stages)}
\label{sec:bubba2} \label{sec:bubba2}
The example above---from the initial {\fgs}---used one very large functional group to model the circuit. The example above---from the initial {\fgs}---used one very large {\fg} to model the circuit.
%This mean a quite large comparison complexity for this final stage. %This mean a quite large comparison complexity for this final stage.
We should be able to determine smaller {\fgs} and refine the model further. We should be able to determine smaller {\fgs} and refine the model further.
@ -1395,7 +1401,7 @@ We should be able to determine smaller {\fgs} and refine the model further.
\centering \centering
\includegraphics[width=400pt]{./CH5_Examples/bubba_euler_2.png} \includegraphics[width=400pt]{./CH5_Examples/bubba_euler_2.png}
% bubba_euler_2.png: 1241x617 pixel, 72dpi, 43.78x21.77 cm, bb=0 0 1241 617 % bubba_euler_2.png: 1241x617 pixel, 72dpi, 43.78x21.77 cm, bb=0 0 1241 617
\caption{Euler diagram showing functional groupings for the Bubba oscillator using a more de-composed approach.} \caption{Euler diagram showing {\fgs} for the Bubba oscillator using a more decomposed approach.}
\label{fig:bubbaeuler2} \label{fig:bubbaeuler2}
\end{figure} \end{figure}
@ -1413,7 +1419,7 @@ $45^{\circ}$ phase shifter circuits in series. Together these apply a $135^{\cir
We use this property to model a higher level {\dc}, that of a $135^{\circ}$ phase shifter. We use this property to model a higher level {\dc}, that of a $135^{\circ}$ phase shifter.
% %
The three $BUFF45$ {\dcs} form a The three $BUFF45$ {\dcs} form a
functional group which is analysed in table~\ref{tbl:phs135buffered}. {\fg} which is analysed in table~\ref{tbl:phs135buffered}.
The result of this analysis is the {\dc} The result of this analysis is the {\dc}
$PHS135BUFFERED$ which represents an actively buffered $135^{\circ}$ phase shifter. $PHS135BUFFERED$ which represents an actively buffered $135^{\circ}$ phase shifter.
% %
@ -1427,7 +1433,7 @@ providing an amplified $225^{\circ}$ phase shift, analysed in table~\ref{tbl:phs
resulting in the {\dc} $PHS225AMP$. resulting in the {\dc} $PHS225AMP$.
Applying FMMD we create a derived component $PHS225AMP$ which has the following failure modes: Applying FMMD we create a derived component $PHS225AMP$ which has the following failure modes:
$$ $$
fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift, fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal \}. % 270\_phaseshift,
$$ $$
% %
%---with the remaining $PHS45$ and the $INVAMP$ (re-used from section~\ref{sec:invamp})in a second group $PHS225AMP$--- %---with the remaining $PHS45$ and the $INVAMP$ (re-used from section~\ref{sec:invamp})in a second group $PHS225AMP$---
@ -1467,7 +1473,7 @@ The $PHS225AMP$ consists of a $PHS45$, providing $45^{\circ}$ of phase shift, an
$INVAMP$, providing $180^{\circ}$ giving a total of $225^{\circ}$. $INVAMP$, providing $180^{\circ}$ giving a total of $225^{\circ}$.
Detailed FMMD analysis may be found in section~\ref{detail:PHS225AMP}. Detailed FMMD analysis may be found in section~\ref{detail:PHS225AMP}.
% %
%
% %
%$$ CC(PHS225AMP) = 7 \times 1 $$ %$$ CC(PHS225AMP) = 7 \times 1 $$
% %
@ -1481,10 +1487,7 @@ and perform FMEA with these (see section~\ref{detail:BUBBAOSC}), to obtain a mod
$$ $$
fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc}, fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc},
$$ $$
%
% %
%We could trace the DAGs here and ensure that both analysis strategies worked ok..... %We could trace the DAGs here and ensure that both analysis strategies worked ok.....
% %
@ -1500,7 +1503,7 @@ $$
% and $250$ for our first stage functional groups analysis. % and $250$ for our first stage functional groups analysis.
% This has meant a drastic reduction in the number of failure-modes to check against components. % This has meant a drastic reduction in the number of failure-modes to check against components.
%It has %also %It has %also
This more de-composed approach has This more decomposed approach has
given us five {\dcs}, building blocks, which could % given us five {\dcs}, building blocks, which could %
be re-used in other projects. be re-used in other projects.
%potentially be re-used for similar circuitry %potentially be re-used for similar circuitry
@ -1511,7 +1514,7 @@ be re-used in other projects.
% %
%In general with large functional groups the comparison complexity %In general with large functional groups the comparison complexity
%is higher, by an order of $O(N^2)$. %is higher, by an order of $O(N^2)$.
Smaller functional groups signify less by-hand checks and Smaller {\fgs} signify less by-hand checks and
a more finely grained model. a more finely grained model.
This means that This means that
there would be more {\dcs} and therefore increases the potential for re-use of pre-analysed {\dcs}. there would be more {\dcs} and therefore increases the potential for re-use of pre-analysed {\dcs}.
@ -1607,14 +1610,14 @@ The parts for the \sd are a mixture of analogue (resistors, capacitors, OpAmps)
(D type flip flop, and a digital clock). We examine the failure modes of all components in this circuit below. (D type flip flop, and a digital clock). We examine the failure modes of all components in this circuit below.
% %
IC1,IC2 and IC3 are all OpAmps and we have failure modes for this component type IC1,IC2 and IC3 are all OpAmps and we have failure modes for this component type
from section~\ref{sec:opamp_fms}. from section~\ref{sec:opamp_fms}:
% %
$$ fm(OPAMP) = \{ HIGH, LOW, NOOP, LOW\_SLEW \} $$ $$ fm(OPAMP) = \{ HIGH, LOW, NOOP, LOW\_SLEW \}. $$
% %
We examine the literature for a failure model for the D-type flip flop~\cite{fmd91}[3-105], for example the CD4013B~\cite{cd4013}, We examine the literature for a failure model for the D-type flip flop~\cite{fmd91}[3-105], for example the CD4013B~\cite{cd4013},
and obtain its failure modes, which we can express using the $fm$ function: and obtain its failure modes, which we can express using the $fm$ function:
%% %%
$$ fm ( CD4013B) = \{ HIGH, LOW, NOOP \} $$ $$ fm ( CD4013B) = \{ HIGH, LOW, NOOP \}. $$
% %
The resistors and capacitor failure modes we take from EN298~\cite{en298}[An.A]. The resistors and capacitor failure modes we take from EN298~\cite{en298}[An.A].
We express the failure modes for the resistors (R) and capacitors (C) thus: We express the failure modes for the resistors (R) and capacitors (C) thus:
@ -1802,7 +1805,7 @@ $$ fm(BISJ) = \{ OUTPUT STUCK , REDUCED\_INTEGRATION \} . $$
%$$ fm (DL2AL^2) = \{ LOW, HIGH, LOW\_SLEW \} $$ %$$ fm (DL2AL^2) = \{ LOW, HIGH, LOW\_SLEW \} $$
%$$ fm ( CD4013B) = \{ HIGH, LOW, NOOP \} $$ %$$ fm ( CD4013B) = \{ HIGH, LOW, NOOP \} $$
The functional group formed by $DIGBUF$ and $DL2AL$ takes the flip flop clocked and buffered The {\fg} formed by $DIGBUF$ and $DL2AL$ takes the flip flop clocked and buffered
value, and outputs it at analogue voltage levels for the summing junction. value, and outputs it at analogue voltage levels for the summing junction.
$ FG = \{ DIGBUF, DL2AL \} $ $ FG = \{ DIGBUF, DL2AL \} $
@ -1816,7 +1819,7 @@ where $$fm (FFB) = \{OUTPUT STUCK, LOW\_SLEW\}$$.
We now have two {\dcs}, $FFB$ and $BISJ$. We now have two {\dcs}, $FFB$ and $BISJ$.
These together represent all base components within this circuit. These together represent all base components within this circuit.
We form a final functional group with these: We form a final {\fg} with these:
$$ FG = \{ FFB , BISJ \} .$$ $$ FG = \{ FFB , BISJ \} .$$
We analyse the buffered {\sd} circuit using FMMD (see section~\ref{detail:SDADC}). We analyse the buffered {\sd} circuit using FMMD (see section~\ref{detail:SDADC}).
%in table~\ref{tbl:sdadc}. %in table~\ref{tbl:sdadc}.
@ -1843,7 +1846,7 @@ We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}.
% \label{fig:sdadc} % \label{fig:sdadc}
% \end{figure} % \end{figure}
\clearpage %\clearpage
% ] % ]
% into % into
% %