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87
submission_thesis/CH5_Examples/copy.tex
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@ -22,7 +22,7 @@ this examines re-use of the potential divider {\dc} from section~\ref{subsec:pot
This amplifier is analysed twice, using different compositions of {\fgs}.
The two approaches, i.e. effects of choice of membership for {\fgs} are then discussed.
%\
fmmdglossOPAMP
\fmmdglossOPAMP
\item Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used
to create a differencing amplifier.
Building on the two approaches from section~\ref{sec:invamp}, re-use of the non-inverting amplifier {\dc} from section~\ref{sec:invamp}
@ -45,7 +45,7 @@ initially identified {\fgs} and the second using a more complex hierarchy of %{\
that a finer grained/more decomposed approach offers greater efficiency and re-use possibilities in future analysis tasks.
%
\item Section~\ref{sec:sigmadelta} demonstrates that FMMD can be applied to mixed analogue and digital circuitry
by applying FMMD to a sigma delta ADC.
by analysing a sigma delta ADC.
%shows FMMD analysing the sigma delta
%analogue to digital converter---again with a circular signal path---which operates on both
%analogue and digital signals.
@ -53,6 +53,11 @@ by applying FMMD to a sigma delta ADC.
safety critical temperature sensor circuit, analysed for single and double failure mode scenarios.
\end{itemize}
\clearpage
\section{Example Analysis: Inverting OPAMP}
%
@ -66,6 +71,19 @@ safety critical temperature sensor circuit, analysed for single and double failu
\label{fig:invamp}
\end{figure}
%
Figure~\ref{fig:invamp} shows a standard configuration inverting amplifier.
A valid range for the output value of this circuit is assumed.
%
%Thus negative or low voltages can be considered as LOW
%and voltages higher than a given threshold considered as HIGH.
%
Because the amplifier inverts and the input is guaranteed positive any
output voltage above or equal to zero would be erroneous.
%
This would be an `$AMP_{HIGH}$' failure symptom.
%
A threshold would be determined for an `$AMP_{LOW}$' failure symptom (i.e. the output voltage more negative than expected). % error given the expected input range.
%
%This configuration is interesting from methodology pers.
There are two obvious ways in which this circuit can be modelled.
%
@ -84,6 +102,7 @@ However,
$PD$ cannot be directly re-used, and not just because
the potential divider is floating i.e. that the polarity of
the R2 side of the potential divider is determined by the output from the op-amp.
%
\fmmdglossOPAMP
%
The circuit schematic stipulates that the input is positive.
@ -99,20 +118,16 @@ In normal operation then, this is an inverted potential divider.
It must therefore be viewed as an inverted potential divider
and analysed as such; see table~\ref{tbl:pdneg}.
%
A valid range for the output value of this circuit is assumed.
%
Thus negative or low voltages can be considered as LOW
and voltages higher than a given threshold considered as HIGH.
%
\begin{table}[h+]
\caption{Inverted Potential divider: Single failure analysis}
\begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Cause} & & \textbf{Inverted Pot Div Effect} & & \textbf{Symptom} \\
\textbf{Failure Cause} & & \textbf{Inverted Pot Divider, $IPD$, Effect} & & \textbf{Symptom} \\
\hline
FC1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline
FC2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline
FC3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline
FC4: R2 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline
FC1: R1 SHORT & & $HIGH$ & & $IPDHigh$ \\ \hline
FC2: R1 OPEN & & $LOW$ & & $IPDLow$ \\ \hline
FC3: R2 SHORT & & $LOW$ & & $IPDLow$ \\ \hline
FC4: R2 OPEN & & $HIGH$ & & $IPDHigh$ \\ \hline
\hline
\end{tabular}
\label{tbl:pdneg}
@ -145,8 +160,8 @@ and voltages higher than a given threshold considered as HIGH.
% Potential divider failure modes
%
\node[symptom] (PDHIGH) at (\layersep*2,-0.7) {$PD_{HIGH}$};
\node[symptom] (PDLOW) at (\layersep*2,-2.2) {$PD_{LOW}$};
\node[symptom] (PDHIGH) at (\layersep*2,-0.5) {$IPD_{HIGH}$};
\node[symptom] (PDLOW) at (\layersep*2,-2.4) {$IPD_{LOW}$};
\path (R1OPEN) edge (PDLOW);
\path (R2SHORT) edge (PDLOW);
@ -156,16 +171,16 @@ and voltages higher than a given threshold considered as HIGH.
\end{tikzpicture}
%
\caption{Failure symptoms of the `Inverted Potential Divider' $INVPD$}
\caption{Failure symptoms of the `Inverted Potential Divider' $IPD$}
\label{fig:pdneg}
\end{figure}
%
%
A {\dc} can be formed from the analysis results in table~\ref{tbl:pdneg} %this,
and called an inverted potential divider $INVPD$.
and called an inverted potential divider ($IPD$).
%
The final stage of analysis for this amplifier, is made by
by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
by forming a {\fg} with the OpAmp and the new {\dc} $IPD$.
%
\begin{table}[h+]
\caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}}
@ -175,8 +190,8 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
\textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\
\hline
FC1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\
FC2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline
FC1: IPD LOW & & Negative on -input & & $ HIGH $ \\
FC2: IPD HIGH & & Positive on -input & & $ LOW $ \\ \hline
FC5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\
@ -191,6 +206,7 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
\end{table}
%
%
\clearpage
%%This gives the same results as the analysis from figure~\ref{fig:invampanalysis}.
%
%
@ -256,8 +272,8 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
% Potential divider failure modes
%
\node[symptom] (PDHIGH) at (\layersep*2,-6) {$PD_{HIGH}$};
\node[symptom] (PDLOW) at (\layersep*2,-7.6) {$PD_{LOW}$};
\node[symptom] (PDHIGH) at (\layersep*2,-5.8) {$IPD_{HIGH}$};
\node[symptom] (PDLOW) at (\layersep*2,-8.1) {$IPD_{LOW}$};
@ -270,9 +286,9 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
\node[symptom] (AMPHIGH) at (\layersep*3.4,-3) {$AMP_{HIGH}$};
\node[symptom] (AMPLOW) at (\layersep*3.4,-5) {$AMP_{LOW}$};
\node[symptom] (AMPLP) at (\layersep*3.4,-7) {$LOWPASS$};
\node[symptom] (AMPHIGH) at (\layersep*4.4,-3) {$AMP_{HIGH}$};
\node[symptom] (AMPLOW) at (\layersep*4.4,-5) {$AMP_{LOW}$};
\node[symptom] (AMPLP) at (\layersep*4.4,-7) {$LOWPASS$};
\path (PDLOW) edge (AMPHIGH);
\path (OPAMPLU) edge (AMPHIGH);
@ -295,25 +311,26 @@ by forming a {\fg} with the OpAmp and our new {\dc} $INVPD$.
Failure modes for the {\dc} $INVAMP$ can be expressed thus;
%% $$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$
$$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \} .$$
% \clearpage
A DAG is drawn representing the failure mode behaviour of
this amplifier (see figure~\ref{fig:invdag1}).
%
Note that this allows us
to trace failure symptoms back to causes, i.e.
Note that this allows failure symptoms to be traced back to causes, i.e.
to traverse from system level or top failure modes to base component failure modes.
%%%%% 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}}
\label{subsec:invamp2}
%
The problem above is analysed without using an intermediate $INVPD$
The problem above is analysed without using an intermediate $IPD$
derived component.
%
If the input voltage was not constrained to being positive this one stage analysis would be necessary.
%
%
This concern is re-visited in the differencing amplifier example in the next section.
%We can view the failure mode mode produced with FMMD as a DAG
%in figure~\ref{fig:
@ -336,13 +353,13 @@ This concern is re-visited in the differencing amplifier example in the next sec
\textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\
\hline
FS1: R1 SHORT & & NEGATIVE out of range & & $ HIGH $ \\
FS1: R1 SHORT & & -ve in high gain & & $ LOW $ \\
% FS1: R1 SHORT -ve in & & POSITIVE out of range & & $ OUT OF RANGE $ \\ \hline
FS2: R1 OPEN & & zero output & & $ LOW $ \\ \hline
FS2: R1 OPEN & & zero volt follower & & $ HIGH $ \\ \hline
% FS2: R1 OPEN -ve in & & zero output & & $ ZERO OUTPUT $ \\ \hline
FS3: R2 SHORT & & $INVAMP_{nogain} $ & & $ LOW $ \\
FS3: R2 SHORT & & $INVAMP_{unitygain} $ & & $ HIGH $ \\
% FS3: R2 SHORT -ve in & & $INVAMP_{nogain} $ & & $ NO GAIN $ \\ \hline
FS4: R2 OPEN & & NEGATIVE out of range $ $ & & $ LOW$ \\ \hline
@ -359,16 +376,16 @@ This concern is re-visited in the differencing amplifier example in the next sec
\label{tbl:invamp}
\end{table}
\clearpage
%\clearpage
\subsection{Comparison between the two approaches}
\label{sec:invampcc}
The first analysis used two FMMD stages.
%
The first stage analysed an inverted potential divider %, analyses its failure modes,
giving the {\dc} (INVPD).
giving the {\dc} (IPD).
%
The next stage analysed a {\fg} comprised of the INVPD and an OpAmp.
The next stage analysed a {\fg} comprised of the IPD and an OpAmp.
%
The second analysis (3 components) looked at the effects of each failure mode of each resistor
and the op-amp. % circuit.
@ -1338,7 +1355,7 @@ This can be the first {\fg} and it is analysed in table~\ref{detail:SUMJINT}: %{
%
$$FG = \{R1, R2, IC1, C1 \} .$$
%
That is, the failure modes (see FMMD analysis at~\ref{detail:SUMJINT}) of our new {\dc}
That is, the failure modes (see FMMD analysis at~\ref{detail:SUMJINT}) of the new {\dc}
$SUMJINT$ are $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$
%
%\clearpage

50
submission_thesis/CH8_Conclusion/copy.tex
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@ -162,6 +162,56 @@ in a way that is compatible with FMEDA/EN61508.
\fmmdglossFIT
\subsection{Composition of {\fgs}.}
%The choice of components for a {\fg} are that they are components that
%work together to perform a pre-defined function.work together to perform a pre-defined function.
The members of a {\fg} are chosen to be components that work together to perform a specific function.
%
The choice of {\fg} membership is made by the analyst.
%
The act of choosing components to form a {\fg}
raises questions about the circuit under investigation.
%
Ideally {\fgs} will be able to act as standalone modules.
%
%That is they should perform their function in the context of teir use, but
%
An inverting amplifier configuration, or a low pass filter are good examples of these:
they have clear inputs and outputs, and are resilient to what they are connected to at
the output (in electronics terms they have low output impedance).
%
In defining members for {\fgs} the analyst is forced to consider the interfaces between elements
of circuitry to identify modules.
%
The aim is to prevent undue influence on modules identified from circuitry
they are/may be connected to.
%
Consider the resistor capacitor low pass stage first looked at in example~\ref{sec:lp}. %\label{sec:lp}
%
This circuit element, while applying a filtering effect, has a high output impedance.
%
With a simple OpAmp buffer amplifier on its output stage, it becomes an effective low impedance output standalone module\footnote{A well behaved, or ideal electronics `module' will
have a high impedance input (i.e. it will not overload and affect any driving stages) and a low output impedance (i.e. it will drive an electrical load at the output without being affected its-self).}.
%
The resistor/capacitor low pass stage and the OpAmp
are good candidates therefore for being considered as a standalone module, and thus a {\fg}.
However, different analysts may choose different {\fgs}
when analysing the same circuit.
%
This means that {\fgs} are not guaranteed to be unique.
%
This apparent anomaly is explored in the examples~\ref{sec:invamp},~\ref{sec:bubba} where different
structures of the FMMD hierarchy were used to analyse the same circuitry.
%
The same system level failure modes were obtained, but the more de-composed examples
offered better performance in terms of comparison complexity.
%
Further work may be required to apply justification for the choice of membership in {\fgs}.
%
For software already written this problem does not exist as the choice of membership has already been made by the programmer.
%
\subsection{Deriving FTA diagrams from FMMD models}
\label{sec:fta}

6
submission_thesis/Makefile
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@ -3,6 +3,12 @@
all: copy bib thesis
dropbox:
pdflatex thesis
makeindex thesis.glo -s thesis.ist -t thesis.glg -o thesis.gls
cp thesis.pdf /home/robin/Dropbox/Robin_PhD_folder/thesis
acroread thesis.pdf || evince thesis.pdf
thesis:
pdflatex thesis
makeindex thesis.glo -s thesis.ist -t thesis.glg -o thesis.gls