diff --git a/submission_thesis/CH1_introduction/copy.tex b/submission_thesis/CH1_introduction/copy.tex index 9e41432..b00e61e 100644 --- a/submission_thesis/CH1_introduction/copy.tex +++ b/submission_thesis/CH1_introduction/copy.tex @@ -1,5 +1,5 @@ -\abstract{ +\paragraph{Abstract}{ The ability to assess the safety of man made equipment has been a concern since the dawn of the industrial age~\cite{indacc01}~\cite{steamboilers}. The philosophy behind safety measure has progressed @@ -27,12 +27,6 @@ and, using contract programmed software, allows the modelling of integrated software/electrical systems. This is followed by two chapters showing examples of the new modular FMEA analysis technique (Failure Mode Modular De-Composition FMMD) firstly looking at electronic circuits and then at electronic/software hybrid systems. - - - - - - } \section{Introduction} diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index 7f2d6e3..0267849 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/submission_thesis/CH5_Examples/copy.tex @@ -33,20 +33,24 @@ a variety of typical embedded system components including analogue/digital and e % %This is followed by several example FMMD analyses, \begin{itemize} - \item The first example applies FMMD to an operational amplifier inverting amplifier (see section~\ref{sec:invamp}), + \item The first example applies FMMD to an operational amplifier inverting amplifier (see section~\ref{sec:invamp}); %using an op-amp and two resistors; this demonstrates re-use of a potential divider {\dc} from section~\ref{subsec:potdiv}. -This inverting amplifier is analysed again, but this time with a different +This inverting amplifier %is analysed again, but this time with a different +re-analysed with a different composition of {\fgs}. The two approaches, i.e. choice of membership for {\fgs}, are then discussed. +% \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} is examined, where re-use is appropriate in the first stage and not in the second. +% \item Section~\ref{sec:fivepolelp} analyses a Sallen-Key based five pole low pass filter. It demonstrates re-use of the first Sallen-Key analysis, %encountered as a {\dc} increasing test efficiency. This example also serves to show a deep hierarchy of {\dcs}. +% \item Section~\ref{sec:bubba} shows FMMD applied to a loop topology---using a `Bubba' oscillator---demonstrating how FMMD differs from fault diagnosis techniques. %which uses @@ -55,8 +59,9 @@ Two analysis strategies are employed, one using initially identified {\fgs} and the second using a more complex hierarchy of %{\fgs} and {\dcs} showing that a finer grained/more de-composed 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 -by analysing a sigma delta ADC. +by applying FMMD to 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. @@ -620,9 +625,16 @@ Both approaches are followed in the next two sub-sections. \subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}} -We cannot simply re-use the {\dc} $PD$ from section~\ref{subsec:potdiv}, not just because -the potential divider is floating. That is the polarity of +Ideally we would like to re-use {\dcs} the the $PD$ from section~\ref{subsec:potdiv}, at first +glance, looks a good candidate for this. +% +However, +We cannot directly re-use $PD$ , and not just because +the potential divider is floating. +% +By floating, we mean that the polarity of the R2 side of the potential divider is determined by the output from the op-amp. +% The circuit schematic stipulates that the input is positive. What we have then, in normal operation, is an inverted potential divider. %, but in addition, it facilitates the @@ -633,7 +645,7 @@ What we have then, in normal operation, is an inverted potential divider. %symptoms. %Were the input to be guaranteed % the input will only be We can therefore view it as an inverted potential divider -and analyse it as such, see table~\ref{tbl:pdneg}. +and analyse it as such; see table~\ref{tbl:pdneg}. We assume a valid range for the output value of this circuit. Thus negative or low voltages can be considered as LOW and voltages higher than this range considered as HIGH. @@ -641,12 +653,12 @@ and voltages higher than this range considered as HIGH. \begin{table}[h+] \caption{Inverted Potential divider: Single failure analysis} \begin{tabular}{|| l | l | c | c | l ||} \hline - \textbf{Failure Scenario} & & \textbf{Inverted Pot Div Effect} & & \textbf{Symptom} \\ + \textbf{Failure Cause} & & \textbf{Inverted Pot Div Effect} & & \textbf{Symptom} \\ \hline - FS1: R1 SHORT & & $HIGH$ & & $PDHigh$ \\ \hline - FS2: R1 OPEN & & $LOW$ & & $PDLow$ \\ \hline - FS3: R2 SHORT & & $LOW$ & & $PDLow$ \\ \hline - FS4: R2 OPEN & & $HIGH$ & & $PDHigh$ \\ \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 \hline \end{tabular} \label{tbl:pdneg} @@ -695,9 +707,10 @@ and voltages higher than this range considered as HIGH. \end{figure} -We can form a {\dc} from this, and call it an inverted potential divider $INVPD$. +We can form a {\dc} from the analysis results in table~\ref{tbl:pdneg} %this, +and call it an inverted potential divider $INVPD$. -We can now form a {\fg} from the OpAmp and the $INVPD$ +We can now progress the the final stage of analysis for this amplifier, by forming a {\fg} with the OpAmp and out new {\dc} $INVPD$. \begin{table}[h+] \caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}} @@ -707,16 +720,16 @@ We can now form a {\fg} from the OpAmp and the $INVPD$ \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\ \hline - FS1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\ - FS2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline + FC1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\ + FC2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline - FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ + FC5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ - FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ + FC6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ - FS7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\ + FC7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\ - FS8: AMP LowSlew & & $ slow output \frac{\delta V}{\delta t} $ & & $ LOW PASS $ \\ \hline + FC8: AMP LowSlew & & $ slow output \frac{\delta V}{\delta t} $ & & $ LOW PASS $ \\ \hline \hline \end{tabular} \label{tbl:invamppd} @@ -824,8 +837,13 @@ We can now form a {\fg} from the OpAmp and the $INVPD$ %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). - +We can now express the failure modes for the {\dc} $INVAMP$ thus; $$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$ +We can draw a DAG representing the failure mode behaviour of +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. +%%%%% 12DEC 2012 UP to here in notes from AF email. + \subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}}