non inv op amp now has conditional compilation for dag or pld
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@ -1,4 +1,5 @@
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\def\layersep{2.5cm}
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\ifthenelse {\boolean{paper}}
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{
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@ -62,6 +63,7 @@ amplifier determined.
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A standard non inverting op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp.234]) is shown in figure \ref{fig:noninvamp}.
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/noninv.png}
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@ -77,6 +79,9 @@ They operate as a potential divider and program the minus input on the op-amp
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to balance them against the positive input, giving the voltage gain ($G_v$)
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defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
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A functional group, is an ideally small in number collection of components,
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that interact to provide
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a function or task within a system.
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@ -84,16 +89,42 @@ As the resistors work to provide a specific function, that of a potential divide
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we can treat them as a functional group. This functional group has two members, $R1$ and $R2$.
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Using the EN298 specification for resistor failure ~\cite{en298}[App.A]
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we can assign failure modes of $OPEN$ and $SHORT$ to the resistors.
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\ifthenelse {\boolean{dag}}
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{
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We can now represent a resistor in terms of its failure modes as a directed acyclic graph (DAG)
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(see figure \ref{fig:rdag}).
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\begin{figure}[h+]
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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\tikzstyle{every pin edge}=[<-,shorten <=1pt]
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\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt]
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\tikzstyle{component}=[fmmde, fill=green!50];
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\tikzstyle{failure}=[fmmde, fill=red!50];
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\tikzstyle{symptom}=[fmmde, fill=blue!50];
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\tikzstyle{annot} = [text width=4em, text centered]
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\node[component] (R) at (0,-3) {$R$};
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\node[failure] (RSHORT) at (\layersep,-2) {$R_{SHORT}$};
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\node[failure] (ROPEN) at (\layersep,-4) {$R_{OPEN}$};
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\path (R) edge (RSHORT);
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\path (R) edge (ROPEN);
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\end{tikzpicture}
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\caption{DAG representing a reistor and its failure modes}
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\label{fig:rdag}
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\end{figure}
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}
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{
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}
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Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$.
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\clearpage
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%\clearpage
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\section{Failure Mode Analysis of the Potential Divider}
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\ifthenelse {\boolean{pld}}
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{
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Modelling this as a functional group, we can draw a simple closed curve
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to represent each failure mode, taken from the components R1 and R2,
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in the potential divider, shown in figure \ref{fig:fg1}.
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\begin{figure}[h]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1.png}
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@ -101,12 +132,68 @@ in the potential divider, shown in figure \ref{fig:fg1}.
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\caption{potential divider `functional group' failure modes}
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\label{fig:fg1}
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\end{figure}
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}
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{
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}
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\ifthenelse {\boolean{dag}}
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{
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Modelling this as a functional group, we can draw this as a directed graph
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failure modes, taken from the components R1 and R2,
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in the potential divider, shown in figure \ref{fig:fg1dag}.
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\begin{figure}
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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\tikzstyle{every pin edge}=[<-,shorten <=1pt]
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\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt]
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\tikzstyle{component}=[fmmde, fill=green!50];
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\tikzstyle{failure}=[fmmde, fill=red!50];
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\tikzstyle{symptom}=[fmmde, fill=blue!50];
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\tikzstyle{annot} = [text width=4em, text centered]
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\node[component] (R1) at (0,-4) {$R_1$};
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\node[component] (R2) at (0,-6) {$R_2$};
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\node[failure] (R1SHORT) at (\layersep,-2) {$R1_{SHORT}$};
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\node[failure] (R1OPEN) at (\layersep,-4) {$R1_{OPEN}$};
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\node[failure] (R2SHORT) at (\layersep,-6) {$R2_{SHORT}$};
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\node[failure] (R2OPEN) at (\layersep,-8) {$R2_{OPEN}$};
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\path (R1) edge (R1SHORT);
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\path (R1) edge (R1OPEN);
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\path (R2) edge (R2SHORT);
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\path (R2) edge (R2OPEN);
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% Potential divider failure modes
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%
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%\node[symptom] (PDHIGH) at (\layersep*2,-4) {$PD_{HIGH}$};
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%\node[symptom] (PDLOW) at (\layersep*2,-6) {$PD_{LOW}$};
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%\path (R1OPEN) edge (PDHIGH);
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%\path (R2SHORT) edge (PDHIGH);
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%\path (R2OPEN) edge (PDLOW);
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%\path (R1SHORT) edge (PDLOW);
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\end{tikzpicture}
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\caption{DAG representing the functional group `Potential Divider'}
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\label{fig:fg1dag}
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\end{figure}
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}
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{
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}
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We can now look at each of these base component failure modes,
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and determine how they will affect the operation of the potential divider.
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%Each failure mode scenario we look at will be given a test case number,
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%which is represented on the diagram, with an asterisk marking
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%which failure modes is modelling (see figure \ref{fig:fg1a}).
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\ifthenelse {\boolean{pld}}
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{
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Each labelled asterisk in the diagram represents a failure mode scenario.
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The failure mode scenarios are given test case numbers, and an example to clarify this follows
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in table~\ref{pdfmea}.
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@ -118,8 +205,76 @@ in table~\ref{pdfmea}.
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\caption{potential divider with test cases}
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\label{fig:fg1a}
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\end{figure}
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}
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{
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}
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\ifthenelse {\boolean{dag}}
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{
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For this example we can look at single failure modes only.
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For each failure mode in our {\fg} `potential~divider'
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we can assign a test case number (see table \ref{pdfmea}).
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Each test case is analysed to determine the `symptom'
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on the potential dividers' operation. For instance
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were the resistor $R_1$ to go open, the circuit would not be grounded and the
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voltage output from it would be the +ve supply rail.
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This would mean the symptom of the failed potential divider, would be that it
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gives an output high voltage reading. We can now consider the {\fg}
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as a component in its own right, and its symptoms as its failure modes.
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From table \ref{pdfmea} we can see that resistor
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failures modes lead to common symptoms.
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By drawing connecting lines in the graph
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we can represent them.
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The {\fg} can now be considered a derived component.
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This is represented in the DAG in figure \ref{fig:fg1adag}.
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\begin{figure}[h+]
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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\tikzstyle{every pin edge}=[<-,shorten <=1pt]
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\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt]
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\tikzstyle{component}=[fmmde, fill=green!50];
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\tikzstyle{failure}=[fmmde, fill=red!50];
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\tikzstyle{symptom}=[fmmde, fill=blue!50];
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\tikzstyle{annot} = [text width=4em, text centered]
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\node[component] (R1) at (0,-4) {$R_1$};
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\node[component] (R2) at (0,-6) {$R_2$};
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\node[failure] (R1SHORT) at (\layersep,-2) {$R1_{SHORT}$};
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\node[failure] (R1OPEN) at (\layersep,-4) {$R1_{OPEN}$};
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\node[failure] (R2SHORT) at (\layersep,-6) {$R2_{SHORT}$};
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\node[failure] (R2OPEN) at (\layersep,-8) {$R2_{OPEN}$};
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\path (R1) edge (R1SHORT);
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\path (R1) edge (R1OPEN);
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\path (R2) edge (R2SHORT);
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\path (R2) edge (R2OPEN);
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% Potential divider failure modes
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%
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\node[symptom] (PDHIGH) at (\layersep*2,-4) {$PD_{HIGH}$};
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\node[symptom] (PDLOW) at (\layersep*2,-6) {$PD_{LOW}$};
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\path (R1OPEN) edge (PDHIGH);
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\path (R2SHORT) edge (PDHIGH);
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\path (R2OPEN) edge (PDLOW);
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\path (R1SHORT) edge (PDLOW);
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\end{tikzpicture}
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\caption{Failure symptoms of the `Potential Divider'}
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\label{fig:fg1adag}
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\end{figure}
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}
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{
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}
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\begin{table}[ht]
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\caption{Potential Divider: Failure Mode Effects Analysis: Single Faults} % title of Table
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\centering % used for centering table
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@ -139,15 +294,13 @@ in table~\ref{pdfmea}.
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\label{pdfmea}
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\end{table}
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\ifthenelse {\boolean{pld}}
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{
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We can now collect the symptoms of failure. From the four base component failure modes, we now
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have two symptoms, where the potential divider will give an incorrect low voltage (which we can term $LowPD$)
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or an incorrect high voltage (which we can term $HighPD$).
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We can represent the collection of these symptoms by drawing connecting lines between
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the test cases and naming them (see figure \ref{fig:fg1b}).
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\begin{figure}[h+]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/fg1b.png}
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@ -155,10 +308,10 @@ the test cases and naming them (see figure \ref{fig:fg1b}).
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\caption{Collection of potential divider failure mode symptoms}
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\label{fig:fg1b}
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\end{figure}
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%\clearpage
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We can now make a `derived component' to represent this potential divider.
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This can be named \textbf{PD}.
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This {\dc} will have two failure modes.
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We can use the symbol $\bowtie$ to represent taking the analysed
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{\fg} and creating from it, a {\dc}.
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@ -171,6 +324,40 @@ We can use the symbol $\bowtie$ to represent taking the analysed
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\caption{From functional group to derived component}
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\label{fig:dc1}
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\end{figure}
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}
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{
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}
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\ifthenelse {\boolean{dag}}
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{
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We can now represent the potential divider as a {\dc}.
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Because have its symptoms or failure mode behaviour,
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we can treat these as the failure modes of a a new {\dc}.
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We can represent it now as a DAG (see \ref{fig:dc1dag}).
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\begin{figure}[h+]
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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\tikzstyle{every pin edge}=[<-,shorten <=1pt]
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\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt]
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\tikzstyle{component}=[fmmde, fill=green!50];
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\tikzstyle{failure}=[fmmde, fill=red!50];
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\tikzstyle{symptom}=[fmmde, fill=blue!50];
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\tikzstyle{annot} = [text width=4em, text centered]
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\node[component] (PD) at (0,-3) {$PD$};
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\node[symptom] (PDHIGH) at (\layersep,-2) {$PD_{HIGH}$};
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\node[symptom] (PDLOW) at (\layersep,-4) {$PD_{LOW}$};
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\path (PD) edge (PDHIGH);
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\path (PD) edge (PDLOW);
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\end{tikzpicture}
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\caption{DAG representing a Potential Divider (PD) its failure symptoms}
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\label{fig:dc1dag}
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\end{figure}
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}
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{
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}
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Because the derived component is defined by its failure modes and
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the functional group used to derive it, we can use it
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@ -184,11 +371,11 @@ Let use now consider the op-amp. According to
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FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes:
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latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
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\ifthenelse {\boolean{pld}}
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{
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We can represent these failure modes on a diagram (see figure~\ref{fig:op1}).
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\begin{figure}[h+]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/op1.png}
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@ -196,22 +383,59 @@ We can represent these failure modes on a diagram (see figure~\ref{fig:op1}).
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\caption{Op Amp failure modes}
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\label{fig:op1}
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\end{figure}
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}
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{
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}
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\ifthenelse {\boolean{dag}}
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{
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We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
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\begin{figure}
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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\tikzstyle{every pin edge}=[<-,shorten <=1pt]
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\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt]
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\tikzstyle{component}=[fmmde, fill=green!50];
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\tikzstyle{failure}=[fmmde, fill=red!50];
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\tikzstyle{symptom}=[fmmde, fill=blue!50];
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\tikzstyle{annot} = [text width=4em, text centered]
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\node[component] (OPAMP) at (0,-4) {$OPAMP$};
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\node[failure] (OPAMPLU) at (\layersep,-0) {latchup};
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\node[failure] (OPAMPLD) at (\layersep,-2) {latchdown};
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\node[failure] (OPAMPNP) at (\layersep,-4) {noop};
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\node[failure] (OPAMPLS) at (\layersep,-6) {lowslew};
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\path (OPAMP) edge (OPAMPLU);
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\path (OPAMP) edge (OPAMPLD);
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\path (OPAMP) edge (OPAMPNP);
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\path (OPAMP) edge (OPAMPLS);
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\end{tikzpicture}
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% End of code
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\caption{DAG representing failure modes of an Op-amp}
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\label{fig:op1dag}
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\end{figure}
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}
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{
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}
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%\clearpage
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\section{Bringing the OP amp and the potential divider together}
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We can now consider bringing the OP amp and the potential divider together to
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for an amplifier. We have the failure modes of the functional group for the potential divider,
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model the non inverting amplifier. We have the failure modes of the functional group for the potential divider,
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so we do not need to consider the individual resistor failure modes that define its behaviour.
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We can make a new functional group to represent the amplifier, by bringing the component \textbf{opamp}
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and the component potential divider into a new functional group.
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and the component potential divider \textbf{PD} into a new functional group.
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\ifthenelse {\boolean{pld}}
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{
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This functional group has the failure modes from the op-amp component, and the failure modes
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from the potential divider {\dc} to analyse represented by figure~\ref{fig:fgamp}.
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from the potential divider {\dc}, represented by figure~\ref{fig:fgamp}.
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\begin{figure}[h+]
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\centering
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@ -232,6 +456,20 @@ regions) see figure~\ref{fig:fgampa}.
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\caption{Amplifier Functional Group with Test Cases}
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\label{fig:fgampa}
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\end{figure}
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}
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{
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}
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\ifthenelse {\boolean{dag}}
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{
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We can now represent the {\fg} for the non-inverting amplifier
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by bringing together the failure modes from \textbf{opamp} and \textbf{PD}.
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Each of these failure modes will be given a test case for analysis,
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and this is represented in table \ref{ampfmea}.
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}
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{
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}
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\clearpage
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@ -264,11 +502,9 @@ TC2 and TC6 can be considered as low output from the OPAMP for the application
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in hand (say milli-volt signal amplification).
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For this amplifier configuration we have three failure modes, $AMPHigh, AMPLow, LowPass$.%see figure~\ref{fig:fgampb}.
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\ifthenelse {\boolean{pld}}
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{
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We can now derive a `component' to represent this amplifier configuration (see figure ~\ref{fig:noninvampa}).
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\begin{figure}[h+]
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\centering
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\includegraphics[width=200pt,keepaspectratio=true]{./noninvopamp/noninvampa.png}
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@ -276,16 +512,85 @@ We can now derive a `component' to represent this amplifier configuration (see f
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\caption{Non Inverting Amplifier Derived Component}
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\label{fig:noninvampa}
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\end{figure}
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}
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{
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}
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\ifthenelse {\boolean{dag}}
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{
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\begin{figure}
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\centering
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\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
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\tikzstyle{every pin edge}=[<-,shorten <=1pt]
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\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt]
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\tikzstyle{component}=[fmmde, fill=green!50];
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\tikzstyle{failure}=[fmmde, fill=red!50];
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\tikzstyle{symptom}=[fmmde, fill=blue!50];
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\tikzstyle{annot} = [text width=4em, text centered]
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\node[component] (OPAMP) at (0,-4) {$OPAMP$};
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\node[failure] (OPAMPLU) at (\layersep,-0) {latchup};
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\node[failure] (OPAMPLD) at (\layersep,-2) {latchdown};
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\node[failure] (OPAMPNP) at (\layersep,-4) {noop};
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\node[failure] (OPAMPLS) at (\layersep,-6) {lowslew};
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\path (OPAMP) edge (OPAMPLU);
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\path (OPAMP) edge (OPAMPLD);
|
||||
\path (OPAMP) edge (OPAMPNP);
|
||||
\path (OPAMP) edge (OPAMPLS);
|
||||
|
||||
|
||||
\node[component] (PD) at (0,-9) {$PD$};
|
||||
\node[symptom] (PDHIGH) at (\layersep,-8) {$PD_{HIGH}$};
|
||||
\node[symptom] (PDLOW) at (\layersep,-10) {$PD_{LOW}$};
|
||||
\path (PD) edge (PDHIGH);
|
||||
\path (PD) edge (PDLOW);
|
||||
|
||||
\node[symptom] (AMPHIGH) at (\layersep*4,-3) {$AMP_{HIGH}$};
|
||||
\node[symptom] (AMPLOW) at (\layersep*4,-5) {$AMP_{LOW}$};
|
||||
\node[symptom] (AMPLP) at (\layersep*4,-7) {$LOWPASS$};
|
||||
|
||||
\path (PDLOW) edge (AMPHIGH);
|
||||
\path (OPAMPLU) edge (AMPHIGH);
|
||||
|
||||
\path (PDHIGH) edge (AMPLOW);
|
||||
\path (OPAMPNP) edge (AMPLOW);
|
||||
\path (OPAMPLD) edge (AMPLOW);
|
||||
\path (OPAMPLS) edge (AMPLP);
|
||||
\end{tikzpicture}
|
||||
% End of code
|
||||
\caption{DAG representing failure modes and symptoms of the Non Inverting Op-amp Circuit}
|
||||
\label{fig:noninvdag0}
|
||||
\end{figure}
|
||||
}
|
||||
{
|
||||
}
|
||||
|
||||
|
||||
%failure mode contours).
|
||||
%\clearpage
|
||||
\clearpage
|
||||
\section{Failure Modes from non inverting amplifier as a Directed Acyclic Graph (DAG)}
|
||||
|
||||
\ifthenelse {\boolean{pld}}
|
||||
{
|
||||
We can now represent the FMMD analysis as a directed graph, see figure \ref{fig:noninvdag0}.
|
||||
With the information structured in this way, we can trace the high level failure mode symptoms
|
||||
back to their potential causes.
|
||||
}
|
||||
{
|
||||
}
|
||||
|
||||
\ifthenelse {\boolean{dag}}
|
||||
{
|
||||
We can now expand the $PD$ {\dc} and now have a full FMMD failure mode model
|
||||
drawn as a DAG, which we can use to traverse to determine the possible causes to
|
||||
the three high level symptoms, or failure~modes of the non-inverting amplifier.
|
||||
Figure \ref{fig:noninvdag0} shows a fully expanded DAG, from which we can derive information
|
||||
to assist in building models for FTA, FMEA, FMECA and FMEDA failure mode analysis methodologies.
|
||||
}
|
||||
{
|
||||
}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
@ -421,7 +726,10 @@ in the FTA diagram. Tracing back from the top level event $AMP Low$ we are lead
|
||||
the $OPAMP latch down$ and $OP amp Noop$. These two events can cause the symptom $AMP Low$.
|
||||
We can also trace back down to the symptom $PD High$. Thus we have three
|
||||
possible cause for $AMP LOW$, and so we can draw a three input
|
||||
`or' gate below $AMP Low$, to which $OPAMP latch down$, $OP amp Noop$ and $PD High$ connect to from below.
|
||||
`xor' gate below $AMP Low$, to which $OPAMP latch down$, $OP amp Noop$ and $PD High$
|
||||
connect to from below\footnote{XOR is used here, because we are considering single failures only.
|
||||
This is a weakness in FTA diagrams, as it is clumsy to represent
|
||||
conjunction and dis-junction sourced from the same failure modes}.
|
||||
$OPAMP latch down$ and $OP amp Noop$ are base level or component events, and so we cannot
|
||||
trace them down any further.
|
||||
$PD High$ is a symptom, and can be traced further.
|
||||
@ -435,7 +743,7 @@ The FTA diagram directly derived from the FMMD DAG is shown in figure \ref{fig:n
|
||||
% Gates and symbols style
|
||||
and/.style={and gate US,thick,draw,fill=blue!40,rotate=90,
|
||||
anchor=east,xshift=-1mm},
|
||||
or/.style={or gate US,thick,draw,fill=blue!40,rotate=90,
|
||||
or/.style={xor gate US,thick,draw,fill=blue!40,rotate=90,
|
||||
anchor=east,xshift=-1mm},
|
||||
be/.style={circle,thick,draw,fill=white!60,anchor=north,
|
||||
minimum width=0.7cm},
|
||||
@ -517,16 +825,10 @@ The FTA diagram directly derived from the FMMD DAG is shown in figure \ref{fig:n
|
||||
\label{fig:noninvfta}
|
||||
\caption{Example FTA Derived from the DAG for symptom `Amp Low'}
|
||||
\end{figure}
|
||||
%\clearpage
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%\clearpage
|
||||
|
||||
%show an example fault tree, showing the causes and logical (only OR's here)
|
||||
|
||||
\subsection{Information missing in FTA}
|
||||
|
||||
to expand: Each FTA deals only with one symptom.
|
||||
|
||||
@ -14,6 +14,13 @@
|
||||
\newboolean{paper}
|
||||
\setboolean{paper}{true} % boolvar=true or false
|
||||
|
||||
\newboolean{pld}
|
||||
\setboolean{pld}{false} % boolvar=true or false : draw analysis using propositional logic diagrams
|
||||
|
||||
\newboolean{dag}
|
||||
\setboolean{dag}{true} % boolvar=true or false : draw analysis using directed acylic graphs
|
||||
\def\layersep{2.5cm}
|
||||
|
||||
|
||||
%\newtheorem{definition}{Definition:}
|
||||
|
||||
|
||||
@ -100,17 +100,27 @@ notation using logic symbols, that guides the analysis.
|
||||
This methodology was designed for
|
||||
experienced engineers sitting around a large diagram and discussing the safety aspects.
|
||||
Also the nature of a large rocket with red wire, and remote detonation
|
||||
failsafes meant that the objective was to iron out common failures
|
||||
fail-safes meant that the objective was to iron out common failures
|
||||
not to rigorously detect all possible failures.
|
||||
Consequently it was not designed to guarantee to covering all component failure modes,
|
||||
and has no rigorous in-built safeguards to ensure coverage of all possible
|
||||
system level outcomes~\cite{nasafta}[Section 1.2].
|
||||
|
||||
\paragraph{FTA: Potential to miss a large proportion of base compoenet failure modes}
|
||||
FTA, like all top~down methodologies introduces the very serious problem
|
||||
of missing component failure modes~\cite{faa}[Ch.9].
|
||||
of potentially missing base component failure modes~\cite{faa}[Ch.9].
|
||||
\paragraph{FTA: difficulty in modelling multiple/simultaneous failure modes}
|
||||
FTA does not lend its self to modelling multiple failure modes.
|
||||
Or conditions are often used where the cases for combinations
|
||||
of the or'd failure modes occurring simultaneously are not defined.
|
||||
It would be more correct, but less intuitive to use XOR gates instead.
|
||||
|
||||
|
||||
|
||||
NEED to FORMALISE EACH OF THESE TECHNIQUES AND SHOW THE WEAKNESSES AT EACH STAGE.
|
||||
|
||||
\paragraph{Outline of FTA Methodology}
|
||||
FTA works by taking an undesireable event
|
||||
FTA works by taking an undesirable event
|
||||
(or SYSTEM level failure mode or TOP level failure)
|
||||
and deciding top-down, what sub-systems it depends upon, and which
|
||||
failure events of those sub-systems could cause the top level failure.
|
||||
|
||||
Loading…
Reference in New Issue
Block a user