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git scare and then a typo in tikz arrghhhh

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Robin Clark 2011-06-12 14:05:30 +01:00
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fmmd_concept/System_safety_2011/pd.dia Normal file
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fmmd_concept/System_safety_2011/submission.tex
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@ -201,6 +201,7 @@ a {\bcfm} and not investigate other possibilities.
From the deficiencies outlined above, ideally we can form a wish list for a better methodology. From the deficiencies outlined above, ideally we can form a wish list for a better methodology.
{ \small { \small
\begin{itemize} \begin{itemize}
\label{fmmdreq}
\item Address the state explosion problem. \item Address the state explosion problem.
\item Ensure that all component failure modes be considered in the model. \item Ensure that all component failure modes be considered in the model.
\item Be easy to integrate mechanical, electronic and software models \cite{sccs}[pp.287]. \item Be easy to integrate mechanical, electronic and software models \cite{sccs}[pp.287].
@ -424,7 +425,7 @@ We can now represent a resistor in terms of its failure modes as a directed acyc
\caption{DAG representing a reistor and its failure modes} \caption{DAG representing a reistor and its failure modes}
\label{fig:rdag} \label{fig:rdag}
\end{figure} \end{figure}
%} %}section
%{ %{
%} %}
Thus or the potential divider in the circuit in figure~\ref{fig:pd}, Thus or the potential divider in the circuit in figure~\ref{fig:pd},
@ -442,6 +443,47 @@ Modelling the two resistors as a functional group, we present this as a directed
%in the potential divider, shown %in the potential divider, shown
in figure \ref{fig:fg1dag}. in figure \ref{fig:fg1dag}.
\begin{figure}[h+]
\centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
\tikzstyle{every pin edge}=[<-,shorten <=1pt]
\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=30pt,inner sep=0pt]
\tikzstyle{component}=[fmmde, fill=green!50];
\tikzstyle{failure}=[fmmde, fill=red!50];
\tikzstyle{symptom}=[fmmde, fill=blue!50];
\tikzstyle{annot} = [text width=4em, text centered]
\node[component] (R1) at (0,-4) {$R_1$};
\node[component] (R2) at (0,-6) {$R_2$};
\node[failure] (R1SHORT) at (\layersep,-2) {$R1_{SHORT}$};
\node[failure] (R1OPEN) at (\layersep,-4) {$R1_{OPEN}$};
\node[failure] (R2SHORT) at (\layersep,-6) {$R2_{SHORT}$};
\node[failure] (R2OPEN) at (\layersep,-8) {$R2_{OPEN}$};
\path (R1) edge (R1SHORT);
\path (R1) edge (R1OPEN);
\path (R2) edge (R2SHORT);
\path (R2) edge (R2OPEN);
% Potential divider failure modes
%
% \node[symptom] (PDHIGH) at (\layersep*2,-4) {$PD_{HIGH}$};
% \node[symptom] (PDLOW) at (\layersep*2,-6) {$PD_{LOW}$};
%
% \path (R1OPEN) edge (PDHIGH);
% \path (R2SHORT) edge (PDHIGH);
%
% \path (R2OPEN) edge (PDLOW);
% \path (R1SHORT) edge (PDLOW);
\end{tikzpicture}
\caption{Component Failure Modes of the `Potential Divider'}
\label{fig:fg1dag}
\end{figure}
We can now look at each of these base component failure modes, We can now look at each of these base component failure modes,
@ -577,9 +619,9 @@ we can use it
as a building block for other {\fgs}.% in the same way as we used the resistors $R1$ and $R2$. as a building block for other {\fgs}.% in the same way as we used the resistors $R1$ and $R2$.
Note that number of base failure modes, four, is reduced to two in the {\dc}. Note that number of base failure modes, four, is reduced to two in the {\dc}.
Not only have we avoided the state explosion problem of having to We avoided the state explosion problem of having to
check $R1$ and $R2$ against all other components in the system they may belong to, check $R1$ and $R2$ against all other components in the system they may belong to.
by making it a derived component, we have reduced the number of errors we need to consider at higher levels Also, by modularising the circuit as a {\dc}, we have reduced the number of errors we need to consider at higher levels
of analysis. of analysis.
% \subsection{Re-Factoring the UML Model} % \subsection{Re-Factoring the UML Model}
% %
@ -643,7 +685,7 @@ of analysis.
%By applying the methodology in section \ref{fmmdproc}, the wishlist can %By applying the methodology in section \ref{fmmdproc}, the wishlist can
%now be evaluated for the proposed FMMD methodology. %now be evaluated for the proposed FMMD methodology.
We can now evaluate the FMMD method using the criteria in section \ref{fmmdproc}. We can now evaluate the FMMD method using the criteria in section \ref{fmmdreq}.
{ \small { \small
\begin{itemize} \begin{itemize}
@ -682,12 +724,12 @@ for all SYSTEM failure modes.
The minimal cuts sets for the SYSTEM level failures can have computed MTTF The minimal cuts sets for the SYSTEM level failures can have computed MTTF
and danger evaluation statistics sourced from the component failure mode statistics \cite {mil1991}. and danger evaluation statistics sourced from the component failure mode statistics \cite {mil1991}.
\item{ It should be easy to use, ideally % \item{ It should be easy to use, ideally
using a graphical syntax (as opposed to a formal mathematical one).} % using a graphical syntax (as opposed to a formal mathematical one).}
A modified form of constraint diagram (an extension of Euler diagrams) has % A modified form of constraint diagram (an extension of Euler diagrams) has
been developed to support the FMMD methodology. % been developed to support the FMMD methodology.
This uses Euler circles to represent failure modes, and spiders to collect symptoms, to % This uses Euler circles to represent failure modes, and spiders to collect symptoms, to
advance a {\fg} to a {\dc}. % advance a {\fg} to a {\dc}.
\item{ From the top down the failure mode model should follow a logical de-composition of the functionality \item{ From the top down the failure mode model should follow a logical de-composition of the functionality
@ -724,7 +766,7 @@ particular field. It can be applied to mechanical, electrical or software domain
It can therefore be used to analyse systems comprised of electrical, It can therefore be used to analyse systems comprised of electrical,
mechanical and software elements in one integrated model. mechanical and software elements in one integrated model.
\today %\today
% %
{ \small { \small
\bibliographystyle{plain} \bibliographystyle{plain}

245
invopamp/invopamp.tex
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@ -5,87 +5,98 @@
{ {
\abstract{ \abstract{
This paper analyses an inverting op-amp This paper analyses an inverting op-amp
configuration, with the opamp and gain resistors using the FMMD configuration %, with the opamp and gain resistors
using the FMMD
methodology. methodology.
% %
It has three base components, two resistors The circuit under analysis has five `base components', four resistors % two resistors programming gain, two programming a reference, or virtual ground voltage
and one op-amp. and one op-amp.
%
Two resistors are used as a current balance/virtual ground to program the gain
of the amplifier and another pair to set the reference or virtual ground voltage.
We consider the resistors setting the reference voltage as a functional group, a potential divider. %.$PD$.
%where their function is to operate as a virtual ground voltage reference.
The gain resistors work with the op-amp to determine the gain characteristics, and therefore the two gain resistors and the op-amp
form a second functional group.% $GAMP$.
%
The base component failure modes
are used to model each functional group %the amplifier from
from a failure mode perspective.
%
We determine the failure symptoms from each of these {\fgs} and
create {\dcs} to represent them.
We can have a {\dc} represetnting the potential~divider and another representing the gain stage.
The two resistors are used as a current balance/virtual ground to program the gain We can now create a functional group representing the inverting amplifier,
of the amplifier. We consider the two resistors as a functional group by bringing the {\dcs} %
where their function is to operate as a current balance/virtual ground. $PD$ and $GMAP$
together to form a higher level functional group .
% %
The base component error modes of the This can be analysed and a derived component, %$INVAMP$
resistors are used to model the current balance/virtual ground from created, to represent the failure mode behaviour of the inverting
a failure mode perspective. amplifier.
%
We determine the failure symptoms of the current balance/virtual ground and
consider these as failure modes of a new derived component.
We can now create a functional group representing the non-inverting amplifier,
by bringing the failure modes from the current balance/virtual ground and
the op-amp into a functional group.
%
This can be analysed and a derived component to represent the non inverting
amplifier determined.
} }
\section{Introduction} \section{Introduction}
} }
{ {
This chapter analyses an inverting op-amp This chapter analyses an inverting op-amp
configuration, with the opamp and gain resistors using the FMMD configuration %, with the opamp and gain resistors
using the FMMD
methodology. methodology.
% %
It has three base components, two resistors The circuit under analysis has five 'base components', four resistors % two resistors programming gain, two programming a reference, or virtual ground voltage
and one op-amp.\section{Introduction} and one op-amp.
%
The two resistors are used as a current balance/virtual ground to program the gain Two resistors are used as a current balance/virtual ground to program the gain
of the amplifier. We consider the two resistors as a functional group of the amplifier and another pair to set the reference or virtual ground voltage.
where their function is to operate as a current balance/virtual ground. We consider the resistors setting the reference voltage as a functional group, a potential divider $PD$.
This chapter re-uses the $PD$ derived component from \ref{lab:nonivopamp}.
%where their function is to operate as a virtual ground voltage reference.
The gain resistors work with the op-amp to determine the gain characteristics, and therefore the two gain resistors and the op-amp
form a second functional group $GAMP$.
% %
The base component error modes of the The base component error modes of the
resistors are used to model the current balance/virtual ground from components are used to model each functional group %the amplifier from
a failure mode perspective. from a failure mode perspective.
% %
We determine the failure symptoms of the current balance/virtual ground and We determine the failure symptoms from each of these {\fgs} and
consider these as failure modes of a new derived component. create {\dcs} to represent them.
We can create a functional group representing the non-inverting amplifier, We can now create a functional group representing the inverting amplifier,
by bringing the failure modes from the current balance/virtual ground and by bringing the {\dcs} $PD$ and $GMAP$ together to form a higher level functional group .
the op-amp into a functional group.
% %
This can now be analysed and a derived component to represent the non inverting This can be analysed and a derived component, $INVAMP$ created, to represent the inverting
amplifier determined. amplifier determined.
\section{Introduction: The non-inverting amplifier} \section{Introduction: The non-inverting amplifier}
} }
A standard non inverting op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp.234]) is shown in figure \ref{fig:noninvamp}. A standard non inverting op amp (from ``The Art of Electronics'' ~\cite{aoe}[pp.178]) is shown in figure \ref{fig:invamp}.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/noninv.png} \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/inv.png}
% noninv.jpg: 341x186 pixel, 72dpi, 12.03x6.56 cm, bb=0 0 341 186 % noninv.jpg: 341x186 pixel, 72dpi, 12.03x6.56 cm, bb=0 0 341 186
\caption{Standard non inverting amplifier configuration} \caption{inverting amplifier configuration with potential divider for reference/virtual ground}
\label{fig:noninvamp} \label{fig:noninvamp}
\end{figure} \end{figure}
The function of the resistors in this circuit is to set the amplifier gain. The voltage gain of this circuit ($G_v$)
They operate as a current balance/virtual ground and program the minus input on the op-amp defined by $ G_v = -\frac{R4}{R3} $.
to balance them against the positive input, giving the voltage gain ($G_v$)
defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
\section{Potential Divider - OP-AMP Virtual ground reference}
A functional group, is an ideally small in number collection of components, A functional group, is an ideally small in number collection of components,
that interact to provide that interact to provide
a function or task within a system. a function or task within a system.
As the resistors work to provide a specific function, that of a current balance/virtual ground, As the resistors work to provide a specific function, that of a potential divider to program a given voltage,
we can treat them as a functional group. This functional group has two members, $R1$ and $R2$. we can treat them as a functional group. This functional group has two members, $R1$ and $R2$.
Using the EN298 specification for resistor failure ~\cite{en298}[App.A] Using the EN298 specification for resistor failure ~\cite{en298}[App.A]
we can assign failure modes of $OPEN$ and $SHORT$ to the resistors. we can assign failure modes of $OPEN$ and $SHORT$ to the resistors.
@ -114,7 +125,7 @@ We can now represent a resistor in terms of its failure modes as a directed acyc
} }
{ {
} }
Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$. Thus for the potential~divider stage $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$.
%\clearpage %\clearpage
@ -124,12 +135,12 @@ Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes
{ {
Modelling this as a functional group, we can draw a simple closed curve Modelling this as a functional group, we can draw a simple closed curve
to represent each failure mode, taken from the components R1 and R2, to represent each failure mode, taken from the components R1 and R2,
in the current balance/virtual ground, shown in figure \ref{fig:fg1}. in the potential divider, shown in figure \ref{fig:fg1}.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png} \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1.png}
% fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 % fg1.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
\caption{current balance/virtual ground `functional group' failure modes} \caption{potential divider failure modes}
\label{fig:fg1} \label{fig:fg1}
\end{figure} \end{figure}
} }
@ -140,7 +151,7 @@ in the current balance/virtual ground, shown in figure \ref{fig:fg1}.
{ {
Modelling this as a functional group, we can draw this as a directed graph Modelling this as a functional group, we can draw this as a directed graph
failure modes, taken from the components R1 and R2, failure modes, taken from the components R1 and R2,
in the current balance/virtual ground, shown in figure \ref{fig:fg1dag}. in the potential divider, shown in figure \ref{fig:fg1dag}.
\begin{figure} \begin{figure}
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -187,7 +198,7 @@ in the current balance/virtual ground, shown in figure \ref{fig:fg1dag}.
} }
We can now look at each of these base component failure modes, We can now look at each of these base component failure modes,
and determine how they will affect the operation of the current balance/virtual ground. and determine how they will affect the operation of the potential divider.
%Each failure mode scenario we look at will be given a test case number, %Each failure mode scenario we look at will be given a test case number,
%which is represented on the diagram, with an asterisk marking %which is represented on the diagram, with an asterisk marking
%which failure modes is modelling (see figure \ref{fig:fg1a}). %which failure modes is modelling (see figure \ref{fig:fg1a}).
@ -202,7 +213,7 @@ in table~\ref{pdfmea}.
\centering \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1a.png} \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1a.png}
% fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 % fg1a.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
\caption{current balance/virtual ground with test cases} \caption{potential divider with test cases}
\label{fig:fg1a} \label{fig:fg1a}
\end{figure} \end{figure}
} }
@ -216,10 +227,10 @@ For this example we can look at single failure modes only.
For each failure mode in our {\fg} `potential~divider' For each failure mode in our {\fg} `potential~divider'
we can assign a test case number (see table \ref{pdfmea}). we can assign a test case number (see table \ref{pdfmea}).
Each test case is analysed to determine the `symptom' Each test case is analysed to determine the `symptom'
on the current balance/virtual grounds' operation. For instance on the potential diverders operation. For instance
were the resistor $R_1$ to go open, the circuit would not be grounded and the were the resistor $R_1$ to go open, the circuit would not be grounded and the
voltage output from it would be the +ve supply rail. voltage output from it would be the +ve supply rail.
This would mean the symptom of the failed current balance/virtual ground, would be that it This would mean the symptom of the failed potential divider, would be that it
gives an output high voltage reading. We can now consider the {\fg} gives an output high voltage reading. We can now consider the {\fg}
as a component in its own right, and its symptoms as its failure modes. as a component in its own right, and its symptoms as its failure modes.
@ -301,13 +312,13 @@ have two symptoms, where the current balance/virtual ground will give an incorre
or an incorrect high voltage (which we can term $HighPD$). or an incorrect high voltage (which we can term $HighPD$).
We can represent the collection of these symptoms by drawing connecting lines between We can represent the collection of these symptoms by drawing connecting lines between
the test cases and naming them (see figure \ref{fig:fg1b}). the test cases and naming them (see figure \ref{fig:fg1b}).
\begin{figure}[h+] % \begin{figure}[h+]
\centering % \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1b.png} % \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/fg1b.png}
% fg1b.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271 % % fg1b.jpg: 430x271 pixel, 72dpi, 15.17x9.56 cm, bb=0 0 430 271
\caption{Collection of current balance/virtual ground failure mode symptoms} % \caption{Collection of current balance/virtual ground failure mode symptoms}
\label{fig:fg1b} % \label{fig:fg1b}
\end{figure} % \end{figure}
%\clearpage %\clearpage
We can now make a `derived component' to represent this current balance/virtual ground. We can now make a `derived component' to represent this current balance/virtual ground.
@ -317,13 +328,13 @@ We can use the symbol $\bowtie$ to represent taking the analysed
{\fg} and creating from it, a {\dc}. {\fg} and creating from it, a {\dc}.
%We could represent it algebraically thus: $ \bowtie(PotDiv) = %We could represent it algebraically thus: $ \bowtie(PotDiv) =
\begin{figure}[h+] % \begin{figure}[h+]
\centering % \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/dc1.png} % \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/dc1.png}
% dc1.jpg: 430x619 pixel, 72dpi, 15.17x21.84 cm, bb=0 0 430 619 % % dc1.jpg: 430x619 pixel, 72dpi, 15.17x21.84 cm, bb=0 0 430 619
\caption{From functional group to derived component} % \caption{From functional group to derived component}
\label{fig:dc1} % \label{fig:dc1}
\end{figure} % \end{figure}
} }
{ {
} }
@ -365,17 +376,61 @@ as a building block for other {\fgs} in the same way as we used the resistors $R
\clearpage \clearpage
\section{Failure Mode Analysis of the OP-AMP} \section{Failure Mode Analysis of the OP-AMP Gain Section}
Let use now consider the op-amp. According to Let use now consider the op-amp. According to
FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes: FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes:
latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%). latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
The op-amp gain section use resistors $R4$ and $R3$ to determine the amount of negative gain.
Each of the reistors have two failure modes $SHORT$ and $OPEN$.
For our gain stage amplifier section, we have a {\fg} comprising
the opamp, R3 and R4.
\paragraph{Functional group context}
We have to consider the context the amplifier is used it to determine its failure mode symptoms.
If this were to be a instrumentaion amplifier, the low slew failure mode may not be a problem at all
but could affect an audio amplifier by introducing low-pass filtering.
TC2, TC1 and TC7, where there is no gain or ref voltage is output, could be very bad for an instrumentation amplifier
because the oputput may be in a valid reading range for the application.
For the purpose of example we shall consider this amplifier to be an instumentation
amplifier.
\begin{table}[ht]
\caption{Inverting Amplifier Gain Stage: Failure Mode Effects Analysis: Single Faults} % title of Table
\centering % used for centering table
\begin{tabular}{||l|c|c|l|l||}
\hline \hline
\textbf{Test} & \textbf{Amplifier} & \textbf{ } & \textbf{General} \\
\textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symtom Description} \\
% R & wire & res + & res - & description
\hline
\hline
TC1: $R3_{OPEN}$ & Ref V. Output & & \\
TC2: $R3_{SHORT}$ & High Gain & & OUT\_OF\_RANGE \\ \hline
TC3: $R4_{OPEN}$ & High Gain & & OUT\_OF\_RANGE \\
TC4: $R4_{SHORT}$ & No Gain & & \\ \hline
TC5: $OPAMP$ LatchUP & High Output +Ve & & OUT\_OF\_RANGE \\
TC6: $OPAMP$ LatchDown & Low Output -Ve & & OUT\_OF\_RANGE \\ \hline
TC7: $OPAMP$ No Operation & Low Output -Ve & & OUT\_OF\_RANGE \\
TC8: $OPAMP$ Low Slew & Low pass filter & & \\ \hline
%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
\hline
\end{tabular}
\label{ampfmea}
\end{table}
\ifthenelse {\boolean{pld}} \ifthenelse {\boolean{pld}}
{ {
We can represent these failure modes on a diagram (see figure~\ref{fig:op1}). We can represent these failure modes of this {\fg} on a diagram (see figure~\ref{fig:op1}).
\begin{figure}[h+] \begin{figure}[h+]
\centering \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/op1.png} \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/op1.png}
@ -389,7 +444,7 @@ We can represent these failure modes on a diagram (see figure~\ref{fig:op1}).
\ifthenelse {\boolean{dag}} \ifthenelse {\boolean{dag}}
{ {
We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}). We can represent the failure modes of this {\fg} on a DAG (see figure~\ref{fig:op1dag}).
\begin{figure} \begin{figure}
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -407,11 +462,30 @@ We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
\node[failure] (OPAMPNP) at (\layersep,-4) {noop}; \node[failure] (OPAMPNP) at (\layersep,-4) {noop};
\node[failure] (OPAMPLS) at (\layersep,-6) {lowslew}; \node[failure] (OPAMPLS) at (\layersep,-6) {lowslew};
\path (OPAMP) edge (OPAMPLU); \path (OPAMP) edge (OPAMPLU);
\path (OPAMP) edge (OPAMPLD); \path (OPAMP) edge (OPAMPLD);
\path (OPAMP) edge (OPAMPNP); \path (OPAMP) edge (OPAMPNP);
\path (OPAMP) edge (OPAMPLS); \path (OPAMP) edge (OPAMPLS);
\node[component] (R3) at (0,-9) {$R3$};
\node[failure] (R3SHORT) at (\layersep,-8) {SHORT};
\node[failure] (R3OPEN) at (\layersep,-10) {OPEN};
\path (R3) edge (R3SHORT);
\path (R3) edge (R3OPEN);
\node[component] (R4) at (0,-14) {$R4$};
\node[failure] (R4SHORT) at (\layersep,-13) {SHORT};
\node[failure] (R4OPEN) at (\layersep,-15) {OPEN};
\path (R4) edge (R4SHORT);
\path (R4) edge (R4OPEN);
\end{tikzpicture} \end{tikzpicture}
% End of code % End of code
\caption{DAG representing failure modes of an Op-amp} \caption{DAG representing failure modes of an Op-amp}
@ -424,7 +498,7 @@ We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
%\clearpage %\clearpage
\section{Bringing the OP amp and the current balance/virtual ground together} \section{{\fg} forrmed from OP amp and the potential divider {\dcs}}
We can now consider bringing the OP amp and the current balance/virtual ground together to We can now consider bringing the OP amp and the current balance/virtual ground together to
model the non inverting amplifier. We have the failure modes of the functional group for the current balance/virtual ground, model the non inverting amplifier. We have the failure modes of the functional group for the current balance/virtual ground,
@ -465,7 +539,6 @@ We can now crate a {\fg} for the non-inverting amplifier
by bringing together the failure modes from \textbf{opamp} and \textbf{PD}. by bringing together the failure modes from \textbf{opamp} and \textbf{PD}.
Each of these failure modes will be given a test case for analysis, Each of these failure modes will be given a test case for analysis,
and this is represented in table \ref{ampfmea}. and this is represented in table \ref{ampfmea}.
} }
{ {
} }
@ -473,7 +546,7 @@ and this is represented in table \ref{ampfmea}.
\clearpage \clearpage
\begin{table}[ht] \begin{table}[ht]
\caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table \caption{Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table
\centering % used for centering table \centering % used for centering table
\begin{tabular}{||l|c|c|l|l||} \begin{tabular}{||l|c|c|l|l||}
\hline \hline \hline \hline
@ -482,12 +555,20 @@ and this is represented in table \ref{ampfmea}.
% R & wire & res + & res - & description % R & wire & res + & res - & description
\hline \hline
\hline \hline
TC1: $OPAMP$ LatchUP & Output High & & AMPHigh \\ % TC1: $R3_{OPEN}$ & Output High & & AMPHigh \\
TC2: $OPAMP$ LatchDown & Output Low : Low gain& & AMPLow \\ \hline % TC2: $R3_{SHORT}$ & Output Low : Low gain& & AMPLow \\ \hline
TC3: $OPAMP$ No Operation & Output Low & & AMPLow \\ %
TC4: $OPAMP$ Low Slew & Low pass filtering & & LowPass \\ \hline % TC3: $R4_{OPEN}$ LatchUP & Output High & & AMPHigh \\
TC5: $PD$ LowPD & Output High & & AMPHigh \\ \hline % TC4: $R4_{SHORT}$ LatchDown & Output Low : Low gain& & AMPLow \\ \hline
TC6: $PD$ HighPD & Output Low : Low Gain& & AMPLow \\ \hline %
% TC5: $OPAMP$ LatchUP & Output High & & AMPHigh \\
% TC6: $OPAMP$ LatchDown & Output Low : Low gain& & AMPLow \\ \hline
% TC7: $OPAMP$ No Operation & Output Low & & AMPLow \\
% TC8: $OPAMP$ Low Slew & Low pass filtering & & LowPass \\ \hline
TC9: $PD$ LowPD & Output High & & AMPHigh \\
TC10: $PD$ HighPD & Output Low : Low Gain& & AMPLow \\ \hline
%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
\hline \hline
\end{tabular} \end{tabular}
@ -504,13 +585,13 @@ For this amplifier configuration we have three failure modes, $AMPHigh, AMPLow,
\ifthenelse {\boolean{pld}} \ifthenelse {\boolean{pld}}
{ {
We can now derive a `component' to represent this amplifier configuration (see figure ~\ref{fig:noninvampa}). We can now derive a `component' to represent this amplifier configuration (see figure ~\ref{fig:noninvampa}).
\begin{figure}[h+] %\begin{figure}[h+]
\centering % \centering
\includegraphics[width=200pt,keepaspectratio=true]{./invopamp/noninvampa.png} % \includegraphics[width=200pt,keepaspectratio=true]{./invopamp/noninvampa.png}
% noninvampa.jpg: 436x720 pixel, 72dpi, 15.38x25.40 cm, bb=0 0 436 720 % % noninvampa.jpg: 436x720 pixel, 72dpi, 15.38x25.40 cm, bb=0 0 436 720
\caption{Non Inverting Amplifier Derived Component} % \caption{Non Inverting Amplifier Derived Component}
\label{fig:noninvampa} % \label{fig:noninvampa}
\end{figure} %\end{figure}
} }
{ {
} }

9
noninvopamp/noninvopamp.tex
View File

@ -1,5 +1,5 @@
\label{lab:nonivopamp}
\ifthenelse {\boolean{paper}} \ifthenelse {\boolean{paper}}
{ {
@ -723,6 +723,13 @@ to assist in building models for FTA, FMEA, FMECA and FMEDA failure mode analysi
\section{Deriving FTA, FMEA, FMECA and FMEDA models from the DAG}
The example here is very low level, or in other words is a very sysple sub-system.
The FTA, FMEA, FMECA and FMEDA would normally be applied to a very large
safety critical system (i.e. a car or a steam producing boiler plant).
Th examples here show how the DAG provides a frame work for
producing skeleton data forms for all these methodologies.
\section{Extracting Fault Trees from the DAG} \section{Extracting Fault Trees from the DAG}

4
thesis.tex
View File

@ -141,14 +141,14 @@
\chapter{FMMD functional~groups to \\derived component example : Non Inverting Op-AMP} \chapter{FMMD functional~groups to \\derived component example : Non Inverting Op-AMP}
\newboolean{dag} \newboolean{dag}
\setboolean{dag}{false} % boolvar=true or false \setboolean{dag}{true} % boolvar=true or false
\newboolean{pld} \newboolean{pld}
\setboolean{pld}{true} % boolvar=true or false \setboolean{pld}{true} % boolvar=true or false
\typeout{ ---------------- non inv op amp} \typeout{ ---------------- non inv op amp}
\input{noninvopamp/noninvopamp} \input{noninvopamp/noninvopamp}
\chapter{FMMD functional~groups to \\derived component example : Inverting Op-AMP} \chapter{FMMD functional~groups to \\derived component example : Inverting Op-AMP}
\setboolean{dag}{false} % boolvar=true or false \setboolean{dag}{true} % boolvar=true or false
\setboolean{pld}{true} % boolvar=true or false \setboolean{pld}{true} % boolvar=true or false
\typeout{ ---------------- non inv op amp} \typeout{ ---------------- non inv op amp}
\input{invopamp/invopamp} \input{invopamp/invopamp}