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363
submission_thesis/CH2_FMEA/copy.tex
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@ -51,6 +51,369 @@ and explores some concepts with which we can discuss and evaluate
the effectiveness of FMEA.
\section{Determining the failure modes of components}
\label{sec:determine_fms}
In order to apply any form of FMEA we need to know the ways in which
the components we are using can fail.
%
A good introduction to hardware and software failure modes may be found in~\cite{sccs}[pp.114-124].
%
Typically when choosing components for a design, we look at manufacturers' data sheets
which describe functionality, physical dimensions
environmental ranges, tolerances and can indicate how a component may fail/misbehave
under given conditions.
%
How base components could fail internally, is not of interest to an FMEA investigation.
The FMEA investigator needs to know what failure behaviour a component may exhibit. %, or in other words, its modes of failure.
%
A large body of literature exists which gives guidance for determining component {\fms}.
%
For this study FMD-91~\cite{fmd91} and the gas burner standard EN298~\cite{en298} are examined.
%Some standards prescribe specific failure modes for generic component types.
In EN298 failure modes for most generic component types are listed, or if not listed,
determined by considering all pins OPEN and all adjacent pins shorted.
%a procedure where failure scenarios of all pins OPEN and all adjacent pins shorted
%are examined.
%
%
FMD-91 is a reference document released into the public domain by the United States DOD
and describes `failures' of common electronic components, with percentage statistics for each failure.
%
FMD-91 entries include general descriptions of internal failures alongside {\fms} of use to an FMEA investigation.
%
FMD-91 entries need, in some cases, some interpretation to be mapped to a clear set of
component {\fms} suitable for use in FMEA.
A third document, MIL-1991~\cite{mil1991} often used alongside FMD-91, provides overall reliability statistics for
component types, but does not detail specific failure modes.
%
Using MIL1991 in conjunction with FMD-91, we can determine statistics for the failure modes
of component types.
%
The FMEDA process from European standard EN61508~\cite{en61508} for instance,
requires statistics for Meantime to Failure (MTTF) for all {\bc} failure modes.
% One is from the US military document FMD-91, where internal failures
% of components are described (with stats).
%
% The other is EN298 where the failure modes for generic component types are prescribed, or
% determined by a procedure where failure scenarios of all pins OPEN and all adjacent pins shorted
% is applied. These techniques
%
% The FMD-91 entries need, in some cases, some interpretation to be mapped to
% component failure symptoms, but include failure modes that can be due to internal failures.
% The EN298 SHORT/OPEN procedure cannot determine failures due to internal causes but can be applied to any IC.
%
% Could I come in and see you Chris to quickly discuss these.
%
% I hope to have chapter 5 finished by the end of March, chapter 5 being the
% electronics examples for the FMMD methodology.
In this section we look in detail at two common electrical components and examine how
the two sources of information define their failure mode behaviour.
We look at the reasons why some known failure modes % are omitted, or presented in
%specific but unintuitive ways.
%We compare the US. military published failure mode specifications wi
can be found in one source but not in the others and vice versa.
%
Finally we compare and contrast the failure modes determined for these components
from the FMD-91 reference source and from the guidelines of the
European burner standard EN298.
\subsection{Failure mode determination for generic resistor.}
\label{sec:resistorfm}
%- Failure modes. Prescribed failure modes EN298 - FMD91
\paragraph{Resistor failure modes according to FMD-91.}
The resistor is a ubiquitous component in electronics, and is therefore a good candidate for detailed examination of its failure modes.
%
FMD-91\cite{fmd91}[3-178] lists many types of resistor
and lists many possible failure causes.
For instance for {\textbf{Resistor,~Fixed,~Film}} we are given the following failure causes:
\begin{itemize}
\item Opened 52\%
\item Drift 31.8\%
\item Film Imperfections 5.1\%
\item Substrate defects 5.1\%
\item Shorted 3.9\%
\item Lead damage 1.9\%
\end{itemize}
% This information may be of interest to the manufacturer of resistors, but it does not directly
% help a circuit designer.
% The circuit designer is not interested in the causes of resistor failure, but to build in contingency
% against {\fms} that the resistor could exhibit.
% We can determine these {\fms} by converting the internal failure descriptions
% to {\fms} thus:
To make this useful for FMEA/FMMD we must assign each failure cause to an arbitrary failure mode descriptor
as shown below.
%
%and map these failure causes to three symptoms,
%drift (resistance value changing), open and short.
\begin{itemize}
\item Opened 52\% $\mapsto$ OPENED
\item Drift 31.8\% $\mapsto$ DRIFT
\item Film Imperfections 5.1\% $\mapsto$ OPEN
\item Substrate defects 5.1\% $\mapsto$ OPEN
\item Shorted 3.9\% $\mapsto$ SHORT
\item Lead damage 1.9\% $\mapsto$ OPEN.
\end{itemize}
%
The main causes of drift are overloading of components.
This is borne out in in the FMD-91~\cite{fmd91}[232] entry for a resistor network where the failure
modes do not include drift.
%
If we can ensure that our resistors will not be exposed to overload conditions, the
probability of drift (sometimes called parameter change) occurring
is significantly reduced, enough for some standards to exclude it~\cite{en298}~\cite{en230}.
\paragraph{Resistor failure modes according to EN298.}
EN298, the European gas burner safety standard, tends to be give failure modes more directly usable by FMEA than FMD-91.
EN298 requires that a full FMEA be undertaken, examining all failure modes
of all electronic components~\cite{en298}[11.2 5] as part of the certification process.
%
Annex A of EN298, prescribes failure modes for common components
and guidance on determining sets of failure modes for complex components (i.e. integrated circuits).
EN298~\cite{en298}[Annex A] (for most types of resistor)
only requires that the failure mode OPEN be considered for FMEA analysis.
%
For resistor types not specifically listed in EN298, the failure modes
are considered to be either OPEN or SHORT.
The reason that parameter change is not considered for resistors chosen for an EN298 compliant system, is that they must be must be {\em downrated}.
That is to say the power and voltage ratings of components must be calculated
for maximum possible exposure, with a 40\% margin of error. This reduces the probability
that the resistors will be overloaded,
and thus subject to drift/parameter change.
% XXXXXX get ref from colin T
%If a resistor was rated for instance for
%These are useful for resistor manufacturersthey have three failure modes
%EN298
%Parameter change not considered for EN298 because the resistors are down-rated from
%maximum possible voltage exposure -- find refs.
% FMD-91 gives the following percentages for failure rates in
% \label{downrate}
% The parameter change, is usually a failure mode associated with over stressing the component.
%In a system designed to typical safety critical constraints (as in EN298)
%these environmentally induced failure modes need not be considered.
\subsubsection{Resistor Failure Modes}
\label{sec:res_fms}
For this study we will take the conservative view from EN298, and consider the failure
modes for a generic resistor to be both OPEN and SHORT.
i.e.
\label{ros}
$$ fm(R) = \{ OPEN, SHORT \} . $$
\subsection{Failure modes determination for generic operational amplifier}
\begin{figure}[h+]
\centering
\includegraphics[width=200pt]{CH5_Examples/lm258pinout.jpg}
% lm258pinout.jpg: 478x348 pixel, 96dpi, 12.65x9.21 cm, bb=0 0 359 261
\caption{Pinout for an LM358 dual OpAmp}
\label{fig:lm258}
\end{figure}
The operational amplifier (op-amp) %is a differential amplifier and
is very widely used in nearly all fields of modern analogue electronics.
They are typically packaged in dual or quad configurations---meaning
that a chip will typically contain two or four amplifiers.
For the purpose of example, we look at
a typical op-amp designed for instrumentation and measurement, the dual packaged version of the LM358~\cite{lm358}
(see figure~\ref{fig:lm258}), and use this to compare the failure mode derivations from FMD-91 and EN298.
\paragraph{ Failure Modes of an OpAmp according to FMD-91 }
%Literature suggests, latch up, latch down and oscillation.
For OpAmp failures modes, FMD-91\cite{fmd91}{3-116] states,
\begin{itemize}
\item Degraded Output 50\% Low Slew rate - poor die attach
\item No Operation - overstress 31.3\%
\item Shorted $V_+$ to $V_-$, overstress, resistive short in amplifier 12.5\%
\item Opened $V_+$ open 6.3\%
\end{itemize}
Again these are mostly internal causes of failure, more of interest to the component manufacturer
than a designer looking for the symptoms of failure.
We need to translate these failure causes within the OpAmp into {\fms}.
We can look at each failure cause in turn, and map it to potential {\fms} suitable for use in FMEA
investigations.
\paragraph{OpAmp failure cause: Poor Die attach}
The symptom for this is given as a low slew rate. This means that the op-amp
will not react quickly to changes on its input terminals.
This is a failure symptom that may not be of concern in a slow responding system like an
instrumentation amplifier. However, where higher frequencies are being processed,
a signal may entirely be lost.
We can map this failure cause to a {\fm}, and we can call it $LOW_{slew}$.
\paragraph{No Operation - over stress}
Here the OP\_AMP has been damaged, and the output may be held HIGH or LOW, or may be effectively tri-stated
, i.e. not able to drive circuitry in along the next stages of the signal path: we can call this state NOOP (no Operation).
%
We can map this failure cause to three {\fms}, $LOW$, $HIGH$, $NOOP$.
\paragraph{Shorted $V_+$ to $V_-$}
Due to the high intrinsic gain of an op-amp, and the effect of offset currents,
this will force the output HIGH or LOW.
We map this failure cause to $HIGH$ or $LOW$.
\paragraph{Open $V_+$}
This failure cause will mean that the minus input will have the very high gain
of the OpAmp applied to it, and the output will be forced HIGH or LOW.
We map this failure cause to $HIGH$ or $LOW$.
\paragraph{Collecting OpAmp failure modes from FMD-91}
We can define an OpAmp, under FMD-91 definitions to have the following {\fms}.
\begin{equation}
\label{eqn:opampfms}
fm(OpAmp) = \{ HIGH, LOW, NOOP, LOW_{slew} \}
\end{equation}
\paragraph{Failure Modes of an OpAmp according to EN298}
EN298 does not specifically define OP\_AMPS failure modes; these can be determined
by following a procedure for `integrated~circuits' outlined in
annex~A~\cite{en298}[A.1 note e].
This demands that all open connections, and shorts between adjacent pins be considered as failure scenarios.
We examine these failure scenarios on the dual packaged $LM358$~\cite{lm358}%\mu741$
and determine its {\fms} in table ~\ref{tbl:lm358}.
Collecting the op-amp failure modes from table ~\ref{tbl:lm358} we obtain the same {\fms}
that we got from FMD-91, listed in equation~\ref{eqn:opampfms}.
%\paragraph{EN298: Open and shorted pin failure symptom determination technique}
\begin{table}[h+]
\caption{LM358: EN298 Open and shorted pin failure symptom determination technique}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{Amplifier Effect} & & \textbf{Symptom(s)} \\
\textbf{Failure} & & \textbf{Amplifier Effect} & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\
\hline
& & & & \\ \hline
FS1: PIN 1 OPEN & & A output open & & $NOOP_A$ \\ \hline
FS2: PIN 2 OPEN & & A-input disconnected, & & \\
& & infinite gain on A+input & & $LOW_A$ or $HIGH_A$ \\ \hline
FS3: PIN 3 OPEN & & A+input disconnected, & & \\
& & infinite gain on A-input & & $LOW_A$ or $HIGH_A$ \\ \hline
FS4: PIN 4 OPEN & & power to chip (ground) disconnected & & $NOOP_A$ and $NOOP_B$ \\ \hline
FS5: PIN 5 OPEN & & B+input disconnected, & & \\
& & infinite gain on B-input & & $LOW_B$ or $HIGH_B$ \\ \hline
FS6: PIN 6 OPEN & & B-input disconnected, & & \\
FS6: PIN 6 OPEN & & infinite gain on B+input & & $LOW_B$ or $HIGH_B$ \\ \hline
FS7: PIN 7 OPEN & & B output open & & $NOOP_B$ \\ \hline
FS8: PIN 8 OPEN & & power to chip & & \\
FS8: PIN 8 OPEN & & (Vcc) disconnected & & $NOOP_A$ and $NOOP_B$ \\ \hline
& & & & \\
& & & & \\
& & & & \\ \hline
FS9: PIN 1 $\stackrel{short}{\longrightarrow}$ PIN 2 & & A -ve 100\% Feed back, low gain & & $LOW_A$ \\ \hline
FS10: PIN 2 $\stackrel{short}{\longrightarrow}$ PIN 3 & & A inputs shorted, & & \\
& & output controlled by internal offset & & $LOW_A$ or $HIGH_A$ \\ \hline
FS11: PIN 3 $\stackrel{short}{\longrightarrow}$ PIN 4 & & A + input held to ground & & $LOW_A$ \\ \hline
FS12: PIN 5 $\stackrel{short}{\longrightarrow}$ PIN 6 & & B inputs shorted, & & \\
& & output controlled by internal offset & & $LOW_B$ or $HIGH_B$ \\ \hline
FS13: PIN 6 $\stackrel{short}{\longrightarrow}$ PIN 7 & & B -ve 100\% Feed back, low gain & & $LOW_B$ \\ \hline
FS14: PIN 7 $\stackrel{short}{\longrightarrow}$ PIN 8 & & B output held high & & $HIGH_B$ \\ \hline
\hline
\end{tabular}
\label{tbl:lm358}
\end{table}
%\clearpage
\subsubsection{Failure modes of an OpAmp}
\label{sec:opamp_fms}
For the purpose of the examples to follow, the op-amp will
have the following failure modes:-
$$ fm(OPAMP) = \{ LOW, HIGH, NOOP, LOW_{slew} \} $$
\subsection{Comparing the component failure mode sources}
The EN298 pinouts failure mode technique cannot reveal failure modes due to internal failures.
The FMD-91 entries for op-amps are not directly usable as
component {\fms} in FMEA or FMMD and require interpretation.
%For our OpAmp example could have come up with different symptoms for both sides. Cannot predict the effect of internal errors, for instance ($LOW_{slew}$)
%is missing from the EN298 failure modes set.
% FMD-91
%
% I have been working on two examples of determining failure modes of components.
% One is from the US military document FMD-91, where internal failures
% of components are described (with stats).
%
% The other is EN298 where the failure modes for generic component types are prescribed, or
% determined by a procedure where failure scenarios of all pins OPEN and all adjacent pins shorted
% is applied. These techniques
%
% The FMD-91 entries need, in some cases, some interpretation to be mapped to
% component failure symptoms, but include failure modes that can be due to internal failures.
% The EN298 SHORT/OPEN procedure cannot determine failures due to internal causes but can be applied to any IC.
%
% Could I come in and see you Chris to quickly discuss these.
%
% I hope to have chapter 5 finished by the end of March, chapter 5 being the
% electronics examples for the FMMD methodology.
\clearpage
%%
%% Paragraph using failure modes to build from bottom up
%%
% \subsection{FMEA}
% This talk introduces Failure Mode Effects Analysis, and the different ways it is applied.

362
submission_thesis/CH5_Examples/copy.tex
View File

@ -154,368 +154,6 @@ by applying FMMD to a sigma delta ADC.
%
%%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
% \section{Determining the failure modes of components}
% \label{sec:determine_fms}
% In order to apply any form of FMEA we need to know the ways in which
% the components we are using can fail.
% %
% A good introduction to hardware and software failure modes may be found in~\cite{sccs}[pp.114-124].
% %
% Typically when choosing components for a design, we look at manufacturers' data sheets
% which describe functionality, physical dimensions
% environmental ranges, tolerances and can indicate how a component may fail/misbehave
% under given conditions.
% %
% How base components could fail internally, is not of interest to an FMEA investigation.
% The FMEA investigator needs to know what failure behaviour a component may exhibit. %, or in other words, its modes of failure.
% %
% A large body of literature exists which gives guidance for determining component {\fms}.
% %
% For this study FMD-91~\cite{fmd91} and the gas burner standard EN298~\cite{en298} are examined.
% %Some standards prescribe specific failure modes for generic component types.
% In EN298 failure modes for most generic component types are listed, or if not listed,
% determined by considering all pins OPEN and all adjacent pins shorted.
% %a procedure where failure scenarios of all pins OPEN and all adjacent pins shorted
% %are examined.
% %
% %
% FMD-91 is a reference document released into the public domain by the United States DOD
% and describes `failures' of common electronic components, with percentage statistics for each failure.
% %
% FMD-91 entries include general descriptions of internal failures alongside {\fms} of use to an FMEA investigation.
% %
% FMD-91 entries need, in some cases, some interpretation to be mapped to a clear set of
% component {\fms} suitable for use in FMEA.
%
% A third document, MIL-1991~\cite{mil1991} often used alongside FMD-91, provides overall reliability statistics for
% component types, but does not detail specific failure modes.
% %
% Using MIL1991 in conjunction with FMD-91, we can determine statistics for the failure modes
% of component types.
% %
% The FMEDA process from European standard EN61508~\cite{en61508} for instance,
% requires statistics for Meantime to Failure (MTTF) for all {\bc} failure modes.
%
%
% % One is from the US military document FMD-91, where internal failures
% % of components are described (with stats).
% %
% % The other is EN298 where the failure modes for generic component types are prescribed, or
% % determined by a procedure where failure scenarios of all pins OPEN and all adjacent pins shorted
% % is applied. These techniques
% %
% % The FMD-91 entries need, in some cases, some interpretation to be mapped to
% % component failure symptoms, but include failure modes that can be due to internal failures.
% % The EN298 SHORT/OPEN procedure cannot determine failures due to internal causes but can be applied to any IC.
% %
% % Could I come in and see you Chris to quickly discuss these.
% %
% % I hope to have chapter 5 finished by the end of March, chapter 5 being the
% % electronics examples for the FMMD methodology.
%
% In this section we look in detail at two common electrical components and examine how
% the two sources of information define their failure mode behaviour.
% We look at the reasons why some known failure modes % are omitted, or presented in
% %specific but unintuitive ways.
% %We compare the US. military published failure mode specifications wi
% can be found in one source but not in the others and vice versa.
% %
% Finally we compare and contrast the failure modes determined for these components
% from the FMD-91 reference source and from the guidelines of the
% European burner standard EN298.
%
% \subsection{Failure mode determination for generic resistor.}
% \label{sec:resistorfm}
% %- Failure modes. Prescribed failure modes EN298 - FMD91
% \paragraph{Resistor failure modes according to FMD-91.}
%
%
% The resistor is a ubiquitous component in electronics, and is therefore a good candidate for detailed examination of its failure modes.
% %
% FMD-91\cite{fmd91}[3-178] lists many types of resistor
% and lists many possible failure causes.
% For instance for {\textbf{Resistor,~Fixed,~Film}} we are given the following failure causes:
% \begin{itemize}
% \item Opened 52\%
% \item Drift 31.8\%
% \item Film Imperfections 5.1\%
% \item Substrate defects 5.1\%
% \item Shorted 3.9\%
% \item Lead damage 1.9\%
% \end{itemize}
% % This information may be of interest to the manufacturer of resistors, but it does not directly
% % help a circuit designer.
% % The circuit designer is not interested in the causes of resistor failure, but to build in contingency
% % against {\fms} that the resistor could exhibit.
% % We can determine these {\fms} by converting the internal failure descriptions
% % to {\fms} thus:
% To make this useful for FMEA/FMMD we must assign each failure cause to an arbitrary failure mode descriptor
% as shown below.
% %
% %and map these failure causes to three symptoms,
% %drift (resistance value changing), open and short.
%
% \begin{itemize}
% \item Opened 52\% $\mapsto$ OPENED
% \item Drift 31.8\% $\mapsto$ DRIFT
% \item Film Imperfections 5.1\% $\mapsto$ OPEN
% \item Substrate defects 5.1\% $\mapsto$ OPEN
% \item Shorted 3.9\% $\mapsto$ SHORT
% \item Lead damage 1.9\% $\mapsto$ OPEN.
% \end{itemize}
% %
% The main causes of drift are overloading of components.
% This is borne out in in the FMD-91~\cite{fmd91}[232] entry for a resistor network where the failure
% modes do not include drift.
% %
% If we can ensure that our resistors will not be exposed to overload conditions, the
% probability of drift (sometimes called parameter change) occurring
% is significantly reduced, enough for some standards to exclude it~\cite{en298}~\cite{en230}.
%
% \paragraph{Resistor failure modes according to EN298.}
%
% EN298, the European gas burner safety standard, tends to be give failure modes more directly usable by FMEA than FMD-91.
% EN298 requires that a full FMEA be undertaken, examining all failure modes
% of all electronic components~\cite{en298}[11.2 5] as part of the certification process.
% %
% Annex A of EN298, prescribes failure modes for common components
% and guidance on determining sets of failure modes for complex components (i.e. integrated circuits).
% EN298~\cite{en298}[Annex A] (for most types of resistor)
% only requires that the failure mode OPEN be considered for FMEA analysis.
% %
% For resistor types not specifically listed in EN298, the failure modes
% are considered to be either OPEN or SHORT.
% The reason that parameter change is not considered for resistors chosen for an EN298 compliant system, is that they must be must be {\em downrated}.
% That is to say the power and voltage ratings of components must be calculated
% for maximum possible exposure, with a 40\% margin of error. This reduces the probability
% that the resistors will be overloaded,
% and thus subject to drift/parameter change.
%
% % XXXXXX get ref from colin T
%
% %If a resistor was rated for instance for
%
% %These are useful for resistor manufacturersthey have three failure modes
% %EN298
% %Parameter change not considered for EN298 because the resistors are down-rated from
% %maximum possible voltage exposure -- find refs.
%
%
% % FMD-91 gives the following percentages for failure rates in
% % \label{downrate}
% % The parameter change, is usually a failure mode associated with over stressing the component.
% %In a system designed to typical safety critical constraints (as in EN298)
% %these environmentally induced failure modes need not be considered.
%
% \subsubsection{Resistor Failure Modes}
% \label{sec:res_fms}
% For this study we will take the conservative view from EN298, and consider the failure
% modes for a generic resistor to be both OPEN and SHORT.
% i.e.
% \label{ros}
% $$ fm(R) = \{ OPEN, SHORT \} . $$
%
% \subsection{Failure modes determination for generic operational amplifier}
%
% \begin{figure}[h+]
% \centering
% \includegraphics[width=200pt]{CH5_Examples/lm258pinout.jpg}
% % lm258pinout.jpg: 478x348 pixel, 96dpi, 12.65x9.21 cm, bb=0 0 359 261
% \caption{Pinout for an LM358 dual OpAmp}
% \label{fig:lm258}
% \end{figure}
%
% The operational amplifier (op-amp) %is a differential amplifier and
% is very widely used in nearly all fields of modern analogue electronics.
% They are typically packaged in dual or quad configurations---meaning
% that a chip will typically contain two or four amplifiers.
% For the purpose of example, we look at
% a typical op-amp designed for instrumentation and measurement, the dual packaged version of the LM358~\cite{lm358}
% (see figure~\ref{fig:lm258}), and use this to compare the failure mode derivations from FMD-91 and EN298.
%
% \paragraph{ Failure Modes of an OpAmp according to FMD-91 }
%
% %Literature suggests, latch up, latch down and oscillation.
% For OpAmp failures modes, FMD-91\cite{fmd91}{3-116] states,
% \begin{itemize}
% \item Degraded Output 50\% Low Slew rate - poor die attach
% \item No Operation - overstress 31.3\%
% \item Shorted $V_+$ to $V_-$, overstress, resistive short in amplifier 12.5\%
% \item Opened $V_+$ open 6.3\%
% \end{itemize}
%
% Again these are mostly internal causes of failure, more of interest to the component manufacturer
% than a designer looking for the symptoms of failure.
% We need to translate these failure causes within the OpAmp into {\fms}.
% We can look at each failure cause in turn, and map it to potential {\fms} suitable for use in FMEA
% investigations.
%
% \paragraph{OpAmp failure cause: Poor Die attach}
% The symptom for this is given as a low slew rate. This means that the op-amp
% will not react quickly to changes on its input terminals.
% This is a failure symptom that may not be of concern in a slow responding system like an
% instrumentation amplifier. However, where higher frequencies are being processed,
% a signal may entirely be lost.
% We can map this failure cause to a {\fm}, and we can call it $LOW_{slew}$.
%
% \paragraph{No Operation - over stress}
% Here the OP\_AMP has been damaged, and the output may be held HIGH or LOW, or may be effectively tri-stated
% , i.e. not able to drive circuitry in along the next stages of the signal path: we can call this state NOOP (no Operation).
% %
% We can map this failure cause to three {\fms}, $LOW$, $HIGH$, $NOOP$.
%
% \paragraph{Shorted $V_+$ to $V_-$}
% Due to the high intrinsic gain of an op-amp, and the effect of offset currents,
% this will force the output HIGH or LOW.
% We map this failure cause to $HIGH$ or $LOW$.
%
% \paragraph{Open $V_+$}
% This failure cause will mean that the minus input will have the very high gain
% of the OpAmp applied to it, and the output will be forced HIGH or LOW.
% We map this failure cause to $HIGH$ or $LOW$.
%
% \paragraph{Collecting OpAmp failure modes from FMD-91}
% We can define an OpAmp, under FMD-91 definitions to have the following {\fms}.
% \begin{equation}
% \label{eqn:opampfms}
% fm(OpAmp) = \{ HIGH, LOW, NOOP, LOW_{slew} \}
% \end{equation}
%
%
% \paragraph{Failure Modes of an OpAmp according to EN298}
%
% EN298 does not specifically define OP\_AMPS failure modes; these can be determined
% by following a procedure for `integrated~circuits' outlined in
% annex~A~\cite{en298}[A.1 note e].
% This demands that all open connections, and shorts between adjacent pins be considered as failure scenarios.
% We examine these failure scenarios on the dual packaged $LM358$~\cite{lm358}%\mu741$
% and determine its {\fms} in table ~\ref{tbl:lm358}.
% Collecting the op-amp failure modes from table ~\ref{tbl:lm358} we obtain the same {\fms}
% that we got from FMD-91, listed in equation~\ref{eqn:opampfms}.
%
%
%
% %\paragraph{EN298: Open and shorted pin failure symptom determination technique}
%
%
%
%
%
% \begin{table}[h+]
% \caption{LM358: EN298 Open and shorted pin failure symptom determination technique}
% \begin{tabular}{|| l | l | c | c | l ||} \hline
% %\textbf{Failure Scenario} & & \textbf{Amplifier Effect} & & \textbf{Symptom(s)} \\
% \textbf{Failure} & & \textbf{Amplifier Effect} & & \textbf{Derived Component} \\
% \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\
%
% \hline
%
% & & & & \\ \hline
%
% FS1: PIN 1 OPEN & & A output open & & $NOOP_A$ \\ \hline
%
% FS2: PIN 2 OPEN & & A-input disconnected, & & \\
% & & infinite gain on A+input & & $LOW_A$ or $HIGH_A$ \\ \hline
%
% FS3: PIN 3 OPEN & & A+input disconnected, & & \\
% & & infinite gain on A-input & & $LOW_A$ or $HIGH_A$ \\ \hline
%
% FS4: PIN 4 OPEN & & power to chip (ground) disconnected & & $NOOP_A$ and $NOOP_B$ \\ \hline
%
%
% FS5: PIN 5 OPEN & & B+input disconnected, & & \\
% & & infinite gain on B-input & & $LOW_B$ or $HIGH_B$ \\ \hline
%
% FS6: PIN 6 OPEN & & B-input disconnected, & & \\
% FS6: PIN 6 OPEN & & infinite gain on B+input & & $LOW_B$ or $HIGH_B$ \\ \hline
%
%
% FS7: PIN 7 OPEN & & B output open & & $NOOP_B$ \\ \hline
%
% FS8: PIN 8 OPEN & & power to chip & & \\
% FS8: PIN 8 OPEN & & (Vcc) disconnected & & $NOOP_A$ and $NOOP_B$ \\ \hline
% & & & & \\
% & & & & \\
%
% & & & & \\ \hline
%
% FS9: PIN 1 $\stackrel{short}{\longrightarrow}$ PIN 2 & & A -ve 100\% Feed back, low gain & & $LOW_A$ \\ \hline
%
% FS10: PIN 2 $\stackrel{short}{\longrightarrow}$ PIN 3 & & A inputs shorted, & & \\
% & & output controlled by internal offset & & $LOW_A$ or $HIGH_A$ \\ \hline
%
% FS11: PIN 3 $\stackrel{short}{\longrightarrow}$ PIN 4 & & A + input held to ground & & $LOW_A$ \\ \hline
%
% FS12: PIN 5 $\stackrel{short}{\longrightarrow}$ PIN 6 & & B inputs shorted, & & \\
% & & output controlled by internal offset & & $LOW_B$ or $HIGH_B$ \\ \hline
%
% FS13: PIN 6 $\stackrel{short}{\longrightarrow}$ PIN 7 & & B -ve 100\% Feed back, low gain & & $LOW_B$ \\ \hline
%
% FS14: PIN 7 $\stackrel{short}{\longrightarrow}$ PIN 8 & & B output held high & & $HIGH_B$ \\ \hline
%
%
% \hline
% \end{tabular}
% \label{tbl:lm358}
% \end{table}
%
%
% %\clearpage
%
% \subsubsection{Failure modes of an OpAmp}
%
% \label{sec:opamp_fms}
% For the purpose of the examples to follow, the op-amp will
% have the following failure modes:-
%
% $$ fm(OPAMP) = \{ LOW, HIGH, NOOP, LOW_{slew} \} $$
%
%
% \subsection{Comparing the component failure mode sources}
%
%
% The EN298 pinouts failure mode technique cannot reveal failure modes due to internal failures.
% The FMD-91 entries for op-amps are not directly usable as
% component {\fms} in FMEA or FMMD and require interpretation.
%
% %For our OpAmp example could have come up with different symptoms for both sides. Cannot predict the effect of internal errors, for instance ($LOW_{slew}$)
% %is missing from the EN298 failure modes set.
%
%
% % FMD-91
% %
% % I have been working on two examples of determining failure modes of components.
% % One is from the US military document FMD-91, where internal failures
% % of components are described (with stats).
% %
% % The other is EN298 where the failure modes for generic component types are prescribed, or
% % determined by a procedure where failure scenarios of all pins OPEN and all adjacent pins shorted
% % is applied. These techniques
% %
% % The FMD-91 entries need, in some cases, some interpretation to be mapped to
% % component failure symptoms, but include failure modes that can be due to internal failures.
% % The EN298 SHORT/OPEN procedure cannot determine failures due to internal causes but can be applied to any IC.
% %
% % Could I come in and see you Chris to quickly discuss these.
% %
% % I hope to have chapter 5 finished by the end of March, chapter 5 being the
% % electronics examples for the FMMD methodology.
%
%
%
%
%
% \clearpage
%
%
% %%
% %% Paragraph using failure modes to build from bottom up
% %%
%
%
%
%
%
% % \section{ FMMD overview}
% %
% % In the next sections we apply FMMD to electronic circuits, analogue/digital and electronic/software hybrids.

68
submission_thesis/CH6_Evaluation/copy.tex
View File

@ -4,19 +4,20 @@
%
It begins be defining a metric for the complexity of an FMEA analysis task.
This chapter begins by defining a metric for the complexity of an FMEA analysis task.
%
This concept is called `comparisson~complexity' and is a means to assess FMMD against current FMEA methodologies.
This concept is called `comparisson~complexity' and is a means to assess
the performance of FMMD against current FMEA methodologies.
%
This metric is developed formally and then formulae are presented for comparing the
complexity of using modularised or straightforward FMEA.
This metric is developed using set threory % formally
and then formulae are presented for calculating the
complexity of applying FMEA to a group of components.
%
These formulae are then used for a hypothetical example, analysed by FMEA and FMMD.
These formulae are then used for a hypothetical example, which is analysed by both FMEA and FMMD.
FMMD makes the claim that it can perform double simultaneous failure mode analysis without an undue
state explosion drawback.
To back this up, an example of double failure analysis is provided, using single and double
failure analysis, using the four wire Pt100
To support this, an example of single and double failure analysis is provided, using the four wire Pt100
temperature measurement sensor circuit. This example is also used to show how component failure rate statistics can be
used with FMMD.
@ -45,9 +46,9 @@ When performing FMEA we consider the system under investigation
to be a collection of components which have associated failure modes.
%
The object of FMEA is to determine cause and effect.
We apply reasoning to calculate, using the failure modes, the effects
%We apply reasoning to calculate, using the failure modes, the effects
%from these failure modes (the causes, {\fms} of {\bcs}) to the effects
(or symptoms of failure) at the top level.
%(or symptoms of failure) at the top level.
%
We can view FMEA as a process, taking each component in the system and for each of its failure modes
applying analysis with respect to the whole system.
@ -93,34 +94,46 @@ The number of checks we have to make to achieve this, gives an indication of the
%
It is desirable to be able to measure the complexity of an analysis task.
%
We term this `comparison~complexity', count the number of
paths between failure modes and components necessary to achieve RFMEA for a given system or {\fg}.
Comparison~complexity is a count of
paths between failure modes and components necessary to achieve RFMEA for a given group G. %system or {\fg}.
% (except its self of course, that component is already considered to be in a failed state!).
%
Obviously, for a small number of components and failure modes, we have a smaller number
%Obviously, f
For a small number of components and failure modes, we have a smaller number
of checks to make than for a complicated larger system.
%
We can consider the system as a large {\fg} of components.
We represent the number of components in the {\fg} $G$, by
$ | G | $,
(an indexing and sub-scripting notation to identify particular {\fgs}
within an FMMD hierarchy is given in section~\ref{sec:indexsub}).
%
\subsection{Formal definitions of entities used in FMEA}
%
\paragraph{Considering a system as a group of Components.}
We can consider the system as a large collection %{\fg}
of components.
We can represent this set of components as $G$, and the number of components in it by
$ | G | $. %,
%(an indexing and sub-scripting notation to identify particular {\fgs}
%within an FMMD hierarchy is given in section~\ref{sec:indexsub}).
\paragraph{Defining Components}
We define the set of all components as $\mathcal{C}$. Individiual components are denoted as $c$
with additional indexing when appropriate.
\paragraph{Defining a function that returns failure modes given a component.}
The function $fm$ has a component as its domain and the components failure modes as its range (see equation~\ref{eqn:fm}).
We can represent the number of potential failure modes of a component $c$, to be $ | fm(c) | .$
\paragraph{Indexing components with the group $G$.}
If we index all the components in the system under investigation $ c_1, c_2 \ldots c_{|\FG|} $ we can express
the number of checks required to rigorously examine every
failure mode against all the other components in the system.
We can define this as a function, Comparison Complexity, $CC$, with its domain as the system
or {\fg}, $\FG$, and
its range as the number of checks to perform to satisfy a rigorous FMEA inspection.
Where $\mathcal{\FG}$ represents the set of all {\fgs}, and $ \mathbb{N} $ any natural integer, $CC$ is defined by,
We can define this as a function, Comparison Complexity, can be represented by a function $CC$, with its domain as $G$, and
its range as the number of checks---or reasoning stages---to perform to satisfy a rigorous FMEA inspection.
Where $\mathcal{G}$ represents the set of all {\fgs}, and $ \mathbb{N} $ any natural integer, $CC$ is defined by,
\begin{equation}
%$$
CC:\mathcal{\FG} \rightarrow \mathbb{N},
CC:\mathcal{G} \rightarrow \mathbb{N},
%$$
\end{equation}
@ -131,7 +144,7 @@ in component ${c_i}$, is given by
\label{eqn:CC}
%$$
%%% when it was called reasoning distance -- 19NOV2011 -- RD(fg) = \sum_{n=1}^{|fg|} |fm(c_n)|.(|fg|-1)
CC(\FG) = (n-1) \sum_{1 \le i \le n} fm(c_i).
CC(G) = (n-1) \sum_{1 \le i \le n} fm(c_i).
%$$
\end{equation}
@ -141,8 +154,15 @@ equation~\ref{eqn:CC} becomes
%$$
\begin{equation}
\label{eqn:rd2}
CC(\FG) = K.(|\FG|-1).
CC(G) = K.(|G|-1).
\end{equation}
An FMMD hierarchy consists of many {\fgs} which are subsets of $G$.
We define the set of all {\fgs} as $\mathcal{FG}$.
We can therefore state $ \forall \in \mathcal{FG} \subset \mathcal{G}$.
We can define individual {\fgs} using $FG$ with an index to identify them and a superscript
to identify the hierarchy level.
%$$
%Equation~\ref{eqn:rd} can also be expressed as
%