From 36025181b7e3e8b501f00fea8215a5d7cb206807 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Sat, 20 Oct 2012 16:45:45 +0100 Subject: [PATCH] Getting Chapter 5 ready... --- submission_thesis/CH4_FMMD/copy.tex | 2 +- submission_thesis/CH5_Examples/Makefile | 3 +- submission_thesis/CH5_Examples/copy.tex | 1262 +++++++++-------- .../CH5_Examples/eulerfivepole.dia | Bin 0 -> 2305 bytes submission_thesis/thesis.tex | 2 +- 5 files changed, 648 insertions(+), 621 deletions(-) create mode 100644 submission_thesis/CH5_Examples/eulerfivepole.dia diff --git a/submission_thesis/CH4_FMMD/copy.tex b/submission_thesis/CH4_FMMD/copy.tex index 80cbd61..4ca2bb4 100644 --- a/submission_thesis/CH4_FMMD/copy.tex +++ b/submission_thesis/CH4_FMMD/copy.tex @@ -488,7 +488,7 @@ FMEA (because the analysis is typically performed in several small stages). \section{Worked Example: Non-Inverting Amplifier} - +\label{sec:noninvamp} %% here bring in sys safety paper from 2011 %% %% GARK BEGIN diff --git a/submission_thesis/CH5_Examples/Makefile b/submission_thesis/CH5_Examples/Makefile index 9da1b77..c6c84ff 100644 --- a/submission_thesis/CH5_Examples/Makefile +++ b/submission_thesis/CH5_Examples/Makefile @@ -5,7 +5,8 @@ PNG_DIA = blockdiagramcircuit2.png bubba_oscillator_block_diagram.png circuit1 poss1finalbubba.png poss2finalbubba.png pt100.png pt100_doublef.png pt100_singlef.png \ pt100_tc.png pt100_tc_sp.png shared_component.png stat_single.png three_tree.png \ tree_abstraction_levels.png vrange.png sigma_delta_block.png ftcontext.png ct1.png hd.png \ - sigdel1.png sdadc.png bubba_euler_1.png bubba_euler_2.png eulersd.png eulersdfinal.png + sigdel1.png sdadc.png bubba_euler_1.png bubba_euler_2.png eulersd.png eulersdfinal.png \ + eulerfivepole.png diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index fb9020d..885c623 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/submission_thesis/CH5_Examples/copy.tex @@ -126,453 +126,461 @@ Finally section~\ref{sec:elecsw} demonstrates FMMD analysis of a combined electr % -\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. + +%%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX % -A good introduction to hardware and software failure modes may be found in~\cite{sccs}[pp.114-124]. +% This section might fit in with the literature review.... Chris thinks its not relevant here +% and I agree 20OCT2012 % -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. - +%%%% XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX -% 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. -% The basic principles of FMMD are presented here for clarity. -% -% \paragraph{ Creating a fault hierarchy.} -% The main concept of FMMD is to build a hierarchy of failure behaviour from the {\bc} -% level up to the top, or system level, with analysis stages between each -% transition to a higher level in the hierarchy. -% -% -% The first stage is to choose -% {\bcs} that interact and naturally form {\fgs}. The initial {\fgs} are collections of base components. -% %These parts all have associated fault modes. A module is a set fault~modes. -% From the point of view of failure analysis, -% we are not interested in the components themselves, but in the ways in which they can fail. -% -% A {\fg} is a collection of components that perform some simple task or function. +% \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. % % -% In order to determine how a {\fg} can fail, -% we need to consider all the failure modes of all its components. +% A good introduction to hardware and software failure modes may be found in~\cite{sccs}[pp.114-124]. % % -% By analysing the fault behaviour of a `{\fg}' with respect to all its components failure modes, -% we can determine its symptoms of failure. -% %In fact we can call these -% %the symptoms of failure for the {\fg}. -% -% With these symptoms (a set of derived faults from the perspective of the {\fg}) -% we can now state that the {\fg} (as an entity in its own right) can fail in a number of well defined ways. +% 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. % % -% In other words, we have taken a {\fg} and analysed how -% \textbf{it} can fail according to the failure modes of its components, and then can -% determine the {\fg} failure modes. -% -% \paragraph{Creating a derived component.} -% We create a new `{\dc}' which has -% the failure symptoms of the {\fg} from which it was derived, as its set of failure modes. -% This new {\dc} is at a higher `failure~mode~abstraction~level' than {\bcs}. +% 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. % % -% \paragraph{An example of a {\dc}.} -% To give an example of this, we could look at the components that -% form, say an amplifier. We look at how all the components within it -% could fail and how that would affect the amplifier. +% A large body of literature exists which gives guidance for determining component {\fms}. % % -% The ways in which the amplifier can be affected are its symptoms. +% 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. +% % % % -% When we have determined the symptoms, we can -% create a {\dc} (called say AMP1) which has a {\em known set of failure modes} (i.e. its symptoms). -% We can now treat $AMP1$ as a pre-analysed, higher level component. -% %The amplifier is an abstract concept, in terms of the components. -% To a make an `amplifier' we have to connect a group of components -% in a specific configuration. This specific configuration corresponds to -% a {\fg}. Our use of it as a subsequent building block corresponds to a {\dc}. -% -% -% %What this means is the `fault~symptoms' of the module have been derived. +% 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. % % -% %When we have determined the fault~modes at the module level these can become a set of derived faults. -% %By taking sets of derived faults (module level faults) we can combine these to form modules -% %at a higher level of fault abstraction. An entire hierarchy of fault modes can now be built in this way, -% %to represent the fault behaviour of the entire system. This can be seen as using the modules we have analysed -% %as parts, parts which may now be combined to create new functional groups, -% %but as parts at a higher level of fault abstraction. -% \paragraph{Building the Hierarchy.} -% We can now apply the same process of building {\fgs} but with {\dcs} instead of {\bcs}. -% We can bring {\dcs} -% together to form functional groups and then create new {\dcs} -% at even higher abstraction levels. Eventually we will have a hierarchy -% that converges to one top level {\dc}. At this stage we have a complete failure -% mode model of the system under investigation. +% 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. % -% \begin{figure}[h] +% +% % 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=300pt,keepaspectratio=true]{CH5_Examples/tree_abstraction_levels.png} -% % tree_abstraction_levels.png: 495x292 pixel, 72dpi, 17.46x10.30 cm, bb=0 0 495 292 -% \caption{FMMD Hierarchy showing ascending abstraction levels} -% \label{fig:treeabslev} +% \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} % -% Figure~\ref{fig:treeabslev} shows an FMMD hierarchy, where the process of creating a {\dc} from a {\fg} -% is shown as a `$\derivec$' symbol. +% 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. +% % The basic principles of FMMD are presented here for clarity. +% % +% % \paragraph{ Creating a fault hierarchy.} +% % The main concept of FMMD is to build a hierarchy of failure behaviour from the {\bc} +% % level up to the top, or system level, with analysis stages between each +% % transition to a higher level in the hierarchy. +% % +% % +% % The first stage is to choose +% % {\bcs} that interact and naturally form {\fgs}. The initial {\fgs} are collections of base components. +% % %These parts all have associated fault modes. A module is a set fault~modes. +% % From the point of view of failure analysis, +% % we are not interested in the components themselves, but in the ways in which they can fail. +% % +% % A {\fg} is a collection of components that perform some simple task or function. +% % % +% % In order to determine how a {\fg} can fail, +% % we need to consider all the failure modes of all its components. +% % % +% % By analysing the fault behaviour of a `{\fg}' with respect to all its components failure modes, +% % we can determine its symptoms of failure. +% % %In fact we can call these +% % %the symptoms of failure for the {\fg}. +% % +% % With these symptoms (a set of derived faults from the perspective of the {\fg}) +% % we can now state that the {\fg} (as an entity in its own right) can fail in a number of well defined ways. +% % % +% % In other words, we have taken a {\fg} and analysed how +% % \textbf{it} can fail according to the failure modes of its components, and then can +% % determine the {\fg} failure modes. +% % +% % \paragraph{Creating a derived component.} +% % We create a new `{\dc}' which has +% % the failure symptoms of the {\fg} from which it was derived, as its set of failure modes. +% % This new {\dc} is at a higher `failure~mode~abstraction~level' than {\bcs}. +% % % +% % \paragraph{An example of a {\dc}.} +% % To give an example of this, we could look at the components that +% % form, say an amplifier. We look at how all the components within it +% % could fail and how that would affect the amplifier. +% % % +% % The ways in which the amplifier can be affected are its symptoms. +% % % +% % When we have determined the symptoms, we can +% % create a {\dc} (called say AMP1) which has a {\em known set of failure modes} (i.e. its symptoms). +% % We can now treat $AMP1$ as a pre-analysed, higher level component. +% % %The amplifier is an abstract concept, in terms of the components. +% % To a make an `amplifier' we have to connect a group of components +% % in a specific configuration. This specific configuration corresponds to +% % a {\fg}. Our use of it as a subsequent building block corresponds to a {\dc}. +% % +% % +% % %What this means is the `fault~symptoms' of the module have been derived. +% % % +% % %When we have determined the fault~modes at the module level these can become a set of derived faults. +% % %By taking sets of derived faults (module level faults) we can combine these to form modules +% % %at a higher level of fault abstraction. An entire hierarchy of fault modes can now be built in this way, +% % %to represent the fault behaviour of the entire system. This can be seen as using the modules we have analysed +% % %as parts, parts which may now be combined to create new functional groups, +% % %but as parts at a higher level of fault abstraction. +% % \paragraph{Building the Hierarchy.} +% % We can now apply the same process of building {\fgs} but with {\dcs} instead of {\bcs}. +% % We can bring {\dcs} +% % together to form functional groups and then create new {\dcs} +% % at even higher abstraction levels. Eventually we will have a hierarchy +% % that converges to one top level {\dc}. At this stage we have a complete failure +% % mode model of the system under investigation. +% % +% % \begin{figure}[h] +% % \centering +% % \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/tree_abstraction_levels.png} +% % % tree_abstraction_levels.png: 495x292 pixel, 72dpi, 17.46x10.30 cm, bb=0 0 495 292 +% % \caption{FMMD Hierarchy showing ascending abstraction levels} +% % \label{fig:treeabslev} +% % \end{figure} +% % +% % Figure~\ref{fig:treeabslev} shows an FMMD hierarchy, where the process of creating a {\dc} from a {\fg} +% % is shown as a `$\derivec$' symbol. +% % +% % +% % +% % \clearpage \section{Example Analysis: Inverting OPAMP} @@ -664,7 +672,7 @@ We can form a {\dc} from this, and call it an inverted potential divider $INVPD$ We can now form a {\fg} from the OpAmp and the $INVPD$ \begin{table}[h+] -\caption{Inverting Amplifier: Single failure analysis} +\caption{Inverting Amplifier: Single failure analysis using the $PD$ {\dc}} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{Inverted Amp Effect} & & \textbf{Symptom} \\ \hline \textbf{Failure} & & \textbf{Inverted Amp. Effect} & & \textbf{Derived Component} \\ @@ -672,13 +680,13 @@ We can now form a {\fg} from the OpAmp and the $INVPD$ \hline FS1: INVPD LOW & & NEGATIVE on -input & & $ HIGH $ \\ - FS2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ + FS2: INVPD HIGH & & Positive on -input & & $ LOW $ \\ \hline - FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ \hline + FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ - FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ \hline + FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ - FS7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\ \hline + FS7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\ FS8: AMP LowSlew & & $ slow output \frac{\delta V}{\delta t} $ & & $ LOW PASS $ \\ \hline \hline @@ -819,20 +827,19 @@ derived component. FS1: R1 SHORT & & NEGATIVE out of range & & $ HIGH $ \\ % FS1: R1 SHORT -ve in & & POSITIVE out of range & & $ OUT OF RANGE $ \\ \hline - FS2: R1 OPEN & & zero output & & $ LOW $ \\ + FS2: R1 OPEN & & zero output & & $ LOW $ \\ \hline % FS2: R1 OPEN -ve in & & zero output & & $ ZERO OUTPUT $ \\ \hline FS3: R2 SHORT & & $INVAMP_{nogain} $ & & $ LOW $ \\ % FS3: R2 SHORT -ve in & & $INVAMP_{nogain} $ & & $ NO GAIN $ \\ \hline - FS4: R2 OPEN & & NEGATIVE out of range $ $ & & $ LOW$ \\ + FS4: R2 OPEN & & NEGATIVE out of range $ $ & & $ LOW$ \\ \hline % FS4: R2 OPEN -ve in & & POSITIVE out of range $ $ & & $OUT OF RANGE $ \\ \hline - FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ \hline + FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ - FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ \hline - - FS7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\ \hline + FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ + FS7: AMP NOOP & & $INVAMP_{nogain} $ & & $ LOW $ \\ FS8: AMP LowSlew & & $ slow output \frac{\delta V}{\delta t} $ & & $ LOW PASS $ \\ \hline \hline @@ -855,15 +862,19 @@ $$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \} $$ \subsection{Comparison between the two approaches} \label{sec:invampcc} -The first analysis looks at an inverted potential divider, analyses its failure modes, -and from this we obtain a {\dc} (INVPD). -We applied a second analysis stage with the known failure modes of the op-amp and the failure modes of INVPD. - +The first analysis used two FMMD stages. +The first stage analysed an inverted potential divider %, analyses its failure modes, +giving the {\dc}(INVPD). +The second stage analysed a {\fg} comprised of the INVPD and an OpAmp. +% The second analysis (3 components) has to look at the effects of each failure mode of each resistor -on the op-amp circuit. This means more work for the analyst---that is -an increase in the complexity of the analysis---than -simply comparing the two known failure modes -from the pre-analysed inverted potential divider. +on the op-amp circuit. This meant more work for the analyst---that is +an increase in the complexity of the analysis---compared to +checking the two known failure modes +from the pre-analysed inverted potential divider against the OpAmp. +% +Both analysis strategies obtained the same failure modes for the +inverting amplifier (i.e. the same failure modes for the {\dc} INVAMP). % METRICS The complexity comparison figures % METRICS bear this out. For the two stage analysis, using equation~\ref{eqn:rd2}, we obtain a CC of $4.(2-1)+6.(2-1)=10$ @@ -902,159 +913,166 @@ the sensors supplying the voltage signals used for measurement. It would be desirable to represent this circuit as a {\dc} called say $DiffAMP$. We begin by identifying functional groups from the components in the circuit. - -\subsection{Functional Group: Potential Divider} -For the gain setting resistors R1,R2 -- we can re-use the potential divider from section~\ref{subsec:potdiv}. - -%R1 and R2 perform as a potential divider. -%Resistors can fail OPEN and SHORT (according to GAS burner standard EN298 Appendix A). -%$$ fm(R) = \{ OPEN, SHORT \}$$ - - - +% WE CAN RE_USE THE NONINVAMP FROM CHAPTER 4 HERE....... +% \subsection{Functional Group: Potential Divider} +% For the gain setting resistors R1,R2 -- we can re-use the potential divider from section~\ref{subsec:potdiv}. +% +% %R1 and R2 perform as a potential divider. +% %Resistors can fail OPEN and SHORT (according to GAS burner standard EN298 Appendix A). +% %$$ fm(R) = \{ OPEN, SHORT \}$$ +% +% +% +% % \begin{table}[ht] +% % \caption{Potential Divider $PD$: 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{Pot.Div} & \textbf{ } & \textbf{General} \\ +% % \textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symtom Description} \\ +% % % R & wire & res + & res - & description +% % \hline +% % \hline +% % TC1: $R_1$ SHORT & LOW & & LowPD \\ +% % TC2: $R_1$ OPEN & HIGH & & HighPD \\ \hline +% % TC3: $R_2$ SHORT & HIGH & & HighPD \\ +% % TC4: $R_2$ OPEN & LOW & & LowPD \\ \hline +% % \hline +% % \end{tabular} +% % \label{tbl:pdfmea} +% % \end{table} +% % +% % By collecting the symptoms in table~\ref{tbl:pdfmea} we can create a derived +% % component $PD$ to represent the failure mode behaviour +% % of a potential divider. +% +% Thus for single failure modes, a potential divider can fail +% with $fm(PD) = \{PDHigh,PDLow\}$. +% +% +% The potential divider is used to program the gain of IC1. +% IC1 and PD provide the function of buffering +% /amplifying the signal $+V1$. +% We can now examine IC1 and PD as a functional group. +% +% \pagebreak[3] +% \subsection{Functional Group: Amplifier first stage} +% +% Let use now consider the op-amp. According to +% 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\%). +% +% +% $$ fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$ +% +% +% By bringing the $PD$ derived component and the $OPAMP$ into +% a functional group we can analyse its failure mode behaviour. +% +% % \begin{table}[ht] -% \caption{Potential Divider $PD$: Failure Mode Effects Analysis: Single Faults} % title of Table +% \caption{Non Inverting Amplifier $NI\_AMP$: 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{Pot.Div} & \textbf{ } & \textbf{General} \\ -% \textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symtom Description} \\ +% %\textbf{Test} & \textbf{Amplifier} & \textbf{ } & \textbf{General} \\ +% %\textbf{Case} & \textbf{Effect} & \textbf{ } & \textbf{Symtom Description} \\ +% \textbf{Failure} & & \textbf{Amplifier Effect} & & \textbf{Derived Component} \\ +% \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\ +% % % R & wire & res + & res - & description % \hline % \hline -% TC1: $R_1$ SHORT & LOW & & LowPD \\ -% TC2: $R_1$ OPEN & HIGH & & HighPD \\ \hline -% TC3: $R_2$ SHORT & HIGH & & HighPD \\ -% TC4: $R_2$ OPEN & LOW & & LowPD \\ \hline +% TC1: $OPAMP$ LatchUP & & Output High & & AMPHigh \\ +% TC2: $OPAMP$ LatchDown & & Output Low : Low gain& & AMPLow \\ \hline +% TC3: $OPAMP$ No Operation & & Output Low & & AMPLow \\ +% TC4: $OPAMP$ Low Slew & & Low pass filtering & & LowPass \\ \hline +% TC5: $PD$ LowPD & & Output High & & AMPHigh \\ \hline +% TC6: $PD$ HighPD & & Output Low : Low Gain& & AMPLow \\ \hline +% %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline % \hline % \end{tabular} -% \label{tbl:pdfmea} +% \label{ampfmea} % \end{table} % -% By collecting the symptoms in table~\ref{tbl:pdfmea} we can create a derived -% component $PD$ to represent the failure mode behaviour -% of a potential divider. +% +% Collecting the symptoms we can see that this amplifier fails +% in 3 ways $\{ AMPHigh, AMPLow, LowPass \}$. +% We can now create a derived component, $NI\_AMP$, to represent it. +% The FMMD reasoning process is represented in the DAG in figure~\ref{fig:noninvdag11}. +% -Thus for single failure modes, a potential divider can fail -with $fm(PD) = \{PDHigh,PDLow\}$. +Looking first at the components in the signal path, we notice that we have a non-inverting +amplifier formed by R1,R2 and IC1. In fact apart from being +inverted visually on the schematic it is identical to the example +used in section~\ref{sec:noninvamp} (the first practical example used to demonstrate FMMD). +We thus re-use this and can express the failure modes for it thus: - -The potential divider is used to program the gain of IC1. -IC1 and PD provide the function of buffering -/amplifying the signal $+V1$. -We can now examine IC1 and PD as a functional group. - -\pagebreak[3] -\subsection{Functional Group: Amplifier first stage} - -Let use now consider the op-amp. According to -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\%). - - -$$ fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$ - - -By bringing the $PD$ derived component and the $OPAMP$ into -a functional group we can analyse its failure mode behaviour. - - -\begin{table}[ht] -\caption{Non Inverting Amplifier $NI\_AMP$: 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} \\ - \textbf{Failure} & & \textbf{Amplifier Effect} & & \textbf{Derived Component} \\ - \textbf{cause} & & \textbf{ } & & \textbf{Failure Mode} \\ - -% R & wire & res + & res - & description -\hline -\hline - TC1: $OPAMP$ LatchUP & & Output High & & AMPHigh \\ - TC2: $OPAMP$ LatchDown & & Output Low : Low gain& & AMPLow \\ \hline - TC3: $OPAMP$ No Operation & & Output Low & & AMPLow \\ - TC4: $OPAMP$ Low Slew & & Low pass filtering & & LowPass \\ \hline - TC5: $PD$ LowPD & & Output High & & AMPHigh \\ \hline - TC6: $PD$ HighPD & & Output Low : Low Gain& & AMPLow \\ \hline - %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline -\hline -\end{tabular} -\label{ampfmea} -\end{table} - - -Collecting the symptoms we can see that this amplifier fails -in 3 ways $\{ AMPHigh, AMPLow, LowPass \}$. -We can now create a derived component, $NI\_AMP$, to represent it. -The FMMD reasoning process is represented in the DAG in figure~\ref{fig:noninvdag11}. - -$$ fm(NI\_AMP) = \{ AMPHigh, AMPLow, LowPass \} $$ - - -\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] (OPAMP) at (0,-1.8) {$OPAMP$}; - \node[component] (R1) at (0,-6) {$R_1$}; - \node[component] (R2) at (0,-7.6) {$R_2$}; - - - \node[failure] (OPAMPLU) at (\layersep,-0) {l-up}; - \node[failure] (OPAMPLD) at (\layersep,-1.2) {l-dn}; - \node[failure] (OPAMPNP) at (\layersep,-2.5) {noop}; - \node[failure] (OPAMPLS) at (\layersep,-3.8) {lowslew}; - - \node[failure] (R1SHORT) at (\layersep,-5.1) {$R1_{Sh}$}; - \node[failure] (R1OPEN) at (\layersep,-6.4) {$R1_{Op}$}; - - \node[failure] (R2SHORT) at (\layersep,-7.7) {$R2_{Sh}$}; - \node[failure] (R2OPEN) at (\layersep,-9.0) {$R2_{Op}$}; - - \path (OPAMP) edge (OPAMPLU); - \path (OPAMP) edge (OPAMPLD); - \path (OPAMP) edge (OPAMPNP); -\path (OPAMP) edge (OPAMPLS); - - \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,-6) {$PD_{HIGH}$}; - \node[symptom] (PDLOW) at (\layersep*2,-7.6) {$PD_{LOW}$}; - \path (R1OPEN) edge (PDHIGH); - \path (R2SHORT) edge (PDHIGH); - \path (R2OPEN) edge (PDLOW); - \path (R1SHORT) edge (PDLOW); - \node[symptom] (AMPHIGH) at (\layersep*3.4,-3) {$AMP_{HIGH}$}; - \node[symptom] (AMPLOW) at (\layersep*3.4,-5) {$AMP_{LOW}$}; - \node[symptom] (AMPLP) at (\layersep*3.4,-7) {$LOWPASS$}; - \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{Full DAG representing failure modes and symptoms of the Non Inverting Op-amp Circuit} - \label{fig:noninvdag11} - \end{figure} +$$ fm(NI\_AMP) = \{ AMPHigh, AMPLow, LowPass \} .$$ +% +% +% \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] (OPAMP) at (0,-1.8) {$OPAMP$}; +% \node[component] (R1) at (0,-6) {$R_1$}; +% \node[component] (R2) at (0,-7.6) {$R_2$}; +% +% +% \node[failure] (OPAMPLU) at (\layersep,-0) {l-up}; +% \node[failure] (OPAMPLD) at (\layersep,-1.2) {l-dn}; +% \node[failure] (OPAMPNP) at (\layersep,-2.5) {noop}; +% \node[failure] (OPAMPLS) at (\layersep,-3.8) {lowslew}; +% +% \node[failure] (R1SHORT) at (\layersep,-5.1) {$R1_{Sh}$}; +% \node[failure] (R1OPEN) at (\layersep,-6.4) {$R1_{Op}$}; +% +% \node[failure] (R2SHORT) at (\layersep,-7.7) {$R2_{Sh}$}; +% \node[failure] (R2OPEN) at (\layersep,-9.0) {$R2_{Op}$}; +% +% \path (OPAMP) edge (OPAMPLU); +% \path (OPAMP) edge (OPAMPLD); +% \path (OPAMP) edge (OPAMPNP); +% \path (OPAMP) edge (OPAMPLS); +% +% \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,-6) {$PD_{HIGH}$}; +% \node[symptom] (PDLOW) at (\layersep*2,-7.6) {$PD_{LOW}$}; +% \path (R1OPEN) edge (PDHIGH); +% \path (R2SHORT) edge (PDHIGH); +% \path (R2OPEN) edge (PDLOW); +% \path (R1SHORT) edge (PDLOW); +% \node[symptom] (AMPHIGH) at (\layersep*3.4,-3) {$AMP_{HIGH}$}; +% \node[symptom] (AMPLOW) at (\layersep*3.4,-5) {$AMP_{LOW}$}; +% \node[symptom] (AMPLP) at (\layersep*3.4,-7) {$LOWPASS$}; +% \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{Full DAG representing failure modes and symptoms of the Non Inverting Op-amp Circuit} +% \label{fig:noninvdag11} +% \end{figure} @@ -1062,7 +1080,7 @@ $$ fm(NI\_AMP) = \{ AMPHigh, AMPLow, LowPass \} $$ The second stage of this amplifier, following the signal path, is the amplifier consisting of $R3,R4,IC2$. - +% This is in exactly the same configuration as the first amplifier, but it is being fed by the first amplifier. The first amplifier was grounded and received as input `+V1' (presumably a positive voltage). @@ -1088,15 +1106,15 @@ Here it is more intuitive to model the resistors not as a potential divider, but \hline \hline TC1: $OPAMP$ LatchUP & Output High & AMPHigh \\ - TC2: $OPAMP$ LatchDown & Output Low : Low gain & AMPLow \\ \hline + TC2: $OPAMP$ LatchDown & Output Low : Low gain & AMPLow \\ TC3: $OPAMP$ No Operation & Output Low & AMPLow \\ TC4: $OPAMP$ Low Slew & Low pass filtering & LowPass \\ \hline - TC5: $R3\_open$ & +V2 follower & AMPIncorrectOutput\\ \hline + TC5: $R3\_open$ & +V2 follower & AMPIncorrectOutput\\ TC6: $R3\_short$ & Undefined & AMPIncorrectOutput \\ & (impedance of IC1 vs +V2) & \\ \hline TC5: $R4\_open$ & High or Low output & AMPIncorrectOutput \\ & +V2$>$+V1 $\mapsto$ High & \\ - & +V1$>$+V2 $\mapsto$ Low & \\ \hline + & +V1$>$+V2 $\mapsto$ Low & \\ TC6: $R4\_short$ & +V2 follower & AMPIncorrectOutput \\ \hline %TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline \hline @@ -1105,11 +1123,11 @@ Here it is more intuitive to model the resistors not as a potential divider, but \end{table} Collecting the symptoms we can see that this amplifier fails -in 4 ways $\{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput\}$. -We can now create a derived component, $SEC\_AMP$, to represent it. - - -$$ fm(SEC\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} $$ +in 4 ways %$\{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput\}$. +%We can now +we create a derived component, $SEC\_AMP$, to represent it +with failure modes described by: +$$ fm(SEC\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} .$$ @@ -1137,14 +1155,14 @@ two derived components of the type $NI\_AMP$ and $SEC\_AMP$. % R & wire & res + & res - & description \hline \hline - TC1: $NI\_AMP$ AMPHigh & opamp 2 driven high & DiffAMPLow \\ - TC2: $NI\_AMP$ AMPLow & opamp 2 driven low & DiffAMPHigh \\ - TC3: $NI\_AMP$ LowPass & opamp 2 driven with lag & DiffAMP\_LP \\ \hline - TC4: $SEC\_AMP$ AMPHigh & Diff amplifier high & DiffAMPHigh\\ - TC5: $SEC\_AMP$ AMPLow & Diff amplifier low & DiffAMPLow \\ - TC6: $SEC\_AMP$ LowPass & Diff amplifier lag/lowpass & DiffAMP\_LP \\ \hline - TC7: $SEC\_AMP$ IncorrectOutput & Output voltage & DiffAMPIncorrect \\ - TC7: $SEC\_AMP$ & $ \neg (V2 - V1) $ & \\ \hline + TC1: $NI\_AMP$ AMPHigh & opamp 2 driven high & DiffAMPLow \\ + TC2: $NI\_AMP$ AMPLow & opamp 2 driven low & DiffAMPHigh \\ + TC3: $NI\_AMP$ LowPass & opamp 2 driven with lag & DiffAMP\_LP \\ \hline + TC4: $SEC\_AMP$ AMPHigh & Diff amplifier high & DiffAMPHigh\\ + TC5: $SEC\_AMP$ AMPLow & Diff amplifier low & DiffAMPLow \\ + TC6: $SEC\_AMP$ LowPass & Diff amplifier lag/lowpass & DiffAMP\_LP \\ + TC7: $SEC\_AMP$ IncorrectOutput & Output voltage & DiffAMPIncorrect \\ + & $ \neg (V2 - V1) $ & \\ \hline \hline \end{tabular} \label{ampfmea} @@ -1188,7 +1206,7 @@ Were this failure to have safety implications this FMMD analysis will have revea the un-observability and would likely prompt re-design of this circuit\footnote{A typical way to solve an un-observability such as this is to periodically switch in test signals in place of the input signal.} -. + \clearpage \section{Five Pole Low Pass Filer, using two Sallen~Key stages.} @@ -1210,8 +1228,9 @@ Starting at the input, we have a first order low pass filter buffered by an op-a the output of this is passed to a Sallen~Key~\cite{aoe}[p.267]~\cite{electronicssysapproach}[p.288] second order low-pass filter. The output of this is passed into another Sallen~Key filter -- which although it may have different values for its resistors/capacitors and thus have a different frequency response -- is identical from a failure mode perspective. -Thus we can analyse the first Sallen~Key low pass filter and re-use the results for the second stage -avoiding the repeat work that would be performed using traditional FMEA. +Thus we can analyse the first Sallen~Key low pass filter and re-use it +for the second stage +(avoiding the repeat work that would have had to be performed using traditional FMEA). \begin{figure}[h] @@ -1357,7 +1376,6 @@ We can analyse the first one and then re-use these results for the second. TC11: C2 OPEN & reduced/incorrect low pass filtering & SKLPfilterIncorrect \\ TC12: C2 SHORT & No input signal, low signal & SKLPnosignal \\ \hline - \hline \hline \end{tabular} \label{tbl:sallenkeylp} @@ -1385,13 +1403,13 @@ and this follows the signal flow in the filter circuit (see figure~\ref{fig:bloc As the signal has to pass though each block/stage in order to be `five~pole' filtered, we need to bring these three blocks together into a {\fg} in order to get a failure mode model for the whole circuit. -We can index the Sallen Key stages, and these are marked on the ciruit schematic in figure~\ref{fig:circuit2002_FIVEPOLE}. +We can index the Sallen Key stages, and these are marked on the circuit schematic in figure~\ref{fig:circuit2002_FIVEPOLE}. \begin{figure}[h]+ \centering \includegraphics[width=200pt]{CH5_Examples/circuit2002_FIVEPOLE.png} % circuit2002_FIVEPOLE.png: 575x331 pixel, 72dpi, 20.28x11.68 cm, bb=0 0 575 331 - \caption{Functional Groups in Five Pole Low Pass Filter on schematic} + \caption{Functional Groups in Five Pole Low Pass Filter: shown as an Euler diagram super-imposed onto the electrical schematic.} \label{fig:circuit2002_FIVEPOLE} \end{figure} @@ -1401,11 +1419,18 @@ So our final {\fg} will consist of the derived components $\{ LP1, SKLP_1, SKLP_ We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}. -\begin{figure}[h]+ +% HTR 20OCT2012 \begin{figure}[h]+ +% HTR 20OCT2012 \centering +% HTR 20OCT2012 \includegraphics[width=300pt]{CH5_Examples/circuit2h.png} +% HTR 20OCT2012 % circuit2h.png: 676x603 pixel, 72dpi, 23.85x21.27 cm, bb=0 0 676 603 +% HTR 20OCT2012 \caption{FMMD Hierarchy for five pole Low Pass Filter} +% HTR 20OCT2012 \label{fig:circuit2h} +% HTR 20OCT2012\end{figure} +\begin{figure}[h] \centering - \includegraphics[width=300pt]{CH5_Examples/circuit2h.png} - % circuit2h.png: 676x603 pixel, 72dpi, 23.85x21.27 cm, bb=0 0 676 603 - \caption{FMMD Hierarchy for five pole Low Pass Filter} + \includegraphics[width=400pt]{./CH5_Examples/eulerfivepole.png} + % eulerfivepole.png: 883x343 pixel, 72dpi, 31.15x12.10 cm, bb=0 0 883 343 + \caption{Euler diagram showing {\fg}/{\dc} relationships for the analysis of the Five Pole Sallen Key filter.} \label{fig:circuit2h} \end{figure} @@ -1591,7 +1616,8 @@ Initially we use the first identified {\fgs} to create our model without further Our functional group for this analysis can be expressed thus: % -$$ G^1_0 = \{ PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} ,$$ +%$$ G^1_0 = \{ PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} ,$$ +$$ G = \{ PHS45, NIBUFF, PHS45, NIBUFF, PHS45, NIBUFF PHS45, INVAMP \} ,$$ or in Euler diagram format as in figure~\ref{fig:bubbaeuler1}. % HTR 23SEP2012 \begin{figure}[h+] % HTR 23SEP2012 \centering @@ -1920,7 +1946,7 @@ to analyse in the future. %is higher, by an order of $O(N^2)$. Smaller functional groups mean less by-hand checks are required. It also means a more finely grained model. 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