diff --git a/submission_thesis/CH2_FMEA/copy.tex b/submission_thesis/CH2_FMEA/copy.tex index deceba3..8e9d5f0 100644 --- a/submission_thesis/CH2_FMEA/copy.tex +++ b/submission_thesis/CH2_FMEA/copy.tex @@ -384,6 +384,7 @@ $$ fm(R) = \{ OPEN, SHORT \} . $$ % The operational amplifier (op-amp) %is a differential amplifier and is very widely used in nearly all fields of modern analogue electronics. +\fmmdglossOPAMP % Only one of two sources of information on {\bc} {\fms} being compared has an entry specific to operational amplifiers (FMD-91). @@ -402,6 +403,7 @@ is applied to a typical op-amp designed for instrumentation and measurement, the (see figure~\ref{fig:lm258}). % The results from both sources of {\fm} definition are then compared. +\fmmdglossOPAMP \paragraph{Failure Modes of an Op-Amp according to FMD-91.} \fmodegloss @@ -424,6 +426,7 @@ Each failure cause is examined in turn, and mapped to potential {\fms} suitable investigations. \paragraph{Op-Amp failure cause: Poor Die attach.} +\fmmdglossOPAMP 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. @@ -476,7 +479,7 @@ are examined and from this its {\fms} are determined. Collating the op-amp failure modes from table ~\ref{tbl:lm358} the same {\fms} from FMD-91 are obtained---listed in equation~\ref{eqn:opampfms}---except for $LOW\_SLEW$. - +\fmmdglossOPAMP %\paragraph{EN298: Open and shorted pin failure symptom determination technique} @@ -559,7 +562,7 @@ are assigned the following failure modes: % $$ fm(OPAMP) = \{ LOW, HIGH, NOOP, LOW\_SLEW \} . $$ % - +\fmmdglossOPAMP \subsection{Comparing the component failure mode sources: EN298 vs FMD-91} @@ -647,6 +650,7 @@ effect of this failure mode. % For instance it has been assumed that the resistor R1 going SHORT will not affect the ADC, the Microprocessor or the UART. +\fmmdglossADC % % % diff --git a/submission_thesis/CH4_FMMD/copy.tex b/submission_thesis/CH4_FMMD/copy.tex index 1ae3b59..43a4242 100644 --- a/submission_thesis/CH4_FMMD/copy.tex +++ b/submission_thesis/CH4_FMMD/copy.tex @@ -136,11 +136,12 @@ two resistors; a circuit schematic for this is shown in figure \ref{fig:noninvam % The function of the resistors in this circuit is to set the amplifier gain. % +\fmmdglossOPAMP The resistors act as a potential divider---assuming the op-amp has high impedance---and program the inverting input on the op-amp to balance them against the positive input, giving the voltage gain ($G_v$) defined by $ G_v = 1 + \frac{R2}{R1} $ at the output. - +\fmmdglossOPAMP \paragraph{Analysing the failure modes of the Potential Divider.} \label{subsec:potdiv} @@ -359,6 +360,7 @@ as a building block for other {\fgs} in the same way that the base components $R \label{sec:opamp_fms} %\clearpage Consider the op-amp as a {\bc}. +\fmmdglossOPAMP % According to FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes %(with assigned probabilities): @@ -409,6 +411,7 @@ These op-amp failure modes are represented on the DAG in figure~\ref{fig:op1dag} %\paragraph{Modelling the OP amp with the potential divider.} The op-amp and the {\dc} {\em PD} now % andrew heavily critised this sentence but it made sense to Chris and I formed into a {\fg} to model the failure mode behaviour of the non-inverting amplifier. +\fmmdglossOPAMP % %piss have the failure modes of the {\dc} for the potential divider, %so we do not need to go back and consider the individual resistor failure modes that defined its behaviour. @@ -429,7 +432,7 @@ as {\fcs} in table~\ref{tbl:ampfmea1}. \centering % used for centering table \begin{tabular}{||l|c|c|l||} \hline \hline -%% FIDDLINGING HATAR HAVING TO REMOVE THE TERM FAILURE SCENARIO --- whats is this the fucking +%% FIDDLINGING HATAR HAVING TO REMOVE THE TERM FAILURE SCENARIO --- whats is this the %%childrens version %\textbf{Failure} & \textbf{Amplifier} & \textbf{Derived component} \\ %Symptom} \\ % \textbf{Scenario} & \textbf{Effect} & \textbf{Failure Modes} \\ %Description} \\ @@ -679,6 +682,7 @@ defines a `part' thus This definition %of a `part' is useful, but consider parts, such as quad packaged op-amps: in this case we have four op-amps on one chip. +\fmmdglossOPAMP % Using traditional FMEA methods~\cite{sccs}[p.34] each op-amp in the package would be considered as a separate building block for a circuit. @@ -697,6 +701,7 @@ used as a starting bottom-up building block. %This is a choice made by the analyst, often guided by the standards to which the analysis is being performed. % to. % Both op-amps and transistors have published statistical failure rates and yet an op-amp is constructed from transistors. +\fmmdglossOPAMP % However, a circuit designer would usually consider individual transistors and individual op-amps as lowest level building blocks. @@ -1053,6 +1058,7 @@ components, {\dcs} may be used to form {\fgs}. Consider the hierarchy from the example in figure~\ref{fig:eulerfmmd}. % ~\ref{fig:dc2}. % The lowest level in this hierarchy are the {\bcs}, the resistors and the op-amp. +\fmmdglossOPAMP % The resistors are collected into a {\fg}, and the ${PD}$ derived component created from its analysis, is shown enclosing R1 and R2. % above the {\fg}. % diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index 300f43d..269d909 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/submission_thesis/CH5_Examples/copy.tex @@ -21,7 +21,8 @@ hybrids. this examines re-use of the potential divider {\dc} from section~\ref{subsec:potdiv}. This amplifier is analysed twice, using different compositions of {\fgs}. The two approaches, i.e. effects of choice of membership for {\fgs} are then discussed. -% +%\ +fmmdglossOPAMP \item Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used to create a differencing amplifier. Building on the two approaches from section~\ref{sec:invamp}, re-use of the non-inverting amplifier {\dc} from section~\ref{sec:invamp} @@ -37,6 +38,7 @@ increasing test efficiency. This example also serves to show a deeper hierarchy loop topology---using a `Bubba' oscillator---demonstrating how FMMD differs from fault diagnosis techniques. %which uses %four op-amp stages with supporting components. +\fmmdglossOPAMP Two analysis strategies are employed, one using initially identified {\fgs} and the second using a more complex hierarchy of %{\fgs} and {\dcs} showing @@ -82,6 +84,7 @@ However, $PD$ cannot be directly re-used, and not just because the potential divider is floating i.e. that the polarity of the R2 side of the potential divider is determined by the output from the op-amp. +\fmmdglossOPAMP % The circuit schematic stipulates that the input is positive. % @@ -305,6 +308,7 @@ to traverse from system level or top failure modes to base component failure mod % \subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}} \label{subsec:invamp2} + % The problem above is analysed without using an intermediate $INVPD$ derived component. @@ -368,6 +372,7 @@ The next stage analysed a {\fg} comprised of the INVPD and an OpAmp. % The second analysis (3 components) looked at the effects of each failure mode of each resistor and the op-amp. % circuit. +\fmmdglossOPAMP % This meant more work for the analyst---that is an increase in the complexity of the analysis---compared to @@ -396,7 +401,7 @@ For the unconstrained case, it is necessary to consider all three components as \caption{Circuit 1} \label{fig:circuit1} \end{figure} - +\fmmdglossOPAMP The circuit in figure~\ref{fig:circuit1} amplifies the difference between the input voltages $+V1$ and $+V2$. @@ -524,7 +529,7 @@ Common symptoms of failure are collected. A derived component to represent the failure mode behaviour of the differencing amplifier circuit (see figure~\ref{fig:circuit1}) is created: $$ fm (DiffAMP) = \{DiffAMPLow, DiffAMPHigh, DiffAMP\_LP, DiffAMPIncorrect\} . $$ - +\fmmdglossOPAMP The failure analysis performed is represented as a directed graph in figure~\ref{fig:circuit1_dag}. %of the failure modes and derived components. @@ -669,11 +674,13 @@ Applying the $fm$ function yields: $$ fm(FirstOrderLP) = \{ LPnofilter,LPnosigna \paragraph{Addition of Buffer Amplifier: First stage.} % The op-amp IC1 is being used simply as a buffer. +\fmmdglossOPAMP % By placing it between the stages %next stages on the signal path the possibility of unwanted signal feedback is avoided. % The buffer is one of the simplest op-amp configurations. +\fmmdglossOPAMP % It has no other components, and a {\fg} is formed from the $FirstOrderLP$ and the OpAmp component. @@ -784,6 +791,7 @@ As the signal has to pass through each block/stage in order to be `five~pole' filtered, these three blocks are brought together to form a {\fg}. % This will give a failure mode model for the whole circuit. +\fmmdglossOPAMP % The Sallen Key stages can be indexed, and these are marked on the circuit schematic in figure~\ref{fig:circuit2002_FIVEPOLE}. @@ -867,7 +875,7 @@ The FMMD hierarchy is shown in figure~\ref{fig:circuit2h}. \label{tbl:fivepole} \end{table} % -% FUCKING HELL WEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE +% A {\dc} is created to represent the circuit in figure~\ref{fig:circuit2}, called $FivePoleLP$: applying the $fm$ function (see table~\ref{tbl:fivepole}) yields $$fm(FivePoleLP) = \{ HIGH, LOW, FilterIncorrect, NO\_SIGNAL \}.$$ @@ -880,6 +888,9 @@ is simple (as it is never inverted). % The circuit under analysis is -- as shown in the block diagram (see figure~\ref{fig:blockdiagramcircuit2}) -- three op-amp driven non-inverting low pass filter elements. +\fmmdglossOPAMP +% +% % It is not surprising therefore that they have very similar failure modes. % @@ -934,7 +945,7 @@ amplifier. % These are named $INVAMP$, $PHS45$ and $NIBUFF$ respectively. These {\fgs} are used to describe the circuit in block diagram form with arrows indicating the signal path, in figure~\ref{fig:bubbablock}. - +\fmmdglossOPAMP \begin{figure}[h] \centering \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/bubba_oscillator_block_diagram.png} @@ -1282,6 +1293,7 @@ IC1,IC2 and IC3 are all OpAmps and have failure modes for this component type (i.e. from section~\ref{sec:opamp_fms}): % $$ fm(OPAMP) = \{ HIGH, LOW, NOOP, LOW\_SLEW \}. $$ +\fmmdglossOPAMP % The literature was examined for a failure model for a D-type flip flop~\cite{fmd91}[3-105], and the CD4013B~\cite{cd4013} chosen. @@ -1342,6 +1354,7 @@ This prevents electrical loading, and thus interference with, the SUMJINT stage. This is simply an op-amp with the input connected to the +ve input and the -ve input grounded. % +\fmmdglossOPAMP This is an OpAmp in a signal buffer configuration and therefore simply has the failure modes of an Op-amp. % @@ -1375,6 +1388,7 @@ $$ % IC3 is an op-amp and has the failure modes $$fm(IC3) = \{ HIGH, LOW, NOOP, LOW\_SLEW \} . $$ +\fmmdglossOPAMP % The digital signal is supplied to the non-inverting input. The output is a voltage level in the analogue domain $-V$ or $+V$. diff --git a/submission_thesis/CH8_Conclusion/copy.tex b/submission_thesis/CH8_Conclusion/copy.tex index 870de53..c2ceef6 100644 --- a/submission_thesis/CH8_Conclusion/copy.tex +++ b/submission_thesis/CH8_Conclusion/copy.tex @@ -37,7 +37,8 @@ both in the same circuit and other circuits and potentially future projects as well. Traditional FMEA methods have been applied to software, but analysis has always been performed separately from -the electronic FMEA~\cite{sfmeaa,sfmea}. %, and while modular kept strictly to a bottom-up approach. +the HFMEA~\cite{sfmeaa,sfmea}. %, and while modular kept strictly to a bottom-up approach. +\fmmdglossHFMEA % Using established concepts from contract programming~\cite{dbcbe} FMMD was extended to analyse software, which facilitated a solution to the software/hardware interfacing problem~\cite{sfmeainterface}. @@ -109,10 +110,10 @@ These are presented below. % \fmmdgloss \fmeagloss -An FMMD model has a data structure (described by UML diagrams, see figure~\ref{fig:cfg}), and by traversing an FMMD hierarchy +An FMMD model has a data structure (described by UML diagrams, see figure~\ref{fig:cfg}) and by traversing an FMMD hierarchy, system level failures can be mapped back to {\bc} {\fms} (or combinations thereof). % -Because these mappings can be determined reports in the traditional FMEA format (i.e. {\bc}~{\fm}~$\mapsto$~{system failure}) can be produced. +Because these mappings can be determined, reports in the traditional FMEA format (i.e. {\bc}~{\fm}~$\mapsto$~{system failure}) can be produced. % With the addition of {\bc} {\fm} statistics~\cite{mil1991} reliability predictions for system level failures can be provided. % @@ -134,7 +135,7 @@ is examined in section~\ref{sec:fta}. \subsection{Statistics: From base component failure modes to System level events/failures.} \label{sec:bcstats} -Knowing the statistical likelihood of a component failing can give a good indication +Knowing the statistical likelihoods of a components failing can give a good indication of the reliability of a system, or in the case of dangerous failures, the Safety Integrity Level of a system. % @@ -148,234 +149,19 @@ into its hierarchical model. Because an FMMD model can be used to generate an FMEA report, with additional {\bc} failure mode statistics an FMEDA report can be produced. +% +FMMD has been applied to the Pt100 example in appendix~\ref{detailed:Pt100stats}. +% +This demonstrates FIT values being obtained for single and doubly sourced system failure modes +in a way that is compatible with FMEDA/EN61508. + + %we can %therefore %use FMMD to produce an FMEDA report. - - -\paragraph{Pt100 Example: Single Failures and statistical data.} %Mean Time to Failure} -\frategloss -From an earlier example, the model for the failure mode behaviour of the Pt100 circuit, -{\bc} {\fm} statistics are added to determine the probability of symptoms of failure. -% -The DOD electronic reliability of components -document MIL-HDBK-217F~\cite{mil1991} gives formulae for calculating -the -%$\frac{failures}{{10}^6}$ -${failures}/{{10}^6}$ % looks better -in hours for a wide range of generic components -\footnote{These figures are based on components from the 1980's and MIL-HDBK-217F -can give conservative reliability figures when applied to -modern components}. -% -Using the MIL-HDBK-217F %~\cite{mil1991} -specifications for resistor and thermistor failure statistics, the reliability for the Pt100 example (see section~\ref{sec:Pt100}) is calculated below. -% -% -\paragraph{Resistor FIT Calculations.} -% -The formula given in MIL-HDBK-217F\cite{mil1991}[9.2] for a generic fixed film non-power resistor -is reproduced in equation \ref{resistorfit}. The meanings -and values assigned to its co-efficients are described in table \ref{tab:resistor}. -\fmmdglossFIT -\fmodegloss -% -\begin{equation} -% fixed comp resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E -resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E - \label{resistorfit} -\end{equation} - -\begin{table}[ht] -\caption{Fixed film resistor Failure In Time (FIT) assessment.} % title of Table -\centering % used for centering table -\begin{tabular}{||c|c|l||} -\hline \hline - \em{Parameter} & \em{Value} & \em{Comments} \\ - & & \\ \hline \hline - ${\lambda}_{b}$ & 0.00092 & stress/temp base failure rate $60^o$ C \\ \hline - %${\pi}_T$ & 4.2 & max temp of $60^o$ C\\ \hline - ${\pi}_R$ & 1.0 & Resistance range $< 0.1M\Omega$\\ \hline - ${\pi}_Q$ & 15.0 & Non-Mil spec component\\ \hline - ${\pi}_E$ & 1.0 & benign ground environment\\ \hline - -\hline \hline -\end{tabular} -\label{tab:resistor} -\end{table} -\frategloss -Applying equation \ref{resistorfit} with the parameters from table \ref{tab:resistor} -give the following failures in ${10}^6$ hours: - -\begin{equation} - 0.00092 \times 1.0 \times 15.0 \times 1.0 = 0.0138 \;{failures}/{{10}^{6} Hours} - \label{eqn:resistor} -\end{equation} - -While MIL-HDBK-217F gives MTTF for a wide range of common components, -it does not specify how the components will fail (in this case OPEN or SHORT). -% -Some standards, notably EN298 only consider most types of resistor as failing in OPEN mode. -%FMD-97 gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. -% FMD-91 gives parameter change as a third failure mode, luvvverly 08FEB2011 -This example -compromises and uses a 9:1 OPEN:SHORT ratio, for resistor failure. -% -Thus for this example resistors are expected to fail OPEN in 90\% of cases and SHORTED -in the other 10\%. -A standard fixed film resistor, for use in a benign environment, non military specification at -temperatures up to {60\oc} is given a probability of 13.8 failures per billion ($10^9$) -hours of operation (see equation \ref{eqn:resistor}). -In EN61508 terminology, this figure is referred to as a Failure in Time FIT\footnote{FIT values are measured as the number of -failures per Billion (${10}^9$) hours of operation, (roughly 114,000 years). The smaller the -FIT number the more reliable the component.}. -% -The formula given for a thermistor in MIL-HDBK-217F\cite{mil1991}[9.8] is reproduced in -equation \ref{thermistorfit}. The variable meanings and values are described in table \ref{tab:thermistor}. -% -\begin{equation} -% fixed comp resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E -resistor{\lambda}_p = {\lambda}_{b}{\pi}_Q{\pi}_E - \label{thermistorfit} -\end{equation} -% -\begin{table}[ht] -\caption{Bead type Thermistor Failure in time assessment} % title of Table -\centering % used for centering table -\begin{tabular}{||c|c|l||} -\hline \hline - \em{Parameter} & \em{Value} & \em{Comments} \\ - & & \\ \hline \hline - ${\lambda}_{b}$ & 0.021 & stress/temp base failure rate bead thermistor \\ \hline - %${\pi}_T$ & 4.2 & max temp of $60^o$ C\\ \hline - %${\pi}_R$ & 1.0 & Resistance range $< 0.1M\Omega$\\ \hline - ${\pi}_Q$ & 15.0 & Non-Mil spec component\\ \hline - ${\pi}_E$ & 1.0 & benign ground environment\\ \hline - -\hline \hline -\end{tabular} -\label{tab:thermistor} -\end{table} -% -\begin{equation} - 0.021 \times 1.0 \times 15.0 \times 1.0 = 0.315 \; {failures}/{{10}^{6} Hours} - \label{eqn:thermistor} -\end{equation} -% -Thus thermistor, bead type, `non~military~spec' is given a FIT of 315.0. -% -\frategloss -Using the RIAC finding the following (table~\ref{tab:stat_single}) can be created which -presents the FIT values for all single failure modes. -%\glossary{name={FIT}, description={Failure in Time (FIT). The number of times a particular failure is expected to occur in a $10^{9}$ hour time period.}} -\fmmdglossFIT -% -\begin{table}[h+] -\caption{Pt100 FMEA Single // Fault Statistics} % title of Table -\centering % used for centering table -\begin{tabular}{||l|c|c|l|l||} -\hline \hline - \textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\ - \textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\ -% R & wire & res + & res - & description -\hline -\hline -TC:1 $R_1$ SHORT & High Fault & - & 1.38 \\ \hline -TC:2 $R_1$ OPEN & Low Fault & Low Fault & 12.42\\ \hline - \hline -TC:3 $R_3$ SHORT & Low Fault & High Fault & 31.5 \\ \hline -TC:4 $R_3$ OPEN & High Fault & Low Fault & 283.5 \\ \hline -\hline -TC:5 $R_2$ SHORT & - & Low Fault & 1.38 \\ -TC:6 $R_2$ OPEN & High Fault & High Fault & 12.42 \\ \hline -\hline -\end{tabular} -\label{tab:stat_single} -\end{table} -% -\frategloss -% -The FIT for the circuit as a whole is the sum of MTTF values for all the -test cases. The Pt100 circuit here has a FIT of 342.6. This is a MTTF of -about $\approx 360$ years per circuit. -% -A probabilistic tree can now be drawn, with a FIT value for the Pt100 -circuit and FIT values for all the component fault modes from which it was calculated. -% -From this it can be seen that the most likely fault is the thermistor going OPEN. -% -This circuit is around 10 times more likely to fail in this way than in any other. -% -If a more reliable temperature sensor was required, this would probably -be the fault~mode scrutinised first. -% -\frategloss -% -\begin{figure}[h+] - \centering - \includegraphics[width=400pt,bb=0 0 856 327,keepaspectratio=true]{./CH5_Examples/stat_single.png} - % stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327 - \caption{Probablistic Fault Tree : Pt100 Single Faults} - \label{fig:stat_single} -\end{figure} -% -The Pt100 analysis presents a simple result for single faults. -The next analysis phase looks at how the circuit will behave under double simultaneous failure -conditions. -% -% -\paragraph{Pt100 Example: Double Failures and statistical data.} -Because double simultaneous failure analysis can be performed under FMMD -failure rate statistics for double failures can also be determined. -% -\frategloss -% -%% -%% Need to talk abou the `detection time' -%% or `Safety Relevant Validation Time' ref can book -%% EN61508 gives detection calculations to reduce -%% statistical impacts of failures. -%% -% -Considering the failure modes to be statistically independent -the FIT values for all the combinations of -failures in the electronic examples from chapter~\ref{sec:chap5} in table~\ref{tab:ptfmea2} can be calculated. -% -The failure mode of most concern, the undetectable {\textbf{FLOATING}} condition, -requires that resistors $R_1$ and $R_2$ both fail. -% -Multiplying the MTTF probabilities for these types of resistor failing gives the MTTF for both failing. -% -The FIT value of 12.42 corresponds to $12.42 \times {10}^{-9}$ failures per hour. -% -Squaring this gives $ 154.3 \times {10}^{-18} $. -% -This is an astronomically small MTTF, and so small that it would -probably fall below a threshold to sensibly consider. -% -However, it is very interesting from a failure analysis perspective, -because an undetectable fault (at least at this -level in the FMMD hierarchy) has been revealed. -% -This means that should it be required to cope with -this fault, a new way of detecting this -condition must be engineered, perhaps in higher levels of the system/FMMD hierarchy. -% -\paragraph{MTTF statistics and FMMD hierarchies.} -% -In a large FMMD model, system/top level failures can be traced -down to {\bc} {\fms}. -% -To determine the MTTF probability -for a system level failure, -the MTTF statistics are added for all its possible causes. -% -Thus even for large FMMD models accurate -statistics for electronic sourced failures can be calculated. -% -%\glossary{name={FIT}, description={Failure in Time (FIT). The number of times a particular failure is expected to occur in a $10^{9}$ hour time period. Associated with continuous demand systems under EN61508~\cite{en61508}}} -% \frategloss \fmmdglossFIT + + % \subsection{Deriving FTA diagrams from FMMD models} \label{sec:fta} @@ -613,7 +399,7 @@ thus it can be verified that all failure modes from the electronics module have been dealt with by the controlling software. % -If not, they would be an un-handled error condition relating to the software hardware interface. +If not, they would be an un-handled error condition relating to the software/hardware interface. % This again can be flagged using an automated tool. % diff --git a/submission_thesis/appendixes/detailed_analysis.tex b/submission_thesis/appendixes/detailed_analysis.tex index e8536c1..060ea30 100644 --- a/submission_thesis/appendixes/detailed_analysis.tex +++ b/submission_thesis/appendixes/detailed_analysis.tex @@ -99,8 +99,8 @@ FMEA study of a resistor and capacitor in use as a phase changer. \end{tabular} \end{table} -Collecting symptoms from table~\ref{tbl:bubbalargefg} we can show that for single failure modes, applying $fm$ to the bubba oscillator -returns three failure modes, +Collecting symptoms from table~\ref{tbl:bubbalargefg} it can be shown that for single failure modes, applying $fm$ to the bubba oscillator +gives three failure modes: % $$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$ @@ -140,7 +140,7 @@ $$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$ \end{table} -collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes: +collecting symptoms from table~\ref{tbl:buff45}, a derived component $BUFF45$ is created which has the following failure modes: $$ fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift, $$ @@ -186,7 +186,7 @@ $$ \end{table} % % -Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes: +Collecting symptoms from table~\ref{tbl:phs135buffered}, a derived component $PHS135BUFFERED$ is created which has the following failure modes: $$ fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal .\} % 180\_phaseshift, $$ @@ -222,7 +222,7 @@ $$ \end{tabular} \end{table} % -Applying FMMD we create a derived component $PHS225AMP$ which has the following failure modes: +Applying FMMD a derived component $PHS225AMP$ is created which has the following failure modes: $$ fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift, $$ @@ -260,7 +260,7 @@ $$ \end{tabular} \end{table} % -Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes: +Collecting symptoms from table~\ref{tbl:bubba2}, a derived component $BUBBAOSC$ is created which has the following failure modes: $$ fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc}, $$ @@ -307,7 +307,7 @@ $$ \end{tabular} \end{table} Collecting the {\dc} failure modes of -$SUMJINT$ we obtain $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ +$SUMJINT$ gives $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ \clearpage @@ -362,7 +362,7 @@ $SUMJINT$ we obtain $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \ \end{tabular} \end{table} -We collect the symptoms of failure $\{ LOW, HIGH, LOW\_{SLEW} \}$. +The symptoms of failure, i.e. $\{ LOW, HIGH, LOW\_{SLEW} \}$ are collected. \clearpage @@ -392,7 +392,7 @@ We collect the symptoms of failure $\{ LOW, HIGH, LOW\_{SLEW} \}$. \end{tabular} \end{table} -We collect the symptoms of failure $\{ LOW, STOPPED \}$. +The symptoms of failure i.e. $\{ LOW, STOPPED \}$ are collected. \clearpage @@ -425,7 +425,7 @@ We collect the symptoms of failure $\{ LOW, STOPPED \}$. \end{tabular} \end{table} -We now collect the symptoms of failure $\{ OUTPUT STUCK , REDUCED\_INTEGRATION \}$, and create a {\dc} +The symptoms of failure $\{ OUTPUT STUCK , REDUCED\_INTEGRATION \}$ collected , a {\dc} created called $BISJ$. \clearpage @@ -459,8 +459,8 @@ called $BISJ$. \end{tabular} \end{table} -We now collect symptoms $\{OUTPUT STUCK, LOW\_SLEW\}$ and create a {\dc} %at the third level of symptom abstraction -called $FFB$. +Symptoms of failure are collected $\{OUTPUT STUCK, LOW\_SLEW\}$ and a {\dc} %at the third level of symptom abstraction +called $FFB$ created. \clearpage \subsection{FMMD Analysis of \sd : SDADC} @@ -490,11 +490,11 @@ called $FFB$. \end{tabular} \end{table} %\clearpage -We now collect the symptoms for the \sd +The symptoms for the \sd are collected $$ \; \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}.$$ -We can now create a {\dc} to represent the analogue to digital converter, $SDADC$. +A {\dc} is created to represent the failure behaviour of the analogue to digital converter, $SDADC$. $$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$$ - +\fmmdglossADC \clearpage @@ -541,6 +541,7 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. \end{tabular} \end{table} } +\fmmdglossADC \clearpage \subsection{ Get\_Temperature: Failure Mode Effects Analysis } @@ -829,7 +830,237 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. } \clearpage -\subsection{Gnuplot script for hypothetical XFMEA FMMD reasoning distance comparision} + +\subsection{Statistics and FMMD: Pt100 example for single and double failures} +\label{detailed:Pt100stats} +\paragraph{Pt100: Single Failures and statistical data.} %Mean Time to Failure} +\frategloss +From an earlier example, the model for the failure mode behaviour of the Pt100 circuit, +{\bc} {\fm} statistics are added to determine the probability of symptoms of failure. +% +The DOD electronic reliability of components +document MIL-HDBK-217F~\cite{mil1991} gives formulae for calculating +the +%$\frac{failures}{{10}^6}$ +${failures}/{{10}^6}$ % looks better +in hours for a wide range of generic components +\footnote{These figures are based on components from the 1980's and MIL-HDBK-217F +can give conservative reliability figures when applied to +modern components}. +% +Using the MIL-HDBK-217F %~\cite{mil1991} +specifications for resistor and thermistor failure statistics, the reliability for the Pt100 example (see section~\ref{sec:Pt100}) is calculated below. +% +% +\paragraph{Resistor FIT Calculations.} +% +The formula given in MIL-HDBK-217F\cite{mil1991}[9.2] for a generic fixed film non-power resistor +is reproduced in equation \ref{resistorfit}. The meanings +and values assigned to its co-efficients are described in table \ref{tab:resistor}. +\fmmdglossFIT +\fmodegloss +% +\begin{equation} +% fixed comp resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E +resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E + \label{resistorfit} +\end{equation} + +\begin{table}[ht] +\caption{Fixed film resistor Failure In Time (FIT) assessment.} % title of Table +\centering % used for centering table +\begin{tabular}{||c|c|l||} +\hline \hline + \em{Parameter} & \em{Value} & \em{Comments} \\ + & & \\ \hline \hline + ${\lambda}_{b}$ & 0.00092 & stress/temp base failure rate $60^o$ C \\ \hline + %${\pi}_T$ & 4.2 & max temp of $60^o$ C\\ \hline + ${\pi}_R$ & 1.0 & Resistance range $< 0.1M\Omega$\\ \hline + ${\pi}_Q$ & 15.0 & Non-Mil spec component\\ \hline + ${\pi}_E$ & 1.0 & benign ground environment\\ \hline + +\hline \hline +\end{tabular} +\label{tab:resistor} +\end{table} +\frategloss +Applying equation \ref{resistorfit} with the parameters from table \ref{tab:resistor} +give the following failures in ${10}^6$ hours: + +\begin{equation} + 0.00092 \times 1.0 \times 15.0 \times 1.0 = 0.0138 \;{failures}/{{10}^{6} Hours} + \label{eqn:resistor} +\end{equation} + +While MIL-HDBK-217F gives MTTF for a wide range of common components, +it does not specify how the components will fail (in this case OPEN or SHORT). +% +Some standards, notably EN298 only consider most types of resistor as failing in OPEN mode. +%FMD-97 gives 27\% OPEN and 3\% SHORTED, for resistors under certain electrical and environmental stresses. +% FMD-91 gives parameter change as a third failure mode, luvvverly 08FEB2011 +This example +compromises and uses a 9:1 OPEN:SHORT ratio, for resistor failure. +% +Thus for this example resistors are expected to fail OPEN in 90\% of cases and SHORTED +in the other 10\%. +A standard fixed film resistor, for use in a benign environment, non military specification at +temperatures up to {60\oc} is given a probability of 13.8 failures per billion ($10^9$) +hours of operation (see equation \ref{eqn:resistor}). +In EN61508 terminology, this figure is referred to as a Failure in Time FIT\footnote{FIT values are measured as the number of +failures per Billion (${10}^9$) hours of operation, (roughly 114,000 years). The smaller the +FIT number the more reliable the component.}. +% +The formula given for a thermistor in MIL-HDBK-217F\cite{mil1991}[9.8] is reproduced in +equation \ref{thermistorfit}. The variable meanings and values are described in table \ref{tab:thermistor}. +% +\begin{equation} +% fixed comp resistor{\lambda}_p = {\lambda}_{b}{\pi}_{R}{\pi}_Q{\pi}_E +resistor{\lambda}_p = {\lambda}_{b}{\pi}_Q{\pi}_E + \label{thermistorfit} +\end{equation} +% +\begin{table}[ht] +\caption{Bead type Thermistor Failure in time assessment} % title of Table +\centering % used for centering table +\begin{tabular}{||c|c|l||} +\hline \hline + \em{Parameter} & \em{Value} & \em{Comments} \\ + & & \\ \hline \hline + ${\lambda}_{b}$ & 0.021 & stress/temp base failure rate bead thermistor \\ \hline + %${\pi}_T$ & 4.2 & max temp of $60^o$ C\\ \hline + %${\pi}_R$ & 1.0 & Resistance range $< 0.1M\Omega$\\ \hline + ${\pi}_Q$ & 15.0 & Non-Mil spec component\\ \hline + ${\pi}_E$ & 1.0 & benign ground environment\\ \hline + +\hline \hline +\end{tabular} +\label{tab:thermistor} +\end{table} +% +\begin{equation} + 0.021 \times 1.0 \times 15.0 \times 1.0 = 0.315 \; {failures}/{{10}^{6} Hours} + \label{eqn:thermistor} +\end{equation} +% +Thus thermistor, bead type, `non~military~spec' is given a FIT of 315.0. +% +\frategloss +Using the RIAC finding the following (table~\ref{tab:stat_single}) can be created which +presents the FIT values for all single failure modes. +%\glossary{name={FIT}, description={Failure in Time (FIT). The number of times a particular failure is expected to occur in a $10^{9}$ hour time period.}} +\fmmdglossFIT +% +\begin{table}[h+] +\caption{Pt100 FMEA Single // Fault Statistics} % title of Table +\centering % used for centering table +\begin{tabular}{||l|c|c|l|l||} +\hline \hline + \textbf{Test} & \textbf{Result} & \textbf{Result } & \textbf{MTTF} \\ + \textbf{Case} & \textbf{sense +} & \textbf{sense -} & \textbf{per $10^9$ hours of operation} \\ +% R & wire & res + & res - & description +\hline +\hline +TC:1 $R_1$ SHORT & High Fault & - & 1.38 \\ \hline +TC:2 $R_1$ OPEN & Low Fault & Low Fault & 12.42\\ \hline + \hline +TC:3 $R_3$ SHORT & Low Fault & High Fault & 31.5 \\ \hline +TC:4 $R_3$ OPEN & High Fault & Low Fault & 283.5 \\ \hline +\hline +TC:5 $R_2$ SHORT & - & Low Fault & 1.38 \\ +TC:6 $R_2$ OPEN & High Fault & High Fault & 12.42 \\ \hline +\hline +\end{tabular} +\label{tab:stat_single} +\end{table} +% +\frategloss +% +The FIT for the circuit as a whole is the sum of MTTF values for all the +test cases. The Pt100 circuit here has a FIT of 342.6. This is a MTTF of +about $\approx 360$ years per circuit. +% +A probabilistic tree can now be drawn, with a FIT value for the Pt100 +circuit and FIT values for all the component fault modes from which it was calculated. +% +From this it can be seen that the most likely fault is the thermistor going OPEN. +% +This circuit is around 10 times more likely to fail in this way than in any other. +% +If a more reliable temperature sensor was required, this would probably +be the fault~mode scrutinised first. +% +\frategloss +% +\begin{figure}[h+] + \centering + \includegraphics[width=400pt,bb=0 0 856 327,keepaspectratio=true]{./CH5_Examples/stat_single.png} + % stat_single.jpg: 856x327 pixel, 72dpi, 30.20x11.54 cm, bb=0 0 856 327 + \caption{Probablistic Fault Tree : Pt100 Single Faults} + \label{fig:stat_single} +\end{figure} +% +The Pt100 analysis presents a simple result for single faults. +The next analysis phase looks at how the circuit will behave under double simultaneous failure +conditions. +% +% +\paragraph{Pt100 Example: Double Failures and statistical data.} +Because double simultaneous failure analysis can be performed under FMMD +failure rate statistics for double failures can also be determined. +% +\frategloss +% +%% +%% Need to talk abou the `detection time' +%% or `Safety Relevant Validation Time' ref can book +%% EN61508 gives detection calculations to reduce +%% statistical impacts of failures. +%% +% +Considering the failure modes to be statistically independent +the FIT values for all the combinations of +failures in the electronic examples from chapter~\ref{sec:chap5} in table~\ref{tab:ptfmea2} can be calculated. +% +The failure mode of most concern, the undetectable {\textbf{FLOATING}} condition, +requires that resistors $R_1$ and $R_2$ both fail. +% +Multiplying the MTTF probabilities for these types of resistor failing gives the MTTF for both failing. +% +The FIT value of 12.42 corresponds to $12.42 \times {10}^{-9}$ failures per hour. +% +Squaring this gives $ 154.3 \times {10}^{-18} $. +% +This is an astronomically small MTTF, and so small that it would +probably fall below a threshold to sensibly consider. +% +However, it is very interesting from a failure analysis perspective, +because an undetectable fault (at least at this +level in the FMMD hierarchy) has been revealed. +% +This means that should it be required to cope with +this fault, a new way of detecting this +condition must be engineered, perhaps in higher levels of the system/FMMD hierarchy. +% +\paragraph{MTTF statistics and FMMD hierarchies.} +% +In a large FMMD model, system/top level failures can be traced +down to {\bc} {\fms}. +% +To determine the MTTF probability +for a system level failure, +the MTTF statistics are added for all its possible causes. +% +Thus even for large FMMD models accurate +statistics for electronic sourced failures can be calculated. +% +%\glossary{name={FIT}, description={Failure in Time (FIT). The number of times a particular failure is expected to occur in a $10^{9}$ hour time period. Associated with continuous demand systems under EN61508~\cite{en61508}}} +% +\frategloss +\fmmdglossFIT + +\clearpage + +\subsection{Gnuplot script for hypothetical XFMEA FMMD reasoning distance comparison} \label{sec:gnuplotxfmeafmmdcomp} \begin{verbatim} diff --git a/submission_thesis/style.tex b/submission_thesis/style.tex index 7a09e61..5a6dd0e 100644 --- a/submission_thesis/style.tex +++ b/submission_thesis/style.tex @@ -81,8 +81,8 @@ %\fmodegloss -\newcommand{\fmmdglossADC}{\glossary{name={system}, description={ -Analogue to digital converter}}} +\newcommand{\fmmdglossADC}{\glossary{name={ADC}, description={ +Analogue to digital converter, a digital device to read voltages into a computer/micro-controller}}} \newcommand{\fmmdglossSYS}{\glossary{name={system}, description={ @@ -123,6 +123,14 @@ Design FMEA. FMEA applied in design stages of a product. Can be used as a discussion/brain~storming method to reveal safety weakness and improve built in safety}}} +\newcommand{\fmmdglossOPAMP}{\glossary{name={Op-Amp},description={ +An Operational Amplifier is a differential input high gain voltage +amplifier typically implemented in an integrated circuit and is +commonly used a building block in analogue circuit design +}}} + + + \newcommand{\fmmdglossPFMEA}{\glossary{name={PFMEA},description={ Production FMEA (PFMEA). FMEA applied for cost benefit analysis typically used in mass production}}}