diff --git a/submission_thesis/CH6_Software_Examples/software.tex b/submission_thesis/CH6_Software_Examples/software.tex index 578d9e3..0215feb 100644 --- a/submission_thesis/CH6_Software_Examples/software.tex +++ b/submission_thesis/CH6_Software_Examples/software.tex @@ -265,7 +265,7 @@ and $0.020A \times \ohms{220} = 4.4V$. % The acceptable voltage range\footnote{For the purpose of clarity resistor tolerance has been ignored. In a practical {\ft} reader resistor tolerance would be factored into the limits, or - `deadbands' of $\approx \half mA$ at either end of the range would be implemented.} +`deadbands' of $\approx \half mA$ at either end of the range would be implemented.} is therefore $$(V \ge 0.88) \wedge (V \le 4.4) \; .$$ @@ -280,7 +280,7 @@ In 'C' a function is declared with parenthesis to differentiate it from other type of variables (data types or pointers). % In this document this format is borrowed, hence the C~language -function called `main' will be presented as \cf{main}. +function called `main' would be presented as \cf{main}. % The software function that performs a conversion from the voltage read to a per~mil representation of the {\ft} input is now discussed. @@ -1184,7 +1184,7 @@ All digital signal processing algorithms are sensitive to calling frequency, and Were this function to be called at an incorrect rate, its output could be erroneous (the differential and integral parameters would effectively have been changed). % -However this problem is a failure mode for the consideration of the function calling it i.e. the context of use (see section~\ref{sec:subjectiveobjective}). +However this problem is a failure mode for the consideration of the function calling it i.e. the context of use. %(see section~\ref{sec:subjectiveobjective}). % That is, the \cf{PID} function is called, but its calling function is responsible for the timing, or in more general terms, diff --git a/submission_thesis/appendixes/detailed_analysis.tex b/submission_thesis/appendixes/detailed_analysis.tex index cd7cbfa..72018af 100644 --- a/submission_thesis/appendixes/detailed_analysis.tex +++ b/submission_thesis/appendixes/detailed_analysis.tex @@ -37,14 +37,16 @@ FMEA study of a resistor and capacitor in use as a phase changer. \end{tabular} \end{table} % PHS45 + +Collecting symptoms from table~\ref{tbl:firstorderlp}, a {\dc}, $PHS45$ is created with the following failure modes: +$$ + fm(PHS45) = \{ 0\_phaseshift, nosignal \} . +$$ \clearpage \subsection{Bubba Oscillator: One Large Functional Group: Detailed Analysis} \label{detail:BUBOSC1} - - - \begin{table}[h+] \caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table \label{tbl:bubbalargefg} @@ -103,10 +105,15 @@ FMEA study of a resistor and capacitor in use as a phase changer. \end{tabular} \end{table} -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: +Collecting symptoms from table~\ref{tbl:bubbalargefg}, the {\dc} $ BubbaOscillator $ is created with the following failure modes: +$$ + fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc} \} . +$$ % -$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$ +%Collecting symptoms from table~\ref{} it can be shown that for single failure modes, applying $fm$ to the bubba oscillator +%gives three failure modes: +% +%$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$ \clearpage \subsection{BUFF45: Detailed Analysis} @@ -141,9 +148,9 @@ $$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$ \end{table} -collecting symptoms from table~\ref{tbl:buff45}, a derived component $BUFF45$ is created which has the following failure modes: +Collecting symptoms from table~\ref{tbl:buff45}, a derived component $BUFF45$ is created which has the following failure modes: $$ -fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift, +fm (BUFF45) = \{ 0\_phaseshift, NO\_signal \} . % 90\_phaseshift, $$ % @@ -189,7 +196,7 @@ $$ % Collecting symptoms from table~\ref{tbl:phs135buffered}, a derived component $PHS135BUFFERED$ is created which has the following failure modes: $$ -fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal .\} % 180\_phaseshift, +fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal \} .% 180\_phaseshift, $$ % \clearpage @@ -223,13 +230,20 @@ $$ \end{tabular} \end{table} % -Applying FMMD a derived component $PHS225AMP$ is created which has the following failure modes: -$$ -fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift, -$$ +% Applying FMMD a {\dc} $PHS225AMP$ is created which has the following failure modes: +% $$ +% fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal \} .% 270\_phaseshift, +% $$ +Collecting symptoms from table~\ref{tbl:phs225amp}, the {\dc} $PHS225AMP $ is created with the following failure modes: +$$ + fm() = \{ 180\_phaseshift, NO\_signal \} . +$$ \clearpage + + + \subsection{BUBBAOSC: Failure Mode Effects Analysis} % title of Table \label{detail:BUBBAOSC} @@ -261,7 +275,7 @@ $$ \end{tabular} \end{table} % -Collecting symptoms from table~\ref{tbl:bubba2}, a derived component $BUBBAOSC$ is created which has the following failure modes: +Collecting symptoms from table~\ref{tbl:bubba2}, a {\dc} $BUBBAOSC$ is created which has the following failure modes: $$ fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal \} . % LO_{fosc}, $$ @@ -271,6 +285,8 @@ $$ \section{Sigma Delta Detailed FMMD Analyses} +This section of the appendix contains FMEA tables for the {\sd}. + \subsection{FMMD Analysis of Summing Junction Integrator: SUMJINT} \label{detail:SUMJINT} \begin{table}[h+] @@ -307,8 +323,13 @@ $$ \hline \end{tabular} \end{table} -Collecting the {\dc} failure modes of -$SUMJINT$ gives $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ + +Collecting symptoms from table~\ref{tbl:sumjint}, the {\dc} $ SUMJINT $ is created with the following failure modes: +$$ + fm() = \{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} . +$$ +% Collecting the {\dc} failure modes of +% $SUMJINT$ gives $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$$ \clearpage @@ -318,6 +339,7 @@ $SUMJINT$ gives $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$ \center % \center \caption{ High Impedance Signal Buffer : Failure Mode Effects Analysis} % title of Table +\label{tbl:HISB} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result} & & \textbf{Symptom} \\ % & & & & \\ @@ -331,6 +353,15 @@ $SUMJINT$ gives $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$ \end{tabular} \end{table} % \hline + + + +Collecting symptoms from table~\ref{tbl:HISB}, the {\dc} $ HISB $ is created with the following failure modes: +$$ + fm(HISB) = \{ HIGH, LOW, NOOP, LOW\_SLEW \} . +$$ + + \clearpage \subsection{FMMD Analysis of Digital level to analogue level converter : DL2AL} @@ -362,12 +393,17 @@ $SUMJINT$ gives $$\{ V_{in} DOM, V_{fb} DOM, NO\_INTEGRATION, HIGH, LOW \} .$ \end{tabular} \end{table} - -The symptoms of failure, i.e. $\{ LOW, HIGH, LOW\_{SLEW} \}$ are collected. +% +%The symptoms of failure, i.e. $\{ LOW, HIGH, LOW\_{SLEW} \}$ are collected. +% +Collecting symptoms from table~\ref{tbl:DL2AL}, the {\dc} $DL2AL$ is created with the following failure modes: +$$ + fm(DL2AL) = \{ LOW, HIGH, LOW\_{SLEW} \} . +$$ \clearpage -\subsection{FMMD Analysis of Digital level to analogue level converter : DL2AL} +\subsection{FMMD Analysis of Digital Buffer : DIGBUF} \label{detail:DIGBUF} \begin{table}[h+] @@ -393,8 +429,13 @@ The symptoms of failure, i.e. $\{ LOW, HIGH, LOW\_{SLEW} \}$ are collected. \end{tabular} \end{table} -The symptoms of failure i.e. $\{ LOW, STOPPED \}$ are collected. - +%The symptoms of failure i.e. $\{ LOW, STOPPED \}$ are collected. +% +Collecting symptoms from table~\ref{tbl:digbuf}, the {\dc} $ DIGBUF $ is created with the following failure modes: +$$ + fm(DIGBUF) = \{ LOW, STOPPED \} . +$$ +% \clearpage \subsection{FMMD Analysis of buffered integrating summing junction : BISJ} @@ -426,9 +467,13 @@ The symptoms of failure i.e. $\{ LOW, STOPPED \}$ are collected. \end{tabular} \end{table} -The symptoms of failure $\{ OUTPUT STUCK , REDUCED\_INTEGRATION \}$ collected , a {\dc} created -called $BISJ$. +%The symptoms of failure $\{ OUTPUT STUCK , REDUCED\_INTEGRATION \}$ collected , a {\dc} created +%called $BISJ$. +Collecting symptoms from table~\ref{tbl:BISJ}, the {\dc} $ BISJ $ is created with the following failure modes: +$$ + fm(BISJ) = \{ OUTPUT STUCK , REDUCED\_INTEGRATION \} . +$$ \clearpage @@ -436,7 +481,7 @@ called $BISJ$. \label{detail:FFB} \begin{table}[h+] \caption{ $DIGBUF,DL2AL$ flip flop buffered($FFB$): Failure Mode Effects Analysis} % title of Table -\label{tbl:digbuf} +\label{tbl:ffb} \begin{tabular}{|| l | l | c | c | l ||} \hline %\textbf{Failure Scenario} & & \textbf{failure result } & & \textbf{Symptom} \\ @@ -459,12 +504,18 @@ called $BISJ$. \hline \end{tabular} \end{table} +% +%Symptoms of failure are collected $\{OUTPUT STUCK, LOW\_SLEW\}$ and a {\dc} %at the third level of symptom abstraction +%called $FFB$ created. +% +Collecting symptoms from table~\ref{tbl:ffb}, the {\dc} $ FFB $ is created with the following failure modes: +$$ + fm(FFB) = \{ OUTPUT STUCK, LOW\_SLEW \} . +$$ -Symptoms of failure are collected $\{OUTPUT STUCK, LOW\_SLEW\}$ and a {\dc} %at the third level of symptom abstraction -called $FFB$ created. \clearpage -\subsection{FMMD Analysis of \sd : SDADC} +\subsection{FMMD Analysis of {\sd} : SDADC} \label{detail:SDADC} \begin{table}[h+] \caption{ $FFB , BISJ $ \sd ($SDADC$): Failure Mode Effects Analysis} % title of Table @@ -491,12 +542,16 @@ called $FFB$ created. \end{tabular} \end{table} %\clearpage -The symptoms for the \sd are collected -$$ \; \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}.$$ -A {\dc} is created to represent the failure behaviour of the analogue to digital converter, $SDADC$. -$$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$$ +% The symptoms for the \sd are collected from table~\ref{tbl:sdadc} +% $$ \; \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}.$$ +% A {\dc} is created to represent the failure behaviour of the analogue to digital converter, $SDADC$, +% $$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$$ \fmmdglossADC +Collecting symptoms from table~\ref{tbl:sdadc}, the {\dc} $SDADC $ is created with the following failure modes: +$$ + fm(SDADC) = \{ OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT \} . +$$ \clearpage @@ -516,33 +571,40 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. % \textbf{Failure} & \textbf{failure} & \textbf{Symptom} \\ % \textbf{Scenario} & \textbf{effect} & \textbf{RADC } \\ \hline \hline - \textbf{Failure} & \textbf{Failure } & \textbf{Symptom} \\ - \textbf{cause} & \textbf{Effect} & \\ + \textbf{Failure} & \textbf{Failure } & \textbf{Symptom} \\ + \textbf{cause} & \textbf{Effect} & \\ \hline - FC1: $RI_{VRGE}$ & voltage & $VOLTAGE\_HIGH$ \\ - & outside range & \\ \hline + FC1: $RI_{VRGE}$ & voltage & $VOLTAGE\_HIGH$ \\ + & outside range & \\ \hline - FC2: $RADC_{VV_ERR}$ & voltage & $VAL\_ERR$ \\ - & incorrect & \\ \hline \hline + FC2: $RADC_{VV_ERR}$ & voltage & $VAL\_ERR$ \\ + & incorrect & \\ \hline \hline FC3: $RADC_{HIGH}$ & voltage value & $VAL\_ERR$ \\ - & incorrect & \\ \hline + & incorrect & \\ \hline - FC4: $RADC_{LOW}$ & ADC may read & $VOLTAGE\_LOW$ \\ \hline + FC4: $RADC_{LOW}$ & ADC may read & $VOLTAGE\_LOW$ \\ \hline - FC5: post condition fails & software failure & $VAL\_ERR$ \\ - in function read\_ADC & read\_ADC & \\ \hline + FC5: post condition fails & software failure & $VAL\_ERR$ \\ + in function read\_ADC & read\_ADC & \\ \hline \end{tabular} \end{table} } \fmmdglossADC +Collecting symptoms from table~\ref{tbl:readPt100}, the {\dc} $Read\_Pt100 $ is created with the following failure modes: +$$ + fm(Read\_Pt100) = \{ VOLTAGE\_HIGH , VOLTAGE\_LOW, VAL\_ERR\} . +$$ + + + \clearpage \subsection{ Get\_Temperature: Failure Mode Effects Analysis } @@ -564,16 +626,12 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. \hline FC1: $Pt100:Voltage\_High$ & Pt100 voltage too high & Pt100\_out\_of\_range \\ - & Pt100\_higher\_voltage & \\ - & OR Pt100\_current & \\ \hline + \hline FC2: $Pt100:Voltage\_Low$ & Pt100 voltage too low & Pt100\_out\_of\_range \\ - & Pt100\_lower\_voltage & \\ - & OR Pt100\_current & \\ \hline + \hline - - - + FC3: $Pt100\_high\_low\_mismatch$ & temperature can be calculated & Pt100\_out\_of\_range \\ & from either high or low & \\ & reading, but should correlate & \\ \hline @@ -586,9 +644,9 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. % FC4: $Pt100:VAL\_ERR$ & could cause an out of & temp\_incorrect\\ - & range error, but may also & \\ - & cause us to read an & \\ - & incorrect temperature & \\ \hline + & range error, but may & \\ + & cause an incorrect & \\ + & temperature reading & \\ \hline FC5: post condition fails & software failure & temp\_incorrect \\ in function convert\_ADC\_to\_T & convert\_ADC\_to\_T & \\ \hline @@ -600,10 +658,24 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. } +Collecting symptoms from table~\ref{tbl:gettemperature}, the {\dc} $Get\_Temperature$ is created with the following failure modes: +$$ + fm(Get\_Temperature) = \{ Pt100\_out\_of\_range, temp\_incorrect \} . +$$ + + + + + \clearpage \subsection{ GetError: Failure Mode Effects Analysis } +The error value being discussed here is an important concept in PID control. +It represents how far from the control target +the measured reading of it is. +The lower the PID error value the closer to the controlled systems target/desired value. + { \tiny \begin{table}[h+] @@ -621,20 +693,31 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. \hline FC1: $ Pt100\_out\_of\_range $ & pre-condition violated & KnownIncorrectErrorValue \\ - & observable/detectable & \\ - & failure mode & \\ \hline + & detectable failure mode & \\ \hline + FC2: $temp\_incorrect$ & pre-condition violated & IncorrectErrorValue \\ - & unobservable & \\ - & undetectable failure mode & \\ \hline + & undetectable failure mode & \\ \hline FC3: post condition fails & software failure & IncorrectErrorValue \\ - in function determine\_set\_point\_error & determine\_set\_point\_error & \\ \hline + in function \cf{determine\_set\_point\_error} & determine\_set\_point\_error & \\ \hline \end{tabular} \end{table} } +% +Collecting symptoms from table~\ref{tbl:geterror}, the {\dc} $ GetError $ is created with the following failure modes: +$$ + fm( GetError ) = \{ KnownIncorrectErrorValue, IncorrectErrorValue \} . +$$ +% +% +% + + + + \clearpage \subsection{PID: Failure Mode Effects Analysis} { @@ -653,41 +736,43 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. \hline - FC1: $ KnownIncorrectErrorValue $ & pre-condition violated & KnownControlValueErrorV \\ - & observable/detectable & \\ + FC1: $ KnownIncorrectErrorValue $ & pre-condition violated & KnownControlValueErrorV \\ + & detectable & \\ & failure mode & \\ \hline FC2: $ IncorrectErrorValue $ & pre-condition violated & IncorrectControlErrorV \\ - & unobservable & \\ & undetectable failure mode & \\ \hline FC3: post condition fails & software failure & IncorrectControlErrorV \\ - in function PID & PID & \\ \hline + in function \cf{PID} & PID & \\ \hline \end{tabular} \end{table} } + + + +Collecting symptoms from table~\ref{tbl:pidfunction}, the {\dc} $PID$ is created with the following failure modes: +$$ + fm(PID) = \{ KnownControlValueErrorV , IncorrectControlErrorV \} . +$$ + \clearpage \subsection{ HeaterOutput: Failure Mode Effects Analysis } - - { \tiny \begin{table}[h+] \center \caption{ HeaterOutput: Failure Mode Effects Analysis} % title of Table \label{tbl:heateroutput} - \begin{tabular}{|| l | c | l ||} \hline % \textbf{Failure} & \textbf{failure} & \textbf{Symptom} \\ % \textbf{Scenario} & \textbf{effect} & \textbf{RADC } \\ \hline \hline \textbf{Failure} & \textbf{Failure } & \textbf{Symptom} \\ \textbf{cause} & \textbf{Effect} & \\ - - \hline FC1: $ PWM stuck HIGH $ & pre-condition violated & HeaterOnFull \\ & PWM module not working & \\ \hline @@ -706,15 +791,26 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. & OPEN no heating effect & \\ \hline FC5: $ output\_control$ post & The software supplies the wrong & HeaterOutputIncorrect \\ - condition failure & value to the PWM register & \\ \hline - - - + condition failure & value to the PWM register & \\ \hline \end{tabular} \end{table} } + + +Collecting symptoms from table~\ref{tbl:heateroutput}, the {\dc} $ HeaterOutput$ is created with the following failure modes: +$$ + fm(HeaterOutput) = \{ HeaterOnFull, HeaterOff, HeaterOutputIncorrect \} . +$$ \clearpage + + + + + + + + \subsection{ LEDOutput: Failure Mode Effects Analysis } @@ -758,6 +854,12 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. \end{tabular} \end{table} } + + +Collecting symptoms from table~\ref{tbl:ledoutput}, the {\dc} $ LEDOutput $ is created with the following failure modes: +$$ + fm() = \{ FailureIndicated, IndicationError \} . +$$ \clearpage @@ -791,20 +893,20 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. FC4: HeaterOutput & no power & ControlFailureIndicated \\ HeaterOFF & supplied to heater & \\ \hline - FC4: HeaterOutput & incorrect power levels & ControlFailure \\ + FC5: HeaterOutput & incorrect power levels & ControlFailure \\ HeaterOutputIncorrect & applied to heater & \\\hline - FC5: LEDOutput & failure of LED system & KnownIndicationError \\ + FC6: LEDOutput & failure of LED system & KnownIndicationError \\ FailureIndicated & where failure is detectable & \\ \hline - FC6: LEDOutput & failure of LED system & UnknownIndicationError \\ + FC7: LEDOutput & failure of LED system & UnknownIndicationError \\ IndicationError & where failure is undetectable & \\ \hline %% PROM\_FAULT, RAM\_FAULT, CPU\_FAULT, ALU\_FAULT, CLOCK\_STOPPED - FC7: micro-controller & un-defined behaviour & ControlFailure \\ + FC8: micro-controller & un-defined behaviour & ControlFailure \\ PROM\_FAULT & & \\ \hline FC9: micro-controller & un-defined behaviour & ControlFailure \\ @@ -819,7 +921,7 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. FC12: micro-controller & processor will not run & ControlFailureIndicated \\ CLOCK\_STOPPED & indicator leds will not flash & \\ \hline - FC8: monitor: & postcondition fails & ControlFailure \\ + FC13: monitor: & postcondition fails & ControlFailure \\ software fails & & \\ \hline @@ -829,6 +931,13 @@ FMMD analysis tables from chapter~\ref{sec:chap6}. \end{tabular} \end{table} } + + +Collecting symptoms from table~\ref{tbl:pid} the {\dc} $TempController$, is created with the following failure modes: +\begin{eqnarray*} + fm ( TempController ) = \{ ControlFailureIndicated, \\ ControlFailure, \\ KnownIndicationError, \\ UnknownIndicationError \}. +\end{eqnarray*} + \clearpage @@ -844,10 +953,10 @@ 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 +in hours for a wide range of generic components. +These figures are based on components from the 1980's and MIL-HDBK-217F can give conservative reliability figures when applied to -modern components}. +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. @@ -946,8 +1055,9 @@ resistor{\lambda}_p = {\lambda}_{b}{\pi}_Q{\pi}_E 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. +%Using the RIAC finding the following (table~\ref{tab:stat_single}) can be created which +%presents the FIT values for all single failure modes. +Using the above table~\ref{tab:stat_single} is presented which lists 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 % @@ -975,13 +1085,13 @@ TC:6 $R_2$ OPEN & High Fault & High Fault & 12.42 \\ \hline \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 +test cases. The Pt100 circuit here has a FIT of 342.6. This is an 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. +A probabilistic tree can now be drawn, with a FIT value for the overall Pt100 +circuit and FIT values for all its component fault modes. % from which it was calculated. % From this it can be seen that the most likely fault is the thermistor going OPEN. % @@ -1001,11 +1111,13 @@ be the fault~mode scrutinised first. \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. +% +%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. % @@ -1034,7 +1146,7 @@ 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, +However, it is interesting from a failure analysis perspective, because an undetectable fault (at least at this level in the FMMD hierarchy) has been revealed. %