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polish polish polish the turd

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Robin Clark 2013-09-26 22:36:58 +01:00
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commit 52bacd1394
2 changed files with 201 additions and 89 deletions
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6
submission_thesis/CH6_Software_Examples/software.tex
View File

@ -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,

280
submission_thesis/appendixes/detailed_analysis.tex
View File

@ -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\} .
$$
\clearpage
\subsection{ Get\_Temperature: Failure Mode Effects Analysis }
@ -564,14 +626,10 @@ FMMD analysis tables from chapter~\ref{sec:chap6}.
\hline
FC1: $Pt100:Voltage\_High$ & Pt100 voltage too high & Pt100\_out\_of\_range \\
& Pt100\_higher\_voltage & \\
& OR Pt100\_current & \\ \hline
\hline
FC2: $Pt100:Voltage\_Low$ & Pt100 voltage too low & Pt100\_out\_of\_range \\
& Pt100\_lower\_voltage & \\
& OR Pt100\_current & \\ \hline
\hline
FC3: $Pt100\_high\_low\_mismatch$ & temperature can be calculated & Pt100\_out\_of\_range \\
@ -586,9 +644,9 @@ FMMD analysis tables from chapter~\ref{sec:chap6}.
%
FC4: $Pt100:VAL\_ERR$ & could cause an out of & temp\_incorrect\\
& range error, but may also & \\
& cause us to read an & \\
& incorrect temperature & \\ \hline
& range error, but may & \\
& cause an incorrect & \\
& temperature reading & \\ \hline
FC5: post condition fails & software failure & temp\_incorrect \\
in function convert\_ADC\_to\_T & convert\_ADC\_to\_T & \\ \hline
@ -600,10 +658,24 @@ FMMD analysis tables from chapter~\ref{sec:chap6}.
}
Collecting symptoms from table~\ref{tbl:gettemperature}, the {\dc} $Get\_Temperature$ is created with the following failure modes:
$$
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 \} .
$$
\clearpage
\subsection{ HeaterOutput: Failure Mode Effects Analysis }
{
\tiny
\begin{table}[h+]
\center
\caption{ HeaterOutput: Failure Mode Effects Analysis} % title of Table
\label{tbl:heateroutput}
\begin{tabular}{|| l | c | l ||} \hline
% \textbf{Failure} & \textbf{failure} & \textbf{Symptom} \\
% \textbf{Scenario} & \textbf{effect} & \textbf{RADC } \\ \hline
\hline
\textbf{Failure} & \textbf{Failure } & \textbf{Symptom} \\
\textbf{cause} & \textbf{Effect} & \\
\hline
FC1: $ PWM stuck HIGH $ & pre-condition violated & HeaterOnFull \\
& PWM module not working & \\ \hline
@ -707,14 +792,25 @@ FMMD analysis tables from chapter~\ref{sec:chap6}.
FC5: $ output\_control$ post & The software supplies the wrong & HeaterOutputIncorrect \\
condition failure & value to the PWM register & \\ \hline
\end{tabular}
\end{table}
}
Collecting symptoms from table~\ref{tbl:heateroutput}, the {\dc} $ HeaterOutput$ is created with the following failure modes:
$$
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.
%