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FMECA added

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Robin Clark 2011-05-17 14:16:24 +01:00
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noninvopamp/noninvopamp.tex
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@ -864,7 +864,7 @@ to expand: Cuts sets and minimal cut sets. show example of detection of mimimal
\clearpage
\section{Assisting FMEA reports from the DAG}
\section{Extracting/Assisting in FMEA reports from the DAG}
A design FMEA, or potential failure mode and effects analysis
will typically require the designer to look at the possible effects
@ -908,10 +908,16 @@ reasoning process behind it, which leads to the symptom.
We have from the DAG model, a direct path from each component failure
mode to top-level symptoms. This allows us to partially fill in
the FMEA report. The detectability and severity of the symptom
are subjective. Given component failure rates, the probability
are subjective.
The $det$ value could influenced by factors such as features only used by a small percentage
of users of a product. In this case the detcability of the problem would be smaller
as many users would not activate/use the feature~\cite{bfmea}.
%strange is'nt it.
Given component failure rates, the probability
of the the potential cause occurring can be calculated, given suitable
component failure mode statistical references (e.g. FMD-91~\cite{fmd91} and MIL1991~\cite{mil1991}).
As these can be determined, they are represented by $Stat()$ in the table~\ref{ampfmea}.
\begin{table}[ht]
\caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table
\centering % used for centering table
@ -920,15 +926,15 @@ component failure mode statistical references (e.g. FMD-91~\cite{fmd91} and MIL1
\textbf{Item} & \textbf{Potential Failure} & \textbf{ Sev } & \textbf{Potential} & \textbf{prob} & \textbf{det} & \textbf{RPN} \\
\textbf{Function} & \textbf{mode} & \textbf{ /cost }& \textbf{Cause} & \textbf{/occ } & \textbf{} & \\\hline
\hline
Non Inverting & $AMP_{high}$ & & $R1_{short} $ & & & \\
Amplifier & $AMP_{low}$ & & $R1_{open} $ & & & \\
Circuit & $AMP_{low}$ & & $R2_{short} $ & & & \\
& $AMP_{high}$ & & $R2_{open}$ & & & \\
Non Inverting & $AMP_{high}$ & & $R1_{short} $ & $Stat(R1_{short}) $ & & \\
Amplifier & $AMP_{low}$ & & $R1_{open} $ & $Stat(R1_{open}) $ & & \\
Circuit & $AMP_{low}$ & & $R2_{short} $ & $Stat(R2_{short}) $ & & \\
& $AMP_{high}$ & & $R2_{open}$ & $Stat(R2_{open})$ & & \\
& $AMP_{lowpass}$ & & $OPAMP_{lowslew}$ & & & \\
& $AMP_{low}$ & & $OPAMP_{latchdown}$ & & & \\
& $AMP_{high}$ & & $OPAMP_{latchup}$ & & & \\
& $AMP_{low}$ & & $OPAMP_{noop} $ & & & \\
& $AMP_{lowpass}$ & & $OPAMP_{lowslew}$ & $Stat(OPAMP_{lowslew})$ & & \\
& $AMP_{low}$ & & $OPAMP_{latchdown}$ & $Stat(OPAMP_{latchdown})$ & & \\
& $AMP_{high}$ & & $OPAMP_{latchup}$ & $Stat(OPAMP_{latchup})$ & & \\
& $AMP_{low}$ & & $OPAMP_{noop} $ & $Stat(OPAMP_{noop}) $ & & \\
\hline
@ -949,11 +955,61 @@ to expand: Each FMEA looses the reasoning in the FMMD Hierarchy/DAG for linking
the symptoms to the potential causes.
FMEA can miss symptoms especially where a component failure mode may cause more than one top-level symptom.
\section{Extracting/Assisting in FMECA from the DAG}
Work out the alpha and beta values !!!
FMECA is a refinement of FMEA and introduces two statistical variables, $\alpha$ and $\beta$.
The $\alpha$ value is the probability of
of a particular component failure
mode occuring.We can trace the DAG from a system level error/top level event, and assign
$\alpha$ values according to published statistics~\cite{fmd91}~\cite{mil1992}.
As for the FMEA example we can denote this using a $Stat()$ function.
The $\beta$ value is the probability that the component failure mode will
cause a given system level error.
This may be determined hueistically or by field data.
A factor of FMECA is criticallity. Each top level event/failure
is assigned a criticallity value. This defines how seriously the problem is
pervcieved. This must be determined by the safety engineers responsible for the equipment and
its environment.
\begin{table}[ht]
\caption{Non Inverting Amplifier: Failure Mode Effects Critcallity Analysis: Single Faults} % title of Table
\centering % used for centering table
\begin{tabular}{||l|c|l|c|c|c|c||}
\hline \hline
\textbf{Item} & \textbf{Potential Failure} & \textbf{Potential} & \textbf{$\alpha$} & \textbf{$\beta$} & \textbf{severity} & \textbf{$C_r$} \\
\textbf{Function} & \textbf{mode} & \textbf{Cause} & \textbf{} & \textbf{} & \textbf{rating} & \\\hline
\hline
Non Inverting & $AMP_{high}$ & $R1_{short} $ & $Stat(R1_{short}) $ & & & \\
Amplifier & $AMP_{low}$ & $R1_{open} $ & $Stat(R1_{open}) $ & & & \\
Circuit & $AMP_{low}$ & $R2_{short} $ & $Stat(R2_{short}) $ & & & \\
& $AMP_{high}$ & $R2_{open}$ & $Stat(R2_{open})$ & & & \\
& $AMP_{lowpass}$ & $OPAMP_{lowslew}$ & $Stat(OPAMP_{lowslew})$ & & & \\
& $AMP_{low}$ & $OPAMP_{latchdown}$ & $Stat(OPAMP_{latchdown})$ & & & \\
& $AMP_{high}$ & $OPAMP_{latchup}$ & $Stat(OPAMP_{latchup})$ & & & \\
& $AMP_{low}$ & $OPAMP_{noop} $ & $Stat(OPAMP_{noop}) $ & & & \\
\hline
\hline
\hline
\end{tabular}
\label{ampfmeca}
\end{table}
%As the $\alpha$ modes are probabilities, the sum of all $\alpha$ modes for a component must equal one.
% Work out the alpha and beta values !!! well alpha is possible, beta and criticallity are not
\section{Extracting FMEDA from the DAG}
safe failure fractions
hmmmm
SD SU DD DU
\section{Conclusion}
We now have a derived component that represents the failure modes of a non-inverting