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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 \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 A design FMEA, or potential failure mode and effects analysis
will typically require the designer to look at the possible effects 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 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 mode to top-level symptoms. This allows us to partially fill in
the FMEA report. The detectability and severity of the symptom 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 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}). 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] \begin{table}[ht]
\caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table \caption{Non Inverting Amplifier: Failure Mode Effects Analysis: Single Faults} % title of Table
\centering % used for centering 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{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 \textbf{Function} & \textbf{mode} & \textbf{ /cost }& \textbf{Cause} & \textbf{/occ } & \textbf{} & \\\hline
\hline \hline
Non Inverting & $AMP_{high}$ & & $R1_{short} $ & & & \\ Non Inverting & $AMP_{high}$ & & $R1_{short} $ & $Stat(R1_{short}) $ & & \\
Amplifier & $AMP_{low}$ & & $R1_{open} $ & & & \\ Amplifier & $AMP_{low}$ & & $R1_{open} $ & $Stat(R1_{open}) $ & & \\
Circuit & $AMP_{low}$ & & $R2_{short} $ & & & \\ Circuit & $AMP_{low}$ & & $R2_{short} $ & $Stat(R2_{short}) $ & & \\
& $AMP_{high}$ & & $R2_{open}$ & & & \\ & $AMP_{high}$ & & $R2_{open}$ & $Stat(R2_{open})$ & & \\
& $AMP_{lowpass}$ & & $OPAMP_{lowslew}$ & & & \\ & $AMP_{lowpass}$ & & $OPAMP_{lowslew}$ & $Stat(OPAMP_{lowslew})$ & & \\
& $AMP_{low}$ & & $OPAMP_{latchdown}$ & & & \\ & $AMP_{low}$ & & $OPAMP_{latchdown}$ & $Stat(OPAMP_{latchdown})$ & & \\
& $AMP_{high}$ & & $OPAMP_{latchup}$ & & & \\ & $AMP_{high}$ & & $OPAMP_{latchup}$ & $Stat(OPAMP_{latchup})$ & & \\
& $AMP_{low}$ & & $OPAMP_{noop} $ & & & \\ & $AMP_{low}$ & & $OPAMP_{noop} $ & $Stat(OPAMP_{noop}) $ & & \\
\hline \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. the symptoms to the potential causes.
FMEA can miss symptoms especially where a component failure mode may cause more than one top-level symptom. 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} \section{Extracting FMEDA from the DAG}
safe failure fractions
hmmmm
SD SU DD DU
\section{Conclusion} \section{Conclusion}
We now have a derived component that represents the failure modes of a non-inverting We now have a derived component that represents the failure modes of a non-inverting