From 53db734172aea952d692d0681088f233137c40ad Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Tue, 17 May 2011 14:16:24 +0100 Subject: [PATCH] FMECA added --- noninvopamp/noninvopamp.tex | 80 +++++++++++++++++++++++++++++++------ 1 file changed, 68 insertions(+), 12 deletions(-) diff --git a/noninvopamp/noninvopamp.tex b/noninvopamp/noninvopamp.tex index 77a8f08..5cf4488 100644 --- a/noninvopamp/noninvopamp.tex +++ b/noninvopamp/noninvopamp.tex @@ -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