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gave it a look over again

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Robin Clark 2011-11-12 15:39:55 +00:00
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opamp_circuits_C_GARRETT/opamps.tex
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@ -666,7 +666,7 @@ mode (i.e. one or more failure modes that caused it).
% %
\subsection{FMMD Hierarchy} \subsection{FMMD Hierarchy}
\;
By applying stages of analysis to higher and higher abstraction By applying stages of analysis to higher and higher abstraction
levels, we can converge to a complete failure mode model of the system under analysis. levels, we can converge to a complete failure mode model of the system under analysis.
Because the symptom abstraction process is defined as surjective (from component failure modes to symptoms) Because the symptom abstraction process is defined as surjective (from component failure modes to symptoms)
@ -811,6 +811,15 @@ its range as the number of checks to perform to satisfy a rigorous FMEA inspecti
This can be simplified if we can determine the total number of failure modes in the system $fT$, (i.e. $ fT = \sum_{n=1}^{|fg|} {|fm(c_n)|}$); This can be simplified if we can determine the total number of failure modes in the system $fT$, (i.e. $ fT = \sum_{n=1}^{|fg|} {|fm(c_n)|}$);
equation~\ref{eqn:rd} becomes $$ RD(fg) = fT.(|fg|-1).$$ equation~\ref{eqn:rd} becomes $$ RD(fg) = fT.(|fg|-1).$$
Equation~\ref{eqn:rd} can also be expressed as
\begin{equation}
\label{eqn:rd2}
%$$
RD(fg) = {|fg|}.{|fm(c_n)|}.{(|fg|-1)} .
%$$
\end{equation}
\pagebreak[4] \pagebreak[4]
\subsection{Reasoning Distance Examples} \subsection{Reasoning Distance Examples}
@ -873,17 +882,17 @@ Starting at the top, we have a {\fg} with three derived components, each of whic
three failure modes. three failure modes.
Thus the number of checks to make in the top level is $3^0.3.2.3=18$. Thus the number of checks to make in the top level is $3^0.3.2.3=18$.
On the level below that, we have three {\fgs} each with a On the level below that, we have three {\fgs} each with a
an identical number of checks, $3^1.3.2.3=56$.{\fg} an identical number of checks, $3^1.3.2.3=56$.%{\fg}
On the level below that we have nine {\fgs}, $3^2.3.2.3=168$. On the level below that we have nine {\fgs}, $3^2.3.2.3=168$.
Adding these together gives $242$ checks to make to perform RFMEA \textbf{within} Adding these together gives $242$ checks to make to perform FMMD (i.e. RFMEA \textbf{within the}
{\fgs}. {\fgs}).
If we were to take the system represented in figure~\ref{fig:three_tree}, and If we were to take the system represented in figure~\ref{fig:three_tree}, and
apply RFMEA on it as a whole system, we can use equation~\ref{eqn:rd}, apply RFMEA on it as a whole system, we can use equation~\ref{eqn:rd},
$ RD(fg) = \sum_{n=1}^{|fg|} |fm(c_n)|.(|fg|-1)$, where $|fg|$ is 27, $fm(c_n)$ is 3 $ RD(fg) = \sum_{n=1}^{|fg|} |fm(c_n)|.(|fg|-1)$, where $|fg|$ is 27, $fm(c_n)$ is 3
and $(|fg|-1)$ is 26. and $(|fg|-1)$ is 26.
This gives: This gives:
$ RD(fg) = \sum_{n=1}^{27} |3|.(|27|-1) = 2106$ $RD(fg) = \sum_{n=1}^{27} |3|.(|27|-1) = 2106$.
In order to get general equations with which to compare RFMEA with FMMD In order to get general equations with which to compare RFMEA with FMMD
we can re-write equation~\ref{eqn:rd} in terms of the number of levels we can re-write equation~\ref{eqn:rd} in terms of the number of levels