From bc2e34b955a51467e4b17a91f21375e37a9b9da8 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Sat, 12 Nov 2011 15:39:55 +0000 Subject: [PATCH] gave it a look over again --- opamp_circuits_C_GARRETT/opamps.tex | 19 ++++++++++++++----- 1 file changed, 14 insertions(+), 5 deletions(-) diff --git a/opamp_circuits_C_GARRETT/opamps.tex b/opamp_circuits_C_GARRETT/opamps.tex index 2369af3..ce47961 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -666,7 +666,7 @@ mode (i.e. one or more failure modes that caused it). % \subsection{FMMD Hierarchy} - +\; 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. 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)|}$); 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] \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. 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 -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}, $3^2.3.2.3=168$. -Adding these together gives $242$ checks to make to perform RFMEA \textbf{within} -{\fgs}. +Adding these together gives $242$ checks to make to perform FMMD (i.e. RFMEA \textbf{within the} +{\fgs}). 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}, $ 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. 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 we can re-write equation~\ref{eqn:rd} in terms of the number of levels