From 7d4f33eaa831950a571fac41f01977f55495a216 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Fri, 18 Nov 2011 17:58:25 +0000 Subject: [PATCH] Meeting with Andrew and John equations made general for the reasoning distance w=hich will now be called comparison complexity --- opamp_circuits_C_GARRETT/opamps.tex | 13 ++++++++----- .../White_board_18NOV2011IMG_0607.JPG | Bin 0 -> 218040 bytes 2 files changed, 8 insertions(+), 5 deletions(-) create mode 100644 related_papers_books/White_board_18NOV2011IMG_0607.JPG diff --git a/opamp_circuits_C_GARRETT/opamps.tex b/opamp_circuits_C_GARRETT/opamps.tex index ce47961..cbf294e 100644 --- a/opamp_circuits_C_GARRETT/opamps.tex +++ b/opamp_circuits_C_GARRETT/opamps.tex @@ -660,7 +660,7 @@ it was derived from. We can stipulate that symptom collection process is surjective. % i.e. $ \forall f in F $ By stipulating surjection for symptom collection, we ensure -that each component failure mode maps to at least one one symptom. +that each component failure mode maps to at least one symptom. We also ensure that all symptoms have at least one component failure mode (i.e. one or more failure modes that caused it). % @@ -670,13 +670,14 @@ mode (i.e. one or more failure modes that caused it). 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) -the number of symptoms is guaranteed to the less than or equal to +the number of symptoms is guaranteed to be less than or equal to the number of component failure modes. In practise however, the number of symptoms greatly reduces as we traverse up the hierarchy. -This is a natural process. When we have a complicated systems -they always have a small number of system failure modes. +This is a natural process. When we have complicated systems +they always have a small number of system failure modes in comparison to +the number of failure modes in its sub-systems/components.. \clearpage \section{Side Effects: A Problem for FMMD analysis} @@ -896,7 +897,9 @@ $RD(fg) = \sum_{n=1}^{27} |3|.(|27|-1) = 2106$. 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 -in an FMMD hierarchy. The number of components in is number of components +in an FMMD hierarchy. +% +The number of components in the system, is number of components in a {\fg} raised to the power of the level plus one. 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