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Trying to intoduce the ideas behind comparison complexity

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Robin Clark 2013-01-15 21:31:46 +00:00
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submission_thesis/CH6_Evaluation/copy.tex
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@ -20,22 +20,57 @@
% RANGE == OUTPUTS
%
When performing FMEA, we have a system under investigation, which will be
comprised of a collection of components which have associated failure modes.
The object of FMEA is to determine cause and effect:
from the failure modes (the causes, {\fms} of {\bcs}) to the effects (or symptoms of failure) at the top level.
When performing FMEA we consider the system under investigation
to be a collection of components which have associated failure modes.
%
The object of FMEA is to determine cause and effect.
We apply reasoning to calculate, using the failure modes, the effects
%from these failure modes (the causes, {\fms} of {\bcs}) to the effects
(or symptoms of failure) at the top level.
%
We can view FMEA as a process, taking each component in the system and for all its failure modes
applying analysis.
%
This however entails a problem: which other components in the system must we
check against the %current failure mode.
each particular failure mode.
%
Often a component failing will have obvious effects on functionally adjacent components.
Sometimes %though, perhaps in the case of de-coupling capacitors in a digital ciruit,
side effects of failure may manifest due interaction with other components not obviously functionally related.
%% CONTEXT OF SYSTEM FAILURE: PERHAPS NOT RELEVANT HERE
%
% The symptoms of failure are dependent upon the context, or environment that the system operates in.
% We can trace all base component failure modes to corresponding system failures: but the effect
% of the system failure depends upon how the system is used.
% %
% A resistor failure could, for instance, make a process reading go out of range.
% This could cause the process to be stopped or simply one reading out of many would
% be marked faulty and be dealt with in the next maintenance phase of the plant.
% %
% Another resistor failing could cause a dangerous control problem.
%
%The context of the system failures is the important thingy bob dooo dah.
%
%
%Also a particular component failure mode may affect the performance of another.
The temptation with FMEA can be to think through a line of failure mode reasoning without considering
side effects.
%%
To perform FMEA rigorously
we could stipulate that every failure mode must be checked for effects
against all the components in the system.
%
This would mean we would be looking for all possible side effects that a base component failure could cause.
%
We could term this `rigorous~FMEA'~(RFMEA).
The number of checks we have to make to achieve this, gives an indication of the complexity of the task.
This is described in section~\ref{sec:rd}, where the reasoning distance, or complexity to
analyse a single FMEA failure scenario, is given in equation~\ref{eqn:complexity}.
%
We could term this `comparison~complexity', as the number of
paths between failure modes and components necessary to achieve RFMEA for a given system/functional~group.
%
We term this `comparison~complexity', the number of
paths between failure modes and components necessary to achieve RFMEA for a given system/{\fg}.
% (except its self of course, that component is already considered to be in a failed state!).
%