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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 % RANGE == OUTPUTS
% %
When performing FMEA, we have a system under investigation, which will be When performing FMEA we consider the system under investigation
comprised of a collection of components which have associated failure modes. to be 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.
% %
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 To perform FMEA rigorously
we could stipulate that every failure mode must be checked for effects we could stipulate that every failure mode must be checked for effects
against all the components in the system. 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). 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. 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 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}. 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!). % (except its self of course, that component is already considered to be in a failed state!).
% %