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Robin Clark 2010-10-26 23:00:40 +01:00
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fmmd_concept/fmmd_concept.tex
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@ -167,7 +167,7 @@ decide which interactions are important.
Let N be the number of components in our system, and K be the average number of component failure modes Let N be the number of components in our system, and K be the average number of component failure modes
(ways in which the component can fail). The total number of base component failure modes (ways in which the component can fail). The total number of base component failure modes
is $N \times K$. To even examine the affect that one failure mode has on all the other components is $N \times K$. To even examine the affect that one failure mode has on all the other components
will be $$(N-1) \times N \times K$$, in effect a set cross product. will be $(N-1) \times N \times K$, in effect a set cross product.
Complicate this further with applied states or environmental conditions Complicate this further with applied states or environmental conditions
@ -179,17 +179,17 @@ failure mode behaviour for say, differnet ambient pressures or temperatures.
If $E$ is the number of applied states or environmental conditions to consider If $E$ is the number of applied states or environmental conditions to consider
in a system, the job of the bottom-up analyst is complicated by a cross product factor again in a system, the job of the bottom-up analyst is complicated by a cross product factor again
$$(N-1) \times N \times K \times E$$. $(N-1) \times N \times K \times E$.
If we were to consider multiple simultaneous failure modes If we were to consider multiple simultaneous failure modes
we have yet another complication cross product. we have yet another complication cross product.
For instance for looking at double simultaneous failure modes For instance for looking at double simultaneous failure modes
the equation reads $$(N-2) \times (N-1) \times N \times K \times E$$. the equation reads $(N-2) \times (N-1) \times N \times K \times E$.
The bottom-up methodologies FMEA, FMECA and FMEDA take single failure modes and link them The bottom-up methodologies FMEA, FMECA and FMEDA take single failure modes and link them
to SYSTEM level failure modes. Because of the number of possible interactions that to SYSTEM level failure modes. Because of the astronomical number of possible interactions,
must be missed, we can term this analysis a `leap of faith' from the some valid ones are in danger of being missed, we can term this analysis a `leap of faith' from the
component failure mode to the SYSTEM level. component failure mode to the SYSTEM level.