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Robin Clark 2010-06-04 08:21:14 +01:00
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6
component_failure_modes_definition/component_failure_modes_definition.tex
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@ -309,9 +309,10 @@ It is an implied requirement of EN298 for instance to consider double simultaneo
To generalise, we may need to consider $N$ simultaneous To generalise, we may need to consider $N$ simultaneous
failure modes when analysing a functional group. This involves finding failure modes when analysing a functional group. This involves finding
all combinations of failures modes of size $N$ and less. all combinations of failures modes of size $N$ and less.
The Powerset concept from Set theory when applied to a set S is the set of all subsets of S, including the empty set and S itself The Powerset concept from Set theory when applied to a set S is the set of all subsets of S, including the empty set
\footnote{The empty set is a special case for FMMD analysis, it simply means there \footnote{The empty set is a special case for FMMD analysis, it simply means there
is no fault active in the functional~group under analysis}. is no fault active in the functional~group under analysis}
and S itself.
In order to consider combinations for the set S where the number of elements in each sub-set of S is $N$ or less, a concept of the `cardinality constrained powerset' In order to consider combinations for the set S where the number of elements in each sub-set of S is $N$ or less, a concept of the `cardinality constrained powerset'
is proposed and described in the next section. is proposed and described in the next section.
@ -393,6 +394,7 @@ The number of combinations to check is thus 11 for this example and this can be
by listing all the required combinations: by listing all the required combinations:
\vbox{ \vbox{
\subsubsection{All Eleven Cardinality Constrained \\ Powerset of 2 Elements Listed}
%\tiny %\tiny
\begin{enumerate} \begin{enumerate}
\item $\{R_o T_o\}$ \item $\{R_o T_o\}$