From 54dc5237d775de303df19e8f75c5edfe095e8749 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Fri, 4 Jun 2010 08:21:14 +0100 Subject: [PATCH] tidied --- .../component_failure_modes_definition.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex index 61147a6..5e6a68f 100644 --- a/component_failure_modes_definition/component_failure_modes_definition.tex +++ b/component_failure_modes_definition/component_failure_modes_definition.tex @@ -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 failure modes when analysing a functional group. This involves finding 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 -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' 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: \vbox{ +\subsubsection{All Eleven Cardinality Constrained \\ Powerset of 2 Elements Listed} %\tiny \begin{enumerate} \item $\{R_o T_o\}$