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Need to do more work on the maths at the end in the algorithm environment.

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John Howse said formalisation is not necessary unless you need to prove something.
OK well good.
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Robin 2010-01-15 20:26:26 +00:00
parent bf1f644698
commit fd4540a246
1 changed files with 11 additions and 10 deletions
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21
symptom_abstraction/symptom_abstraction.tex
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@ -502,21 +502,22 @@ The algorithm has been broken down into five stages, each following on from the
\STATE { Let $FG$ be a set of components } \COMMENT{ The functional group should be chosen to be minimally sized collections of components that perform a specific function} \STATE { Let $FG$ be a set of components } \COMMENT{ The functional group should be chosen to be minimally sized collections of components that perform a specific function}
\STATE { Let $c$ represent a component} \STATE { Let $c$ represent a component}
\STATE { let $CFM$ represent a set of failure modes } \STATE { Let $CFM$ represent a set of failure modes }
\STATE { $FM(c) \mapsto CFM $} \COMMENT {let the function $FM$ take a component and return a set of all its failure modes} \STATE { $FM(c) \mapsto CFM $} \COMMENT {Let the function $FM$ take a component and return a set of all its failure modes}
%\ENSURE { $ \forall c | c \in FG \wedge FM(c) \neq \emptyset $} %\ENSURE { $ \forall c | c \in FG \wedge FM(c) \neq \emptyset $}
\ENSURE { $ c | c \in FG \wedge FM(c) \neq \emptyset $} %\ENSURE { $ c | c \in FG \wedge FM(c) \neq \emptyset $}
\COMMENT{ i.e. for each component $c \in FG $ has a known set of failure modes } \ENSURE{ Each component $c \in FG $ has a known set of failure modes i.e. $FM(c) \neq \emptyset$ }
%\REQUIRE{ Ensure that all components belong to at least one functional group $\bigcup_{i=1...n} fg_i = S $ } %\REQUIRE{ Ensure that all components belong to at least one functional group $\bigcup_{i=1...n} fg_i = S $ }
%symptom_abstraction %symptom_abstraction
% okular % okular
\STATE {let $FG_{cfm}$ be a set of failure modes} \STATE {let $FG_{cfm}$ be a set of failure modes}
\FORALL { $c \in FG $ } \STATE {Collect all failure modes from the components into the set $FM_{cfm}$}
\STATE { $ FM(c) \in FG_{cfm} $ } \COMMENT {Collect all failure modes from the components into the set $FM_{cfm}$} %\FORALL { $c \in FG $ }
\ENDFOR %\STATE { $ FM(c) \in FG_{cfm} $ } \COMMENT {Collect all failure modes from the components into the set $FM_{cfm}$}
%\ENDFOR
%\hline %\hline
Algorthim \ref{alg:sympabs11} has taken a functional group $FG$ and returned a set of failure~modes $FG_{cfm}$. Algorthim \ref{alg:sympabs11} has taken a functional group $FG$ and returned a set of failure~modes $FG_{cfm}$.
@ -539,11 +540,10 @@ in the analysis stages.
component failures are investigated component failures are investigated
with some specially selected combination faults} with some specially selected combination faults}
\STATE { Let $TC$ be a set of test cases }
\STATE { Let $tc_j$ be set of component failure modes where $j$ is an index of $J$} \STATE { Let $tc_j$ be set of component failure modes where $j$ is an index of $J$}
\COMMENT { Each set $tc_j$ is a `test case' } \COMMENT { Each set $tc_j$ is a `test case' }
\STATE { Let $TC$ be a set of test cases }
\STATE { $ \forall j \in J | tc_j \in TC $ } \STATE { $ \forall j \in J | tc_j \in TC $ }
\COMMENT { Let $TC$ be the set test cases to be applied to the functional group}
%\STATE { $ \bigcup_{j=1...N} tc_j = \bigcup TC $ } %\STATE { $ \bigcup_{j=1...N} tc_j = \bigcup TC $ }
%\COMMENT { All $tc_j$ test cases sets belong to $TC$ } %\COMMENT { All $tc_j$ test cases sets belong to $TC$ }
@ -557,7 +557,8 @@ in the analysis stages.
\COMMENT { Ensure the test cases are complete and unique } \COMMENT { Ensure the test cases are complete and unique }
\FORALL { $tc_j \in TC$ } \FORALL { $tc_j \in TC$ }
\ENSURE {$ tc_j \subset \bigcap FG_{cfm} $} %\ENSURE {$ tc_j \in \bigcap FG_{cfm} $}
\ENSURE {$ tc_j \in \mathcal{P} FG_{cfm} $}
\COMMENT { require that the test case is a member of the powerset of $FM_{cfm}$ } \COMMENT { require that the test case is a member of the powerset of $FM_{cfm}$ }
\ENSURE { $ \forall \; j2 \; \in J ( \forall \; j1 \; \in J | tc_{j1} \neq tc_{j2} \; \wedge \; j1 \neq j2 ) $} \ENSURE { $ \forall \; j2 \; \in J ( \forall \; j1 \; \in J | tc_{j1} \neq tc_{j2} \; \wedge \; j1 \neq j2 ) $}
\COMMENT { Test cases must be unique } \COMMENT { Test cases must be unique }