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AF appendix B comments

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Robin Clark 2013-09-18 11:31:29 +01:00
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18
submission_thesis/appendixes/algorithmic.tex
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@ -26,7 +26,7 @@ The FMMD process is described in chapter~\ref{sec:chap4}.
\item collection of components to form {\fgs}, \item collection of components to form {\fgs},
\item applying FMEA to the {\fgs}, \item applying FMEA to the {\fgs},
\item collecting common symptoms from the FMEA results, \item collecting common symptoms from the FMEA results,
\item creating a {\dc} representing the failure mode behaviour of the {\fg}. \item creating a {\dc} modelling the failure mode behaviour of the {\fg}.
\end{itemize} \end{itemize}
% %
\fmmdgloss \fmmdgloss
@ -283,10 +283,13 @@ The algorithm, represented by the symbol `$\derivec$', is described using five a
The symptom abstraction process allows us to take a {\fg} of components, The symptom abstraction process allows us to take a {\fg} of components,
analyse the failure analyse the failure
mode behaviour and create a new entity, a {\dc} that has its own set of failure modes. mode behaviour and create a new entity, a {\dc} that has its own set of failure modes.
%
The checks and constraints applied in the algorithm ensure that all component failure The checks and constraints applied in the algorithm ensure that all component failure
modes are covered. modes are covered.
%
This process provides the analysis `step' to building a hierarchical failure mode model This process provides the analysis `step' to building a hierarchical failure mode model
from the bottom-up. from the bottom-up.
%
\fmmdgloss \fmmdgloss
@ -331,7 +334,9 @@ test cases must next be determined.
%we now need to determine test cases. %we now need to determine test cases.
% %
The test cases are collections of failure modes. The test cases are collections of failure modes.
%
These can be formed from single failure modes or failure modes in combination. These can be formed from single failure modes or failure modes in combination.
%
Let $\mathcal{TC}$ be the set of all test cases, $\mathcal{F}$ Let $\mathcal{TC}$ be the set of all test cases, $\mathcal{F}$
be the set of all failure modes. be the set of all failure modes.
%(associated with the functional group $FG$). %(associated with the functional group $FG$).
@ -378,9 +383,9 @@ all failure modes in components in the {\fg} are included in at least one test~c
component failures are investigated component failures are investigated
with some specially selected combination faults} with some specially selected combination faults}
\State { Let $TC$ be the set of test cases } \State { Let $TC$ be a set of test cases } \Comment {this set is used to collect the test cases}
\State { Let $tc_j$ be a set of component failure modes where $j$ is an index of $J$} \State { Let $tc_j$ be a set of component failure modes where $j$ is an index of $J$}
\Comment { Each set $tc_j$ is a `test~case' and $TC = \bigcup_{j \in J} \{tc_j\}$ where $J \in \mathbb{N}_{+}$ } \Comment { Each set $tc_j$ is a `test~case' and $TC = \bigcup_{j \in J} \{tc_j\}$ where $J \subset \mathbb{N}_{+}$ }
\State { $ TC := \emptyset $ } \Comment{Initialise set of test cases} \State { $ TC := \emptyset $ } \Comment{Initialise set of test cases}
\State { $ j := 1 $ } \Comment{Initialise index of test cases} \State { $ j := 1 $ } \Comment{Initialise index of test cases}
@ -437,14 +442,14 @@ all failure modes in components in the {\fg} are included in at least one test~c
\State { let $f$ represent a component failure mode } \State { let $f$ represent a component failure mode }
%\ENSURE { That all failure modes are represented in at least one test case } %\ENSURE { That all failure modes are represented in at least one test case }
\Ensure { $ \forall f \;such\;that\; (f \in F)) \wedge (f \in \bigcup TC) $ } \Ensure { $ \forall f \;such\;that\; (f \in F)) \wedge (f \in \bigcup TC) $ }
\Comment { Check that at each single failure mode is \Comment { Check that at each single failure mode in the {\fg} is
included as a test case.} included as a test case.}
%\EndIf %\EndIf
%\If{Double fault checking} %\If{Double fault checking}
\State { let $f1,f2$ represent component failure modes, and $c$ any component in the functional group } \State { let $f1,f2$ represent component failure modes, and $c$ any component in the functional group }
%\ENSURE { That all failure modes are represented in at least one test case } %\ENSURE { That all failure modes are represented in at least one test case }
\Ensure { $ \forall f1,f2 \;where\; (f1 \wedge f2) \not\in (\forall c) \;such\;that\; (f1,f2 \in F)) \wedge ( \{f1,f2\} \in \bigcup TC) \wedge ({DoubleFaultChecking} = TRUE)$ } \Ensure { $ \forall f1,f2 \;where\; (f1 \wedge f2) \not\in (\forall c) \;such\;that\; (f1,f2 \in F)) \wedge ( \{f1,f2\} \in \bigcup TC) \wedge ({DoubleFaultChecking} = TRUE)$ }
\Comment { If ${DoubleFaultChecking}$ is required, check that all possible double failure modes (see section~\ref{sec:unitarystate}) are included \Comment { If ${DoubleFaultChecking}$ is required, check that all possible double failure modes in the {\fg} (see section~\ref{sec:unitarystate}) are included
as a test cases.} as a test cases.}
\State \textbf{return} $TC$ \State \textbf{return} $TC$
\end{algorithmic} \end{algorithmic}
@ -505,6 +510,7 @@ The analysis is primarily a human activity.
Calculations or simulations Calculations or simulations
are performed to determine how the failure modes in each test case will are performed to determine how the failure modes in each test case will
affect the functional~group. affect the functional~group.
%
Ideally field data and/or formal physical testing should be used in addition to static failure mode reasoning Ideally field data and/or formal physical testing should be used in addition to static failure mode reasoning
where possible. where possible.
% %
@ -525,7 +531,9 @@ A set of
results corresponding to our test cases is now available. results corresponding to our test cases is now available.
% %
These share a common index value ($j$ in the algorithm description). These share a common index value ($j$ in the algorithm description).
%
These results are the failure modes of the {\fg}. These results are the failure modes of the {\fg}.
%
\fmmdgloss \fmmdgloss
%Once a functional group has been analysed, it can be re-used in %Once a functional group has been analysed, it can be re-used in
%any other design that uses it. %any other design that uses it.