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final printout and pencil then edit

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Robin Clark 2013-08-16 17:47:11 +01:00
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52
submission_thesis/appendixes/algorithmic.tex
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@ -264,11 +264,11 @@ The algorithm, represented by the symbol `$\derivec$', is described using five a
%These are described using the Algorithm environment in the next section \ref{algorithms}. %These are described using the Algorithm environment in the next section \ref{algorithms}.
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
As a function $\derivec$ has the following signature: % As a function $\derivec$ has the following signature:
%
%
%\clearpage % %\clearpage
$$ \derivec: \mathcal{FG} \rightarrow \mathcal{DC} .$$ % $$ \derivec: \mathcal{FG} \rightarrow \mathcal{DC} .$$
\begin{algorithm} \begin{algorithm}
\caption{Derive new `Component' $DC$ from a given {\fg} $FG$: $\derivec(FG)$} \caption{Derive new `Component' $DC$ from a given {\fg} $FG$: $\derivec(FG)$}
@ -322,8 +322,8 @@ all components within the given {\fg}.
% % % %
% % % %
% % % %
The next task is to formulate `test~cases'. These are a collection of combinations of these {\fms} and will be used %The next task is to formulate `test~cases'. These are a collection of combinations of these {\fms} and will be used
in the analysis stages. %in the analysis stages.
@ -366,7 +366,7 @@ all failure modes in components in the {\fg} are included in at least one test~c
%{ \footnotesize %{ \footnotesize
\begin{algorithm}[h+] \begin{algorithm}[h+]
\caption{Determine Test Cases: dtc: (F)} \caption{Determine Test Cases: dtc: (F)}
%\label{alg22} \label{alg22}
\begin{algorithmic}[1] \begin{algorithmic}[1]
\Require {F is a non empty flat set of failure modes} \Require {F is a non empty flat set of failure modes}
\State { All test cases are chosen by the investigating engineer(s). Typically all single \State { All test cases are chosen by the investigating engineer(s). Typically all single
@ -423,23 +423,23 @@ all failure modes in components in the {\fg} are included in at least one test~c
%\algstore %\algstore
%\algrestore %\algrestore
% %
\algstore{myalg} % \algstore{myalg}
\end{algorithmic} % \end{algorithmic}
\end{algorithm} % \end{algorithm}
%
\begin{algorithm} % \begin{algorithm}
\begin{algorithmic} [1] % \begin{algorithmic} [1]
\algrestore{myalg} % \algrestore{myalg}
\Ensure { $ \forall j_1,j_2 \in J \; such\; that\; j_1 \neq j_2 \big( tc_{j_1} \neq tc_{j_2} \big) $} \Comment{Ensure test cases are distinct} \Ensure { $ \forall j_1,j_2 \in J \; such\; that\; j_1 \neq j_2 \big( tc_{j_1} \neq tc_{j_2} \big) $} \Comment{Ensure test cases are distinct}
\Ensure { $ \forall tc \in TC \big( tc \in \mathcal{P}(F) \big) $ } \Comment{Ensure each test case is a subset of F} \Ensure { $ \forall tc \in TC \big( tc \in \mathcal{P}(F) \big) $ } \Comment{Ensure each test case is a subset of F}
\If{Single fault checking} % \If{Single fault checking}
\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 { This corresponds to checking that at least each single failure mode is \Comment { This corresponds to checking that at least each single failure mode 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 }
@ -518,7 +518,7 @@ When all the test cases have been analysed,
we will have a `result' for each `test case'. we will have a `result' for each `test case'.
% %
Each result will be described from the perspective of %{\wrt} to Each result will be described from the perspective of %{\wrt} to
the {\fg}, not the components failure modes. the {\fg}, not the members of it i.e. the components. % failure modes.
%in its test case. %in its test case.
% %
%In the case of a simple %In the case of a simple
@ -647,13 +647,13 @@ new {\fgs} at higher levels of fault abstraction.
Let $DC$ be a derived component with its own set of failure~modes. Let $DC$ be a derived component with its own set of failure~modes.
We define the function $cdc$ thus: We define the function $cdc$ thus:
$$ cdc: \mathcal{SP} \rightarrow \mathcal{DC} , $$ $$ cdc: \mathcal{SP} \rightarrow \mathcal{DC} , $$
%
given by given by
%
$$ cdc(SP) = DC . $$ $$ cdc(SP) = DC . $$
%
The new component will have a set of failure modes that correspond to the common symptoms collected from the $FG$. The new component will have a set of failure modes that correspond to the common symptoms collected from the $FG$.
%
%\begin{algorithm}[h+] %\begin{algorithm}[h+]
% ~\label{alg5} % ~\label{alg5}
% %
@ -674,9 +674,10 @@ The new component will have a set of failure modes that correspond to the common
% %
%\end{algorithmic} %\end{algorithmic}
%\end{algorithm} %\end{algorithm}
%
%Algorithm \ref{alg55} %Algorithm \ref{alg55}
The function $cdc$ is the final stage in the process. We now have a %The function $cdc$ is the final stage in the process.
We now have a
derived~component $DC$, which has its own set of failure~modes. This can now be derived~component $DC$, which has its own set of failure~modes. This can now be
used in with other components (or derived~components) used in with other components (or derived~components)
to form functional~groups at higher levels of failure~mode~abstraction. to form functional~groups at higher levels of failure~mode~abstraction.
@ -739,7 +740,8 @@ in FMMD analysis hierarchies.
These trees can be also traversed to produce These trees can be also traversed to produce
minimal cut sets\cite{nasafta} or entire FTA trees\cite{nucfta}, and by minimal cut sets\cite{nasafta} or entire FTA trees\cite{nucfta}, and by
analysing the statistical likelihood of the component failures, analysing the statistical likelihood of the component failures,
the Mean Time to Failure (MTTF) and SIL\cite{en61508} levels can be automatically calculated. the Mean Time to Failure (MTTF) and Failure in Time(FIT)\cite{en61508}
levels can be automatically calculated.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %