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final printout and pencil then edit

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Robin Clark 2013-08-16 17:47:11 +01:00
parent 097c23b4e9
commit dc4ecbea45
1 changed files with 27 additions and 25 deletions
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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}.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
As a function $\derivec$ has the following signature:
%\clearpage
$$ \derivec: \mathcal{FG} \rightarrow \mathcal{DC} .$$
% As a function $\derivec$ has the following signature:
%
%
% %\clearpage
% $$ \derivec: \mathcal{FG} \rightarrow \mathcal{DC} .$$
\begin{algorithm}
\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
in the analysis stages.
%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.
@ -366,7 +366,7 @@ all failure modes in components in the {\fg} are included in at least one test~c
%{ \footnotesize
\begin{algorithm}[h+]
\caption{Determine Test Cases: dtc: (F)}
%\label{alg22}
\label{alg22}
\begin{algorithmic}[1]
\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
@ -423,23 +423,23 @@ all failure modes in components in the {\fg} are included in at least one test~c
%\algstore
%\algrestore
%
\algstore{myalg}
\end{algorithmic}
\end{algorithm}
\begin{algorithm}
\begin{algorithmic} [1]
\algrestore{myalg}
% \algstore{myalg}
% \end{algorithmic}
% \end{algorithm}
%
% \begin{algorithm}
% \begin{algorithmic} [1]
% \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 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 }
%\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) $ }
\Comment { This corresponds to checking that at least each single failure mode is
included as a test case.}
\EndIf
%\EndIf
\If{Double fault checking}
\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'.
%
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 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.
We define the function $cdc$ thus:
$$ cdc: \mathcal{SP} \rightarrow \mathcal{DC} , $$
%
given by
%
$$ cdc(SP) = DC . $$
%
The new component will have a set of failure modes that correspond to the common symptoms collected from the $FG$.
%
%\begin{algorithm}[h+]
% ~\label{alg5}
%
@ -674,9 +674,10 @@ The new component will have a set of failure modes that correspond to the common
%
%\end{algorithmic}
%\end{algorithm}
%
%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
used in with other components (or derived~components)
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
minimal cut sets\cite{nasafta} or entire FTA trees\cite{nucfta}, and by
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.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %