From dc4ecbea45467fa88d2a1bda65a974d7a09b2fc7 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Fri, 16 Aug 2013 17:47:11 +0100 Subject: [PATCH] final printout and pencil then edit --- submission_thesis/appendixes/algorithmic.tex | 52 ++++++++++---------- 1 file changed, 27 insertions(+), 25 deletions(-) diff --git a/submission_thesis/appendixes/algorithmic.tex b/submission_thesis/appendixes/algorithmic.tex index dcacca2..8190827 100644 --- a/submission_thesis/appendixes/algorithmic.tex +++ b/submission_thesis/appendixes/algorithmic.tex @@ -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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %