From c3e8946c39f3bb897cfa4796de4d744b714ae642 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Sat, 30 Oct 2010 12:29:15 +0100 Subject: [PATCH] Looking through for errors b4 John Howse submssn --- symptom_ex_process/process.tex | 63 ++++++++++++++++++++++++---------- 1 file changed, 44 insertions(+), 19 deletions(-) diff --git a/symptom_ex_process/process.tex b/symptom_ex_process/process.tex index e32d6fc..e34694e 100644 --- a/symptom_ex_process/process.tex +++ b/symptom_ex_process/process.tex @@ -270,6 +270,11 @@ from base level components cannot be overlooked. The process must not allow failure modes to be ignored or forgotten (see project aims in section \ref{requirements}). } % +This sub-system or {\dc} $DC$, with its three error modes, can now be treated as a component +with known failure modes +(although at a higher level of abstraction). +This process can be repeated using {\dcs} to build a +hierarchical fault~mode model. The newly derived component $DC$ is available for use to form higher level functional groups, and we can thus consider DC as being in the set of components i.e. $DC \in \mathcal{C}$ @@ -277,11 +282,11 @@ consider DC as being in the set of components i.e. $DC \in \mathcal{C}$ \subsection{Defining the analysis process \\ as a function} -Where $\mathcal{F}$ is the set of all sets of failure modes, and $\mathcal{DC}$ +Where $\mathcal{FG}$ is the set of all sets of functional groups, and $\mathcal{DC}$ is the set of all derived components, we can define the symptom abstraction process thus: $$ %\bowtie : SubSystemComponentFaultModes \rightarrow DerivedComponent -\bowtie : \mathcal{F} \rightarrow \mathcal{DC} +\bowtie : \mathcal{FG} \rightarrow \mathcal{DC} $$ \paragraph{Extending $\bowtie$ to {\dcs}} @@ -293,21 +298,38 @@ This generalises the function $\bowtie$ and allows us to build hierarchical failure mode models. Where a {\fg} is composed of derived components, for sake of example -where $DC_1, DC_2, DC_3 $ are {\dc}s and $DCFM$ is a set of failure modes thus -$FG = \{ DC_1, DC_2, DC_3 \}$ and $DCFM = FM(FG)$. +where $DC_1, DC_2, DC_3 $ are {\dc}s we could collect these into a {\fg} thus +$FG_{derived} = \{ DC_1, DC_2, DC_3 \}$. + +$DCFM$ is a set of failure modes from the new {\fg} $FG_{derived},$ +$DCFM = fm(FG_{derived})$. We can apply the symptom abstraction process $\bowtie$ -to the failure mode set $DCFM$. +to the {\fg} comprised of derived components +because we can obtain a failure mode set, +(the failure mode set we have named $DCFM$). + +Thus we can now move up another abstaction level by applying +symptom abstraction/extraction to the functional group +$FG_{derived}$ shown in equation \ref{eqn:fgderived}. + +\begin{equation} +\label{eqn:fgderived} + \bowtie ( FG_{derived} ) = DC_{derived} +\end{equation} + The case where a {\fg} has been created from {\dcs} using function `$\bowtie$' leads us to -{\dc}s at a higher level of fault abstraction. +{\dc}s at a higher level of failure mode abstraction. +A notation will be described in the next section +to keep track of the abstraction level of a {\dc}. -$$ +%%$$ %\bowtie : SubSystemComponentFaultModes \rightarrow DerivedComponent -\bowtie : DCFM \rightarrow DC -$$ +%%\bowtie : FG_{derived} \rightarrow DC +%%$$ % %\begin{equation} % \bowtie(FG_{cfm}) = DC @@ -315,14 +337,21 @@ $$ % %or applying the function $fm$ to obtain the $FG_{cfm}$ set % -To put this in context, where FG is a functional group, sourced from base or derived components, -we may state the process of -analysing the failure modes in the {\fg} and returning a {\dc} thus: -\begin{equation} - \bowtie(fm(FG)) = DC -\end{equation} +%%To put this in context, where FG is a functional group, sourced from base or derived components, +%%we may state the process of +%%analysing the failure modes in the {\fg} and returning a {\dc} thus: +%%\begin{equation} +%% \bowtie((FG)) = DC +%%\end{equation} +In other words by analysing a functional group containing derived components +we have a new derived component as our result. +This naturally +builds a bottom-up failure mode model, +with each iteration the model becomes more abstract will eventually reach +the SYSTEM level. + %The $SS_{fm}$ set of fault modes can be represented as a diagram with each fault~mode of $SS$ being a contour. %The derivation of $SS_{fm}$ is represented graphically using the `$\bowtie$' symbol, as in figure \ref{fig:gensubsys4} @@ -334,10 +363,6 @@ analysing the failure modes in the {\fg} and returning a {\dc} thus: % \caption{Deriving a new diagram} -This sub-system or {\dc} $DC$, with its three error modes, can now be treated as a component (although at a higher level of abstraction) -with known failure modes. -This process can be repeated using {\dcs} to build a -hierarchical fault~mode model.