Looking through for errors b4 John Howse submssn

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.