D instead of bowtie notation used

for symptom abstraction in tex
and diagrams now.

Next add the software with FMMD.

AND after thatfinish off the sigma delta ADC
analysis.

submission_thesis/CH4_FMMD/copy.tex

@@ -413,11 +413,11 @@ fault behaviour.
 
 The UML representation  (in figure \ref{fig:cfg}) shows a `functional group' having a one to one relationship with a derived~component.
 
-The symbol $\bowtie$ is used to indicate the analysis process that takes a
+The symbol $\derivec$ is used to indicate the analysis process that takes a
 functional group and converts it into a new component.
 \begin{definition}
 With $\mathcal{\FG}$ representing the set of all functional groups, and $\mathcal{{\DC}}$ the set of all derived components,
-this can be expressed as  $$ \bowtie : \mathcal{\FG}  \rightarrow \mathcal{{\DC}} $$ .
+this can be expressed as  $$ \derivec : \mathcal{\FG}  \rightarrow \mathcal{{\DC}} $$ .
 \end{definition}
 
 \begin{figure}[h]
@@ -442,7 +442,7 @@ objects, functional~groups formed with derived~components, and after symptom~abs
 derived components yet higher up in the structure.
 %
 To keep track of the level in the hierarchy (i.e. how many stages of component 
-derivation `$\bowtie$' have lead to the current derived component)
+derivation `$\derivec$' have lead to the current derived component)
 we can add an attribute to the component data type. 
 This can be a natural number called the level variable $\abslev \in \mathbb{N}$.
 % J. Howse says zero is a given in comp sci. This can be a natural number called the level variable $\alpha \in \mathbb{N}_0$.
@@ -468,10 +468,10 @@ would have an $\abslev$ value of 1.
 % 
 % $$ FunctionalGroup  \stackrel{has}{\longrightarrow} Components $$
 % 
-% Using the symbol $\bowtie$ to indicate an analysis process that takes a
+% Using the symbol $\derivec$ to indicate an analysis process that takes a
 % functional group and converts it into a new component.
 % 
-% $$ \bowtie ( FG ) \rightarrow DerivedComponent $$
+% $$ \derivec ( FG ) \rightarrow DerivedComponent $$
 % 
 
 \subsection{Relationships between functional~groups and failure modes}
@@ -1209,17 +1209,17 @@ We can apply symptom abstraction to a {\fg} to find
 its symptoms. 
 %We are interested in the failure modes
 %of all the components in the {\fg}. An analysis process
-We define the symptom abstraction process with the symbol  `$\bowtie$'.% is applied to the {\fg}.
+We define the symptom abstraction process with the symbol  `$\derivec$'.% is applied to the {\fg}.
 %
-The $\bowtie$ function takes a {\fg}
+The $\derivec$ function takes a {\fg}
 as an argument and returns a newly created {\dc}.
 %
-%The $\bowtie$ analysis, a symptom extraction process, is described in chapter \ref{chap:sympex}.
+%The $\derivec$ analysis, a symptom extraction process, is described in chapter \ref{chap:sympex}.
 The symptom abstraction process must always raise the abstraction level
 for the newly created {\dc}.
 Using $\abslev$ (as described in~\ref{sec:alpha}) to symbolise the fault abstraction level, we can now state:
 
-$$ \bowtie({\FG}^{\abslev}) \rightarrow c^{{\abslev}+N} | N \ge 1. $$ 
+$$ \derivec({\FG}^{\abslev}) \rightarrow c^{{\abslev}+N} | N \ge 1. $$ 
 
 \paragraph{Functional Groups may be indexed.}
 We will typically have more than one {\fg} on each level of FMMD hierarchy ( expect the top level where there will only be one)
@@ -1227,12 +1227,27 @@ we could index the {\fgs} with a sub-script, and can then uniquely identify them
 For example ${\FG}^{3}_{2}$ would be the second  {\fg} at the third level of abstraction in an FMMD hierarchy.
 
 \paragraph{The symptom abstraction process in outline.} 
-The $\bowtie$ function processes each component in the {\fg} and 
-extracts all the component failure modes.
-With all the failure modes, an analyst can   
-determine how each failure mode will affect the {\fg}, and then collect common symptoms.
-A new {\dc} is created
-where its failure modes,  are the symptoms from {\fg}.
+The $\derivec$ function processes a functional group and returns a derived component.
+Firstly, all the failure modes from all the components in the {\fg} 
+are used to create failure scenarios, which can be single failure modes
+or combinations of failure modes (where unitray state failure mode constraints do not apply).
+%
+With all the failure scenarios, an analyst can   
+determine how each scenario will affect the {\fg}.
+This will give one failure mode behaviour result for each failure scenario.
+With these results, we collect common symptoms.
+That is to say, that many of the resultant failure modes, will ehibit the same symptom of failure from the perspective
+of a user of the {\fg}.
+%
+We now can treat the functional group as a sort of `super~component'.
+%
+In order to make this new `super~component' usable, it needs to be in the form of a
+component, that is it has a name, and a set of failure modes.
+We can do this by creating a new {\dc} and assigning a name to it, as as its set of 
+failure modes, the failure symptoms from the {\fg} from which it was derived.
+%A new {\dc} is created
+%where its failure modes,  are the symptoms from {\fg}.
+%
 Note that the component must have a higher abstraction level than the {\fg}
 it was derived from.
 
@@ -2278,20 +2293,20 @@ consider DC as being in the set of components i.e. $DC \in \mathcal{C}$
 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:
 $$
-%\bowtie : SubSystemComponentFaultModes \rightarrow DerivedComponent 
-\bowtie : \mathcal{FG} \rightarrow \mathcal{DC} .
+%\derivec : SubSystemComponentFaultModes \rightarrow DerivedComponent 
+\derivec : \mathcal{FG} \rightarrow \mathcal{DC} .
 $$
 
 Given by
-$ \bowtie ( FG ) = DC $
+$ \derivec ( FG ) = DC $
 as per the example in precedeing section \ref{theoreticalsx}.
 
-\paragraph{Extending $\bowtie$ to {\dcs}}
+\paragraph{Extending $\derivec$ to {\dcs}}
 
-It is useful to further define the $\bowtie$ function, to
+It is useful to further define the $\derivec$ function, to
 take the failure modes from derived components (as well as base components)
 and return a new derived component.
-This generalises the function $\bowtie$ and allows us to build
+This generalises the function $\derivec$ and allows us to build
 hierarchical failure mode models.
 
 Where a {\fg} is composed of derived components, for sake of example
@@ -2301,7 +2316,7 @@ $FG_{derived} = \{ DC_1, DC_2, DC_3 \}$.
 $DCFM$ is a set of failure modes from the new {\fg} $FG_{derived},$ 
 $DCFM = fm(FG_{derived})$.
 
-We can apply the symptom abstraction process $\bowtie$
+We can apply the symptom abstraction process $\derivec$
 to the {\fg} comprised of derived components
 because we can obtain a failure mode set,
 (the failure mode set we have named $DCFM$).
@@ -2312,24 +2327,24 @@ $FG_{derived}$ shown in equation \ref{eqn:fgderived}.
 
 \begin{equation}
 \label{eqn:fgderived}
- \bowtie ( FG_{derived} ) = DC_{derived} 
+ \derivec ( FG_{derived} ) = DC_{derived} 
 \end{equation}
 
 
 The case 
 where a {\fg} has been created from {\dcs} 
-using function `$\bowtie$' leads us to
+using function `$\derivec$' leads us to
 {\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}.
 
 %%$$
-%\bowtie : SubSystemComponentFaultModes \rightarrow DerivedComponent 
-%%\bowtie : FG_{derived} \rightarrow DC 
+%\derivec : SubSystemComponentFaultModes \rightarrow DerivedComponent 
+%%\derivec : FG_{derived} \rightarrow DC 
 %%$$
 %
 %\begin{equation}
-%  \bowtie(FG_{cfm}) = DC
+%  \derivec(FG_{cfm}) = DC
 %\end{equation} 
 %
 %or applying the function $fm$ to obtain the $FG_{cfm}$ set 
@@ -2338,7 +2353,7 @@ to keep track of the abstraction level of a {\dc}.
 %%we may state the process of 
 %%analysing the failure modes in the {\fg} and returning a {\dc} thus:
 %%\begin{equation}
-%%  \bowtie((FG)) = DC
+%%  \derivec((FG)) = DC
 %%\end{equation}
 
 
@@ -2350,7 +2365,7 @@ 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}
+%The derivation of $SS_{fm}$ is represented graphically using the `$\derivec$' symbol, as in figure \ref{fig:gensubsys4}
 
 % \begin{figure}[h+]
 %  \centering
@@ -2388,8 +2403,8 @@ fm : FG \rightarrow \mathcal{F}
 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:
 $$
-%\bowtie : SubSystemComponentFaultModes \rightarrow DerivedComponent 
-\bowtie : \mathcal{FG} \rightarrow \mathcal{DC} .
+%\derivec : SubSystemComponentFaultModes \rightarrow DerivedComponent 
+\derivec : \mathcal{FG} \rightarrow \mathcal{DC} .
 $$
 
 The next section describes the details of the symptom extraction process.
@@ -2406,7 +2421,7 @@ this section
 %describes the symptom abstraction process 
 using set theory and procedural descriptions.  
 %
-The {\em symptom abstraction process} (given the symbol `$\bowtie$') takes a functional group $FG$
+The {\em symptom abstraction process} (given the symbol `$\derivec$') takes a functional group $FG$
 and a new derived~component/sub-system $DC$.
 %The sub-system $SS$ is a collection
 %of failure~modes of the sub-system.
@@ -2422,7 +2437,7 @@ as a component with a known set of failure modes.
 We can assign an attribute  of abstraction level $\abslev$  to
 components, where $\abslev$ is a natural number, ($\abslev \in \mathbb{N}_0$).
 For a base component, let the abstraction level be zero.
-If we apply the symptom abstraction process $\bowtie$,
+If we apply the symptom abstraction process $\derivec$,
 the resulting derived~component will have an $\abslev$ value
 one higher that the highest $\abslev$ value of any of the components
 in the functional group used to derive it.
@@ -2453,7 +2468,7 @@ naturally formed with the abstraction levels increasing with each tier.
 %\ENDFOR
 
 
-The algorithm, represented by the symbol `$\bowtie$', has been broken down into five consecutive stages.
+The algorithm, represented by the symbol `$\derivec$', has been broken down into five consecutive stages.
 %These are described using the Algorithm environment in the next section \ref{algorithms}.
 By defining the process and describing it using set theory. Constraints and 
 verification checks in the process are stated formally.
@@ -2463,11 +2478,11 @@ verification checks in the process are stated formally.
 
 \section{Algorithmic Description of Symptom Abstraction}
 %\clearpage
-$$ \bowtie: \mathcal{FG} \rightarrow \mathcal{DC} $$
+$$ \derivec: \mathcal{FG} \rightarrow \mathcal{DC} $$
 
 \begin{algorithm}[h+]
 
-\caption{Derive new `Component' from Functional Group: $\bowtie(FG)$} \label{alg66}
+\caption{Derive new `Component' from Functional Group: $\derivec(FG)$} \label{alg66}
 
 \begin{algorithmic}[1]
 

submission_thesis/CH5_Examples/Makefile

@@ -32,3 +32,7 @@ copy: $(PNG_DIA)
 bib:
 	bibtex discussion_doc
 	#makeindex opamps.glo -s opamps.ist -t opamps.glg -o opamps.gls
+
+
+clean:
+	rm ${PNG_DIA}

submission_thesis/CH5_Examples/copy.tex

@@ -475,7 +475,7 @@ mode model of the system under investigation.
 \end{figure}
 
 Figure~\ref{fig:treeabslev} shows an FMMD hierarchy, where the process of creating a {\dc} from a {\fg}
-is shown as a `$\bowtie$' symbol.
+is shown as a `$\derivec$' symbol.
 
 
 

submission_thesis/style.tex

@@ -15,6 +15,7 @@
 \setlength{\textwidth}{160mm}      \setlength{\textheight}{220mm}
 \setlength{\oddsidemargin}{0mm}    \setlength{\evensidemargin}{0mm}
 %
+\newcommand{\derivec}{{D}}
 \newcommand{\abslev}{\ensuremath{\alpha}}
 \newcommand{\oc}{\ensuremath{^{o}{C}}}
 \newcommand{\adctw}{{${\mathcal{ADC}}_{12}$}}