context.........

logic_diagram/logic_diagram.tex

@@ -350,14 +350,14 @@ i.e. the contours $\mathcal{X}$ from the zone it inhabits.
 {
 \definition{
  
-Let $\mathcal{F_t}$  be a function mapping a test case $t \in T$,  to a proposition / logical equation $p \in P$.
+Let $\mathcal{F}_{t}$  be a function mapping a test case $t \in T$,  to a proposition / logical equation $p \in P$.
 The test case $t$, inhabits the zone $\mathcal{Z}$ which is a collection of contours (the contours that enclose the test case).
 We can express this as
-$$ \mathcal{F_t}:T \rightarrow P\;, $$
+$$ \mathcal{F}_{t}:T \rightarrow P\;, $$
 
 %$$ \mathcal{F}(t): p  = \bigwedge_{c \in \mathcal{Z}}  \Lambda c  $$  
 given by
-$$ \mathcal{F_t}(t): p  = \bigwedge_{c \in \mathcal{Z}}  c \;. $$
+$$ {F}_{t}(t): p  = \bigwedge_{c \in \mathcal{Z}}  c \;. $$
 }
 }
 
@@ -378,7 +378,7 @@ $$ \mathcal{G}:SMG \rightarrow P. $$
 
 The logic equation (using $oplus$ to represent exclusive-or) representing an SMG $p_{fmg}$ is given thus;
 
-$$\mathcal{G}(fmg) = \bigoplus_{t \in fmg} (\; \mathcal{F_t} (t) \;) \; .$$
+$$\mathcal{G}(fmg) = \bigoplus_{t \in fmg} (\; \mathcal{F}_{t} (t) \;) \; .$$
 }
 }
 
@@ -396,10 +396,22 @@ and unused available zones.
 \subsection{Symptom Collection}
 
 The methodology using these propositional logic diagrams is concerned with
-taking functional groups of components, and representing the failure
-modes of those components as contours in the diagram.
-The test cases, when analysed can be grouped into $SMG$s which
-define the failure mode behaviour of the functional group.
+taking functional groups of components, analysing how the functional group
+can fail, and then deriving a failure mode model for the functional group
+so that we can treat it as a component in its own right, or as a `derived component'
+
+We represent the failure
+modes of the components within a {\fg} as contours in the diagram.
+The test cases represent combinations of component failure modes
+within the functional group.
+The test cases, when analysed can be grouped into $SMG$s.
+The SMG, Symptomatically merged group, is a collection of test
+cases where the failure symptom is the same.
+%
+Each SMG
+defines a failure mode behaviour of the functional group as though the
+{\fg} were considered as a high level component.
+%
 As we may be interested in treating the functional group
 and a component to model higher levels of design, or failure mode abstraction,
 we can derive a new diagram from the $SMG$s. Each $SMG$ represents a failure