Tuesday morning edit

thought about cycling in, drove in early and did this instead. Snow.

fmmd_concept/fmmd_concept.tex

@@ -887,10 +887,10 @@ Environmental conditions may affect different components in a {\fg}
 in different ways.
 
 For instance a system may be specified for
-0 to 85oC operation, but some components
+$0\oc$  to {85\oc} operation, but some components
-may show failure behaviour between 60 and 85
+may show failure behaviour between $60\oc$  and $85\oc$ 
 \footnote{Opto-islolators typically show marked performace decrease after
-60oC whereas another common component, the resistor will be unaffected.}.
+60oC \cite{tlp181}, whereas another common component, the resistor will be unaffected.}.
 Other components may operate comfortably within that whole temperature range specified.
 Environmental conditions will have an effect on the {\fg} and the {\dc}
 but they will have specific effects on individual components.

fmmd_data_model/fmmd_data_model.tex

@@ -150,7 +150,8 @@ We shall begin  with the $FG^0$ level functional groups $ FG^0_1, FG^0_2 $ and $
 %  \label{fig:cfg2fmmd_data}
 % \end{figure}
 
-\paragraph{Find Failure Modes}
+\pagebreak[4]
+\subsection{Find Failure Modes}
 
 Consider the SYSTEM environment with its temperature range of ${{0}\oc}$ to ${{125}\oc}$.
 We must check this against all components used.
@@ -161,6 +162,7 @@ gives the following failure modes, $fm{K} =\{ K_a, K_b, K_d \}$.
 Were our system specified for a ${{0}\oc}$ to ${{80}\oc}$  range
 we could say $fm{K} =\{ K_a, K_b \}$.
 
+\pagebreak[3]
 \paragraph{Get the failure modes from the functional groups.}
 Applying the function $fm$ to our functional groups, with the SYSTEM environmental
 constraint applied to component type `K',  yields
@@ -170,7 +172,7 @@ constraint applied to component type `K',  yields
 %%$$ FG^0_3 = \{C_5, C_6, K_7\}.$$
 
 $$ fm(FG^0_1) = \{C_{1 a}, C_{1 b}, C_{2 a}, C_{2 b}\},$$
-$$ fm(FG^0_2) = \{C_{1 a}, C_{1 b}, C_{2 a}, C_{2 b}, K_{4 a}, K_{4 b}, K_{4 d}\},$$
+$$ fm(FG^0_2) = \{C_{1 a}, C_{1 b}, C_{3 a}, C_{3 b}, K_{4 a}, K_{4 b}, K_{4 d}\},$$
 $$ fm(FG^0_3) = \{C_{5 a}, C_{5 b}, C_{6 a}, C_{6 b}, K_{7 a}, K_{7 b}, K_{7 d}\}.$$
 
 The next stage is to look at the failure modes from the perspective of
@@ -221,13 +223,35 @@ We can represent $ DC^1_1 $ as an addition to the DAG (see figure \ref{fig:dag1}
  \centering
  \includegraphics[width=300pt,bb=0 0 466 270,keepaspectratio=true]{./fmmd_data_model/dag1.jpg}
  % dag0.jpg: 466x270 pixel, 72dpi, 16.44x9.52 cm, bb=0 0 466 270
- \caption{DAG reprsenting the failure modes from $FG^0_1$ and $ DC^1_1 $.}
+ \caption{DAG reprsenting the failure modes from $FG^0_1$ and $ DC^1_0 $.}
  \label{fig:dag1}
 \end{figure}
 
 
-UML OBJECT MODEL OF  DERIVED COMPONENT TOO
+\subsection{ Creating Derived components from $FG^0_2$ and $FG^0_3$ }
 
+Applying the FMMD process for $FG^0_2$ and $FG^0_3$.
+
+\paragraph{Applying FMMD $ \bowtie fm(FG^0_2) $:}
+
+The failure modes $fm(FG^0_2) =  \{C_{1 a}, C_{1 b}, C_{3 a}, C_{3 b}, K_{4 a}, K_{4 b}, K_{4 d}\}.$
+Let us say new symptom s3 can be caused by failure modes $\{C_{1 a},  C_{3 b}, K_{4 b} \}$
+, let us say new symptom s4 can be caused by failure modes $\{C_{1 b},  C_{3 a}, K_{4 d} \}$
+and let us say new symptom s5 can be caused by failure mode $\{K_{4 a} \}$.
+
+We can create a derived component $DC^1_2$ using
+$\bowtie fm(FG^0_2) = DC^1_2$.
+Applying $fm$ to our {\dcs} gives $fm(DC^1_2) = \{ s3,s4,s5 \}$.
+
+
+\paragraph{Applying FMMD $\bowtie fm(FG^0_3) $ :}
+Let us say new symptom s6 can be caused by failure modes $\{C_{5 a},  C_{6 b}, K_{4 b} \}$
+, let us say new symptom s7 can be caused by failure modes $\{C_{5 b},  C_{6 a}, K_{7 d} \}$
+and let us say new symptom s8 can be caused by failure mode $\{K_{7 a} \}$.
+
+We can create a derived component $DC^1_3$ using
+$\bowtie fm(FG^0_3) = DC^1_3$
+where $fm(DC^1_3) = \{ s6,s7,s8 \}$.
 
 
 \pagebreak[4]