DAG DAG DAG DAG DAGAGAGAGAGAGAGAGA

fmmd_data_model/fmmd_data_model.tex

@@ -186,10 +186,25 @@ its range and {\dc} as its domain.
 For the sake of example let us determine some arbitary collections
 into symptoms. Let us group the symptoms from $ FG^0_1 $ as the following
 $ s1 = \{ C_{1 a}, C_{2 b} \}$ and $ s2  = \{ C_{1 b}, C_{2 a} \}$.
-We can now create a new {\dc}. This will have an $\alpha$ value higher
-than the {\fg} it was derived from.
+We can represent the relationships between the failure modes, and desired failure modes or symptoms
+as a directed acyclic graph (see figure \ref{fig:dag0}).
 
-thus
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,bb=0 0 466 270,keepaspectratio=true]{./fmmd_data_model/dag0.jpg}
+ % dag0.jpg: 466x270 pixel, 72dpi, 16.44x9.52 cm, bb=0 0 466 270
+ \caption{DAG reprsenting the failure modes from $FG^0_1$.}
+ \label{fig:dag0}
+\end{figure}
+
+
+We can now create a new {\dc}. This will have an $\alpha$ value higher
+than the any of the components in the {\fg} that it was derived from.
+In this case all components were base components and therefore have an $\alpha$ value of zero.
+Our derived component can thus take a n $\alpha$ value of one.
+
+Our newly derived component can be 
 $$ DC^1_1 = \bowtie fm(FG^0_1) .$$
 
 Applying $fm$ to our new derived component will give us our symptoms from functional group $ FG^0_1 $
@@ -197,6 +212,18 @@ thus
 
 $$ fm(DC^1_1) = \{s1, s2 \}.$$
 
+We can represent $ DC^1_1 $ as an addition to the DAG (see figure \ref{fig:dag1}).
+
+
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt,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 $.}
+ \label{fig:dag1}
+\end{figure}
+
 
 UML OBJECT MODEL OF  DERIVED COMPONENT TOO