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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