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Your Name 2012-04-17 14:31:26 +01:00
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18
papers/software_fmea/software_fmea.tex
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@ -927,11 +927,23 @@ as a hierarchical diagram, see figure~\ref{fig:hd}.
We can represent the hierarchy in figure~\ref{fig:hd} algebraically, using the $\bowtie$ function
definition nested thus:
We can represent the hierarchy in figure~\ref{fig:hd} algebraically, using the `$\bowtie$' function
using the groups as intermediate stages:
\begin{eqnarray*}
G_1 = \{R,ADC\} \\
CMATV = \;\bowtie (G_1) \\
G_2 = \{CMATV, read\_4\_20\_input \} \\
RADC = \; \bowtie (G_2) \\
G_3 = \{ RADC, read\_4\_20\_input \} \\
R420I = \; \bowtie (G_3) \\
\end{eqnarray*}
or, a nested definition,
$$ \bowtie \Big( \bowtie \big( \bowtie(R,ADC), read\_4\_20\_input \big), read\_4\_20\_input \Big). $$
This nested structure means that we have multiple traceable
stages of failure mode reasoning in our analysis. Traditional FMEA would have only one stage
of reasoning for each component failure mode.