diff --git a/papers/software_fmea/software_fmea.tex b/papers/software_fmea/software_fmea.tex
index 125c80d..e1105a4 100644
--- a/papers/software_fmea/software_fmea.tex
+++ b/papers/software_fmea/software_fmea.tex
@@ -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.