diff --git a/symptom_ex_process/symptom_ex_process.tex b/symptom_ex_process/symptom_ex_process.tex
index 8c6c68a..f06521e 100644
--- a/symptom_ex_process/symptom_ex_process.tex
+++ b/symptom_ex_process/symptom_ex_process.tex
@@ -500,6 +500,11 @@ verification checks in the process can be stated formally.
 
 \clearpage
 \subsection{Algorithmic Description of Symptom Abstraction \\ Determine Failure Modes to examine}
+
+The first stage is to find the failure modes to consider for
+analysis.
+Let $FG$ be the set of components in the functional group under analysis, and $c$
+be components that are members of it.
 %%
 %% Algorithm 1
 %%
@@ -515,9 +520,9 @@ verification checks in the process can be stated formally.
 %\STATE Determine functional groups $fg_n \subset S$ of components, where n is an index number and the number of functional groups found. 
 
 \STATE  { Let $FG$ be a set of components } \COMMENT{ The functional group should be chosen to be minimally sized collections of components that perform a specific function}
-\STATE { Let $C$ represent a component}
+\STATE { Let $c$ represent a component}
 
-\ENSURE{  Each component $C \in FG $ has a known set of failure modes i.e. $FM(C) \neq \emptyset$ }
+\ENSURE{  Each component $c \in FG $ has a known set of failure modes i.e. $ \forall c \in FG | FM(c) \neq \emptyset$ }
  
 \STATE {let $F=FM(FG)$ be a set of all failure modes to consider for the functional~group $FG$}
 
@@ -537,6 +542,13 @@ in the analysis stages.
 
 \clearpage
 \subsection{Algorithmic Description of Symptom Abstraction \\ Determine Test Cases}
+
+From the failure modes associated with the functional~group
+we now need to determine test cases.
+The test cases are collections of failure modes.
+These could be formed from single failure modes or failure modes in combination.
+Let $TC$ be the set of test cases associated withthe functional group $FG$.
+
 %%
 %% Algorithm 2
 %%
@@ -556,18 +568,7 @@ in the analysis stages.
    \STATE   { Let $TC$ be a set of test cases }
    \STATE { Let $tc_j$ be set of component failure modes where $j$ is an index of $J$} 
    \COMMENT { Each set $tc_j$ is a `test case' }
-   \STATE   { $ \forall j \in J  |  tc_j \in TC $ } 
-
-   %\STATE { $ \bigcup_{j=1...N} tc_j =  \bigcup TC $ } 
-   %\COMMENT { All $tc_j$ test cases sets belong to $TC$ }
- 
-    %\REQUIRE { $ TC \subset  \bigcup (FM_{cfm}) $ }  
-   %\COMMENT { $TC$ is the set of all test_cases
-% Let TC be a subset of the powerset of the failure modes $ FG_{cfm} $, 
-%i.e. only failure modes present in $ FG_{cfm} $ are present in sets belonging to $ TC $}
-
-
-   \COMMENT { Ensure the test cases are complete and unique }
+   \STATE   { $ \forall j \in J  |  tc_j \in TC $ } \COMMENT {Ensure the test cases are complete and unique}
 
    \FORALL { $tc_j \in TC$ }
      %\ENSURE   {$ tc_j  \in \bigcap FG_{cfm} $}
@@ -582,12 +583,16 @@ in the analysis stages.
    \STATE { let $f$ represet a component failure mode }
    \REQUIRE { That all failure modes are represented in at least one test case }
    \ENSURE { $ \forall f | (f \in F))    \wedge  (f \in \bigcup TC) $ }
-   \COMMENT { This corresponds to checking that at least each failure mode is considered at least once in the analysis; some european standards
-imply checking all double fault combinations\cite{en298} }
+   \COMMENT { This corresponds to checking that at least each failure mode is considered at 
+              least once in the analysis; more rigorous cardinality constraint
+              checks may be required for some safety standards}
+
+% some european standards
+%                imply checking all double fault combinations\cite{en298} }
 
 %\hline
 Algorithm \ref{alg:sympabs22} has taken the set of failure modes $ F=FM(FG) $ and returned a set of test cases $TC$.
-The next stages is to analyse the effect of each test case on the functional group.
+The next stage is to analyse the effect of each test case on the functional group.
 
 \end{algorithmic}
 \end{algorithm}
@@ -597,6 +602,9 @@ The next stages is to analyse the effect of each test case on the functional gro
 %%
 %% Algorithm 3
 %%
+The test cases are now analysed for their impact on the behaviour of the functional~group.
+Let $R$ be a set of results indexed by $j$ (the same index used to identify the test cases $tc_{j}$).
+
 
 \begin{algorithm}[h+]
  ~\label{alg:sympabs3}
@@ -605,9 +613,9 @@ The next stages is to analyse the effect of each test case on the functional gro
  \STATE  { let r be a `test case result'}
  \STATE  { Let the function $Analyse : tc \mapsto r $ } \COMMENT { This analysis is a human activity, examining the failure~modes in the test case and determining how the functional~group will fail under those conditions}
  \STATE  { $ R $ is a set of test case results $r_j \in R$ where the index $j$ corresponds to $tc_j \in TC$}
- \FORALL { $tc_j \in TC$ }
+ \FORALL { $tc_j \in TC$ } 
      \STATE { $ rc_j = Analyse(tc_j) $} \COMMENT {this is Fault Mode Effects Analysis (FMEA) applied in the context of the functional group}
-     \STATE { $ rc_j \in R $ }
+     \STATE { $ rc_j \in R $ } \COMMENT{Add $rc_j$ to the set R}
    \ENDFOR 
 
 %\hline
@@ -621,6 +629,9 @@ Algorithm \ref{alg:sympabs33} has built the set $R$, the sub-system/functional g
 %%
 %% Algorithm 4
 %%
+This stage analyses the results from bottom-up FMEA analysis ($R$), and collects
+results that, from the perspective of the functional~group, have the same failure symptom.
+Let set $SP$ be the set of symptoms for the functional group $FG$.
 
 \begin{algorithm}[h+]
  ~\label{alg:sympabs4}
@@ -667,6 +678,10 @@ We now have a set $SP$ of the symptoms of failure.
 %%
 %% Algorithm 5
 %%
+This final stage, is the creation of the derived component.
+This derived component may now be used to build
+new functional groups at higher levels of fault abstraction.
+Let $DC$ be a derived component with its own set of failure~modes.
 
 \begin{algorithm}[h+]
  ~\label{alg:sympabs5}
@@ -693,7 +708,10 @@ Hierarchies of fault abstraction can be built that can model an entire SYSTEM.
 
 \section{To conclude}
 
-The technique provides a methodology for bottom-up analysis of the fault behaviour of complex safety critical systems.
+The symptom abstraction technique allows us to take a functional group of components, analyse the failure
+mode behaviour and create a new entity, a derived~component, that has its own set of failure modes.
+This process naturally takes one step to building a hierarchical failure mode model
+from the bottom-up. 
 
 \subsection{Hierarchical Simplification}
 
@@ -717,3 +735,7 @@ Minimal cut sets \cite{nasafta} can be determined from these, and by
 analysing the statistical likelyhood of the component failures,
 the MTTF and SIL\cite{en61508} levels can be automatically calculated.
 
+
+\vspace{40pt}
+\today
+