diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex
index b4f25fd..abd4889 100644
--- a/component_failure_modes_definition/component_failure_modes_definition.tex
+++ b/component_failure_modes_definition/component_failure_modes_definition.tex
@@ -80,6 +80,21 @@ the failure mode set is not unitary~state and does not exist in the family of se
 
 
 
+\subsection{Component Failure Modes and Statistical Sample Space}
+
+A sample space is defined as the set of all possible outcomes.
+When dealing with failure modes, we are not interested in 
+the state where the compoent is working perfectly or `OK' (i.e. operating with no error).
+We are interested only in ways in which it can fail.
+By definition while all components in a system are `working perfectly' 
+that system will not exhibit faulty behavuiour.
+Thus the statistical sample space $\Omega$ for a component/sub-system K is
+%$$ \Omega = {OK, failure\_mode_{1},failure\_mode_{2},failure\_mode_{3} ... failure\_mode_{N} $$
+$$ \Omega(K) = \{OK, failure\_mode_{1},failure\_mode_{2},failure\_mode_{3} ... failure\_mode_{N}\} $$
+The failure mode set for a given component or sub-system $F$
+is therefore
+$$ F = \Omega(K) \backslash OK $$
+
 \subsection{Bayes Theorem}
 
 Describe application - likely hood of faults being the cause of symptoms -
@@ -97,8 +112,6 @@ to
 %Thus if the failure~modes are pairwaise mutually exclusive they qualify for inclusion into the 
 %unitary~state set family.
 
-
-
 \subsection{Tests of Hypotheses and Significance}
 
 In high reliability systems the fauls are often logged - strange occurances - 
diff --git a/symptom_abstraction/symptom_abstraction.tex b/symptom_abstraction/symptom_abstraction.tex
index 25a9d21..66de095 100644
--- a/symptom_abstraction/symptom_abstraction.tex
+++ b/symptom_abstraction/symptom_abstraction.tex
@@ -21,7 +21,7 @@ of a system can be built.
 %FMMD hierarchy
 The hierarchy is built from the bottom up.
 Starting with component failure modes at the bottom.
-Because the process is bottom-up
+Because the process is bottom-up, syntax checking and tracking can ensure that
 no component failure mode can be overlooked.
 Once a hierarchy is in place it can be converted into a fault data model.
 
@@ -38,6 +38,24 @@ This paper focuses on the process of building the blocks that are used in the hi
 
 \section{Introduction}
 
+Fault finding is intinctively performed from the top-down.
+A faulty peice of equipement is examined and will have a 
+symptom or specific fault. The area or sub-system within the 
+equipemnt will next be looked into. Secific measurements
+and checks will be made, and finally a component or a low level sub-system
+will be found to be faulty.
+The technique here works the other way. It works from the bottom up.
+Starting with a collection of compoents that form
+a simple functional group, the effect of all component error modes are
+examined, as to their effect on the functional group.
+The effects on the functional group can then be collected as common symptoms,
+and now we may treat the functional group as a component. It has a known set of failure modes.
+By working from the bottom up, we can trace all possible sources
+that could cause a particular mode of equipment failure.
+This means that we can obtainm statistical estimates based on the known reliabilities
+of the components.
+It also means that every component failure mode must at the very least be considered.
+
 \subsection{Static Analysis}
 
 In the field of safety critical engineering; to comply with 
@@ -74,9 +92,9 @@ For instance a stereo amplifier separate is a sub-system. The
 whole Sound System, consists perhaps of the following `sub-systems': 
 CD-player, tuner, amplifier~separate, loudspeakers and ipod~interface.
  
-Thinking like this is a top~down analysis approach
-and is the way in which FTA\cite{nucfta} analyses a System
-and breaks it down.
+%Thinking like this is a top~down analysis approach
+%and is the way in which FTA\cite{nucfta} analyses a System
+%and breaks it down.
 
 A sub-system will be composed of component parts, which
 may themselves be sub-systems. However each `component part'
@@ -107,7 +125,7 @@ for the smallest `functional~groups' of components within a system. A functional
 to perform a specific function.
 
 When we have analysed the fault behaviour of a functional group, we can treat it as a `black box'.
-We can now call our functional~group a sub-system. We know how will behave under fault conditions !
+We can now call our functional~group a sub-system. The goal here is to  know how will behave under fault conditions !
 %Imagine buying one such `sub~system'  from a very honest vendor.
 %One of those sir, yes but be warned it may fail in these distinct ways, here
 %in the honest data sheet the set of failure modes is listed!