diff --git a/component_failure_modes_definition/Makefile b/component_failure_modes_definition/Makefile
index ff49043..fae8c9b 100644
--- a/component_failure_modes_definition/Makefile
+++ b/component_failure_modes_definition/Makefile
@@ -13,5 +13,5 @@ paper:	paper.tex component_failure_modes_definition_paper.tex
 
 # Remove the need for referncing graphics in subdirectories
 #
-component_failure_modes_definition_paper.tex: component_failure_modes_definition.tex
+component_failure_modes_definition_paper.tex: component_failure_modes_definition.tex paper.tex
 	cat component_failure_modes_definition.tex | sed 's/component_failure_modes_definition\///' > component_failure_modes_definition_paper.tex
diff --git a/component_failure_modes_definition/cfg.dia b/component_failure_modes_definition/cfg.dia
index 6945670..034f5cc 100644
Binary files a/component_failure_modes_definition/cfg.dia and b/component_failure_modes_definition/cfg.dia differ
diff --git a/component_failure_modes_definition/cfg.jpg b/component_failure_modes_definition/cfg.jpg
index 56dc26a..ab3ee50 100644
Binary files a/component_failure_modes_definition/cfg.jpg and b/component_failure_modes_definition/cfg.jpg differ
diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex
index 3ee9b56..cd02e29 100644
--- a/component_failure_modes_definition/component_failure_modes_definition.tex
+++ b/component_failure_modes_definition/component_failure_modes_definition.tex
@@ -10,14 +10,16 @@ Mathematical constraints and definitions are made using set theory.
 
  
 \section{Introduction}
-
+This chapter describes the data types and concepts for the Failure Mode Modular De-composition (FMMD) method.
 When analysing a safety critical system using the 
-FMMD technique, we need clearly defined failure modes for
+this technique, we need clearly defined failure modes for
 all the components that are used to model the system.
 These failure modes have a constraint such that
-the compoent failure modes must be mutually exclusive.
-This and the definition of a component are 
-described in this chapter.
+the component failure modes must be mutually exclusive.
+When this constraint is complied with we can use the FMMD process to 
+build hierarchical bottom-up models of failure mode behaviour.
+%This and the definition of a component are 
+%described in this chapter.
 %When building a system from components, 
 %we should be able to find all known failure modes for each component.
 %For most common electrical and mechanical components, the failure modes
@@ -104,8 +106,8 @@ We can term this a `Functional~Group'. When we have a
 `Functional~Group' we can look at the failure modes of all the components
 in it and decide how these will affect the Group.
 Or in other words we can determine the failure modes of the functional
-group. These failure modes are derived from the functional group, as so we can call
-them `derived failure modes'.
+group. These failure modes are derived from the functional group, we can therefore call 
+these `derived failure modes'.
 We now have something very useful, because
 we can now treat this functional group as a component with a known set of failure modes.
 This newly derived component can be used as a higher level
@@ -115,7 +117,7 @@ to form higher level functional groups.
 This process can continue until have build a hierarcy that converges to a failure model of the entire system.
 To differentiate the components derived from functional groups, we can
 add a new attribute to the class `Component', that of analysis
-level.
+level. The UML representation shows a `functional group' having a one to one relationship with a derived component.
 We can represet this in a UML diagram see figure \ref{fig:cfg}
 
 \begin{figure}[h]
@@ -125,8 +127,8 @@ We can represet this in a UML diagram see figure \ref{fig:cfg}
  \caption{Components Derived from Functional Groups}
  \label{fig:cfg}
 \end{figure}
-
-\section{Set theory description}
+\clearpage
+\section{Set Theory Description}
 
 $$ System \stackrel{has}{\longrightarrow} PartsList $$
 
@@ -312,7 +314,7 @@ It should not be possible for instance for
 a component to have two or more failure modes active at once.
 
 Having a set of failure modes where $N$ modes could be active simultaneously
-would mean having to consider $2^N$ failure mode scenarios.
+would mean having to consider $2^N-1$ failure mode scenarios.
 % 
 Should a component be analysed and simultaneous failure mode cases exit,
 the combinations could be represented by new failure modes, or
@@ -348,10 +350,10 @@ A component with simple ``unitary~state'' failure modes is the electrical resist
 
 Electrical resistors can fail by going OPEN or SHORTED.
 
-For a given resistor R we can assign it the failure mode by applying
-the function $FM$ thus  $ FM(R) =  \{R_{SHORTED},R_{OPEN}\} $.
-Nothing can fail with both conditions open and short active at the same time ! The conditions
-OPEN and SHORT are mutually exclusive.
+For a given resistor R we can apply the 
+the function $FM$ to find its set of failure modes thus  $ FM(R) =  \{R_{SHORTED},R_{OPEN}\} $.
+A resistor cannot fail with both conditions open and short active at the same time ! The conditions
+OPEN and SHORT are thus mutually exclusive.
 Because of this the failure mode set $F=FM(R)$ is `unitary~state'.
 
 
@@ -370,7 +372,7 @@ $$ c1 \cap c2 \neq \emptyset  | c1 \neq c2 \wedge c1,c2 \in C \wedge C \not\in U
 That is to say that it is impossible that any pair of failure modes can be active at the same time
 for the failure mode set $C$ to exists in the family of sets $U$
 
- Note where that are more than two failure~modes, by banning pairs from happening at the same time
+ Note where that are more than two failure~modes, by banning pairs from being active at the same time
  we have banned larger combinations as well.