diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex
index 90001a0..7b968c2 100644
--- a/component_failure_modes_definition/component_failure_modes_definition.tex
+++ b/component_failure_modes_definition/component_failure_modes_definition.tex
@@ -2,7 +2,8 @@
 \abstract{ This chapter defines what is meant by the terms
 components, component fault modes and `unitary~state' component fault modes.
 The application of Bayes theorem  in current methodologies, and
-the unsuitability of the `null hypothesis' or p value statistical approach.
+the suitability of the `null hypothesis' or `P' value statistical approach
+ar discussed.
 Mathematical constraints and definitions are made using set theory.
 }
 
@@ -19,12 +20,12 @@ Using these failure modes we can build a `failure model' from the bottom-up.
 Traditional static fault analysis methods work from the top down.
 They identify faults that can occur in a system, and then work down
 to see how they could be caused. Some apply statistical tequniques to
-determine the likelyhood of component failures causing specific system level errors (see Bayes theorem \ref{bayes}).
+determine the likelihood of component failures causing specific system level errors (see Bayes theorem \ref{bayes}).
 Another top down technique is ato apply cost benifit analysis 
 to determine which faults are the highest priority to fix\cite{FMEA}.
 
 The aim of this study is to produce complete  failure
-models of safety critical systems  from the bottom-up
+models of safety critical systems  from the bottom-up,
 starting, where possible with known component failure modes.
 
 
@@ -33,7 +34,7 @@ starting, where possible with known component failure modes.
 It is helpful here to define some terms, `system', `functional~group', `component', `base~component' and `sub-system'.
 
 A System, is really any coherent entity that would be sold as a safety critical product.
-A sub-system is a system that is part of some larger system.
+A sub-system is a  part of some larger system.
 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.
@@ -43,18 +44,23 @@ CD-player, tuner, amplifier~separate, loudspeakers and ipod~interface.
 %and breaks it down.
 
 A sub-system will be composed of component parts, which
-may themselves be sub-systems. However each `component part'
-will have a fault/failure behaviour and it should
-always be possible to obtain a set of failure modes
-for each `component'. 
+may themselves be sub-systems.
+
+Eventually by a recursive downwards process we would be able to identify
+sub-systems built from base component parts.
+Each `component part'
+will have a known fault/failure behaviour.
+That is to say, each base component has a set of known
+ways in which it can fail.
 
 If we look at the sound system again as an
 example; the CD~player could fail in serveral distinct ways, no matter
 what has happened to it or has gone wrong inside it.
 
-
+A top down approach has an intrinsic problem in that we cannot guess
+every possible failure mode at the SYSTEM level.
 Using the reasoning that working from the bottom up forces the consideration of all possible
-component failures (which can be missed in a top~down approach)
+component failures (which could be missed in a top~down approach)
 we are presented with a problem. Which initial collections of base components should we choose ?
 
 For instance in the CD~player example; to start at the bottom; we are presented with
@@ -92,8 +98,8 @@ Currently this sort of information is generally only  available for generic comp
 %At higher levels of analysis, functional~groups are pre-analysed sub-systems that interact to
 %erform a given function.
 
-\vspace{0.3cm}
-%\begin{table}[p]
+%\vspace{0.3cm}
+\begin{table}[p]
 \begin{tabular}{||l|l||} \hline \hline
   {\em Definition } & {\em Description}    \\ \hline
 System & A product designed to  \\
@@ -113,10 +119,11 @@ Failure mode & of a `Failure Mode Group' \\ \hline
 Base Component & Any bought in component, which \\
                & hopefully has a known set of failure modes  \\    \hline  
  \hline
-\label{tab:def}
+
 \end{tabular}
-%\end{table}
-\vspace{0.3cm}
+\label{tab:def}
+\end{table}
+%\vspace{0.3cm}
 
 \section{A UML Model of terms introduced}
 
@@ -130,43 +137,54 @@ Base Component & Any bought in component, which \\
 \end{figure}
 
 The diagram in figure \ref{fig:fmmd_uml}
-shows the relationships between the terms defined in table \ref{tab:def}.
+shows the relationships between the terms defined in table \ref{tab:def} as classes in a UML model.
 We can start with the functional group. This is a minimal collection
 of components that perform a simple given function.
 For our audio separates rig, this could be 
 the compoents that supply power to the laser diode.
-From the `Functional Group we can now collect
-all the `failure modes of the `components, and 
-produce a `Failure Mode Group. This
-has a reference to the `Functional Group, and is a collection
+From the `Functional~Group' we can now collect
+all the `failure modes of the `components', and 
+produce a `Failure~Mode~Group'. This
+has a reference to the `Functional~Group', and is a collection
 of `failure modes.
-By analysing the effects of the failure modes in the `Failure Mode Group'
+By analysing the effects of the failure modes in the `Failure~Mode~Group'
 we can determine the failure mode behaviour of the functional group.
 This failure mode behaviour is a collection of derived failure modes.
 We can now consider the Functional group as a component now, because
 we have a set of failure modes for it.
-We can term this set of failure modes a sub-system.
 
-Note that this is recursive. We can build functional groups using sub-systems
+\subsection{Sub-System Class Definition}
+A sub-system can now be defined by the classes used to create it, and 
+its set of derived failure modes.
+
+Note that the UML model is recursive. We can build functional groups using sub-systems
 as components. This UML model naturally therefore, forms a hierarchy
 of failure mode analysis, which has a one top level entry, that being the SYSTEM.
 The TOP level entry will determine the failure modes 
 for the product/system under analysis.
 
-
+\subsection{Refining the UML model to use inheritance}
 We can refine this model a little by noticing that a system is merely the 
 top level sub-system. We can thus have System inherit sub-system.
 A derived failure mode, is simply a failure mode at a higher level of analysis
 it can therefore inherit `failure\_mode'.
 
-The modified UML diagram using inheritance is figure \ref{fig:fmmd_uml2}
+The modified UML diagram using inheritance is figure \ref{fig:fmmd_uml2}.
 \begin{figure}[h]
  \centering
- \includegraphics[width=350pt,bb=0 0 680 500,keepaspectratio=true]{component_failure_modes_definition/fmmd_uml2.jpg}
- % fmmd_uml.jpg: 680x500 pixel, 72dpi, 23.99x17.64 cm, bb=0 0 680 500
- \caption{UML respresentation of Failure Mode Data types}
+ \includegraphics[width=350pt,bb=0 0 877 675,keepaspectratio=true]{./fmmd_uml2.jpg}
+ % fmmd_uml2.jpg: 877x675 pixel, 72dpi, 30.94x23.81 cm, bb=0 0 877 675
+ \caption{UML Representation of Failure Mode Data Types}
  \label{fig:fmmd_uml2}
 \end{figure}
+% 
+% \begin{figure}[h]
+%  \centering
+%  \includegraphics[width=350pt,bb=0 0 680 500,keepaspectratio=true]{component_failure_modes_definition/fmmd_uml2.jpg}
+%  % fmmd_uml.jpg: 680x500 pixel, 72dpi, 23.99x17.64 cm, bb=0 0 680 500
+%  \caption{UML respresentation of Failure Mode Data types}
+%  \label{fig:fmmd_uml2}
+% \end{figure}
 
 
 \subsection{Unitary State Component Failure Mode sets}
@@ -181,7 +199,7 @@ Having a set of failure modes where $N$ modes could be active simultaneously
 would mean having to consider $2^N$ failure mode scenarios.
 % 
 Should a component be analysed and simultaneous failure mode cases exit,
-the combinations could be represented by a new failure modes, or
+the combinations could be represented by new failure modes, or
 the component should be considered from a fresh perspective,
 perhaps considering it as several smaller components
 within one package.
@@ -239,7 +257,7 @@ 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}
-
+%\paragraph{NOT WRITTEN YET PLEASE IGNORE}
 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).
@@ -254,6 +272,7 @@ is therefore
 $$ F = \Omega(K) \backslash OK $$
 
 \subsection{Bayes Theorem}
+ \paragraph{NOT WRITTEN YET PLEASE IGNORE}
 \label{bayes}
 Describe application - likely hood of faults being the cause of symptoms -
 probablistic approach - no direct causation paths to the higher~abstraction fault mode.
@@ -271,6 +290,7 @@ to
 %unitary~state set family.
 
 \subsection{Tests of Hypotheses and Significance}
+\paragraph{NOT WRITTEN YET PLEASE IGNORE}
 Linked in with Bayes theorem
 Accident analysis
 plane crashes and faults etc