diff --git a/fmmd_concept/System_safety_2011/submission.tex b/fmmd_concept/System_safety_2011/submission.tex
index 615005a..add52b9 100644
--- a/fmmd_concept/System_safety_2011/submission.tex
+++ b/fmmd_concept/System_safety_2011/submission.tex
@@ -65,8 +65,8 @@ failure mode of the component or sub-system}}}
 \abstract{
 The certification process of safety critical products for European and 
 other international standards often involve environmental stress, 
-endurance and EMC testing. Theoretical, or 'static testing',
-is often also required to highlight modifications that must be made to
+endurance and Electro Magnetic Compatibility (EMC) testing. Theoretical, or 'static testing',
+is often also required. In general this will reveal modifications that must be made to
 improve the product safety, or identify theoretical weaknesses in the design.
 This paper proposes a new theoretical methodology for creating failure mode models of safety critical systems.
 It has a common notation for mechanical, electronic and software domains and is modular and hierarchical.
@@ -158,7 +158,7 @@ via self checking statistical mitigation.
 
 \paragraph{Top Down approach} The top down technique FTA, introduces the possibility of missing base component
 level failure modes~\cite{faa}[Ch.9]. Also one FTA treee is drawn for each top level
-event, leading to repreated work, with limitied ability for cross checking.
+event, leading to repreated work, with limitied ability for cross checking/model validation.
 
 \paragraph{State Explosion problem}
 The bottom -up techniques all suffer from a problem of state explosion.
@@ -187,11 +187,22 @@ To look in detail at a half of a million test cases is obviously impractical.
 % current methodologies are used to establish criteria for an improved methodology.
 
 \paragraph{Reasoning distance - complexity and reachability}
-Tracing a component level failure up to a top level event, without rigour involving state explosion, involves
-working heuistically. A base component failure will typically 
-be concepually removed by several stages from a top level event.
-The reasoning distance can be determined by the number of components
+Tracing a component level failure up to a top level event, without the rigour accompanying state explosion, involves
+working heuristically. A base component failure will typically 
+be conceptually removed by several stages from a top level event.
+The `reasoning~distance' $R_D$ can be calculated by summing the number of components
+involved, multiplied by the number of failure modes in each component,
 that must interact to reach the top level event.
+Where $C$ represents the set of components in a failure mode causation chain,
+$c$ represents a component and
+the function $fn$ returns the number of failure modes for a given component, equation
+\ref{eqn:complexity}, returns a value representing the complexity
+from the base component failure to the SYSTEM level event.
+\begin{equation}
+R_D = \sum_{i=1}^{|C|} {fn(c)}  %\; where \; c \in C
+\label{eqn:complexity} 
+\end{equation}
+
 % could have a chapter on this.
 % take a circuit or system and follow all the interactions
 % to the components that cause the system level event.
@@ -202,21 +213,24 @@ SYSTEM level failure mode.
 It could be possible to identify one top level event asssociated with
 a {\bcfm} and not investigate other possibilities. 
  
-\section{Requirements for a new static faiilure mode Analysis methodology}
+\section{Requirements for a new static failure mode Analysis methodology}
 
 A new methodology must ensure that it represents all component failure modes and it therefore should be bottom-up, 
 starting with individual component failure modes. 
 
 In order to control the state explosion problem, the process must be modular
-and deal with small groups of components.
+and deal with small groups of components. The design process follows this 
+rationale, sub-systems are build to perform often basic functions from base components.
+We can term these small groups {\fgs}.
 
-
-Components should be broken 
-down into small functional groups to enable the examination of the effect of a
+Components should be collected
+into small functional groups to enable the examination of the effect of a
 component failure mode on the other components in the group.
-The functional group can now be considered as `derived component' with a known set 
+Once we have the failure modes, or symptoms of failure of a {\fg}
+it can now be considered as `derived component' with a known set 
 of failure symptoms. We can use this `derived component' to build higher level 
 functional groups.
+
 This helps with the reasoning distance problem,
 because we can trace failure modes back through complex interactions and have a structure to
 base our reasoning on, at each stage.