OK Appendix B AF notes, then........ well its cosmetic time I hope

submission_thesis/CH2_FMEA/copy.tex

@@ -979,7 +979,7 @@ deduced).
 
 
 
-\paragraph{Reasoning distance.}
+\subsection{Reasoning distance.}
 \label{reasoningdistance}
 \fmmdglossRD
 Reasoning distance,   is the number of stages of logic and reasoning used

submission_thesis/CH5_Examples/copy.tex

@@ -2192,46 +2192,46 @@ This cuts the supply from Vcc. Both sense lines will be at zero.
 Thus both values will be out of range.
 %
 %
-\paragraph{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN } 
+\paragraph{ TC 9 : Voltages $R_1$ OPEN $R_3$ OPEN.} 
 %
 Sense- will be floating.
 Sense+ will be tied to Vcc and will thus be out of range.
 %
-\paragraph{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT } 
+\paragraph{ TC 10 : Voltages $R_1$ OPEN $R_3$ SHORT.} 
 %
 This shorts ground to
 both of the sense lines.
 Both values will be  out of range.
 %
-\paragraph{ TC 11 : Voltages $R_1$ SHORT $R_2$ OPEN } 
+\paragraph{ TC 11 : Voltages $R_1$ SHORT $R_2$ OPEN.} 
 %
 This shorts both sense lines to Vcc.
 Both values will be out of range.
 %
 %
-\paragraph{ TC 12 : Voltages $R_1$ SHORT $R_2$ SHORT }
+\paragraph{ TC 12 : Voltages $R_1$ SHORT $R_2$ SHORT.}
 %
 This shorts the sense+ to Vcc and the sense- to ground.
 Both values will be out of range.
 %
 %
-\paragraph{ TC 13 : Voltages $R_1$ SHORT $R_3$ OPEN }
+\paragraph{ TC 13 : Voltages $R_1$ SHORT $R_3$ OPEN.}
 %
 This shorts the sense+ to Vcc and the sense- to ground.
 Both values will be out of range.
 %
-\paragraph{ TC 14 : Voltages $R_1$ SHORT $R_3$ SHORT }
+\paragraph{ TC 14 : Voltages $R_1$ SHORT $R_3$ SHORT.}
 %
 This shorts the sense+ and sense- to Vcc.
 Both values will be out of range.
 %
-\paragraph{ TC 15 : Voltages $R_2$ OPEN $R_3$ OPEN }
+\paragraph{ TC 15 : Voltages $R_2$ OPEN $R_3$ OPEN.}
 %
 This shorts the sense+ to Vcc and causes sense- to float.
 The sense+ value will be out of range.
 %
 %
-\paragraph{ TC 16 : Voltages $R_2$ OPEN $R_3$ SHORT }
+\paragraph{ TC 16 : Voltages $R_2$ OPEN $R_3$ SHORT.}
 %
 This shorts the sense+ and sense- to Vcc.
 Both values will be out of range.
@@ -2240,13 +2240,13 @@ Both values will be out of range.
 %
 %
 %
-\paragraph{ TC 17 : Voltages $R_2$ SHORT $R_3$ OPEN }
+\paragraph{ TC 17 : Voltages $R_2$ SHORT $R_3$ OPEN.}
 %
 This shorts the sense- to ground.
 The sense- value will be out of range.
 %
 %
-\paragraph{ TC 18 : Voltages $R_2$ SHORT $R_3$ SHORT }
+\paragraph{ TC 18 : Voltages $R_2$ SHORT $R_3$ SHORT.}
 %
 This shorts the sense+ and sense- to Vcc.
 Both values will be out of range.

submission_thesis/CH7_Evaluation/copy.tex

@@ -8,7 +8,8 @@ This chapter defines %begins by defining
 a metric for  the complexity of an FMEA analysis task.
 %
 This  concept is called `comparison~complexity' and is a means to assess
-the performance of FMMD against current FMEA methodologies. 
+the performance of FMMD against current FMEA methodologies. This
+concept was introduced as reasoning distance in section~\ref{reasoningdistance}.
 \fmmdglossRD
 %
 This metric is developed using set theory % formally 
@@ -35,7 +36,7 @@ the cardinality constrained power-set.
 %
 Using this in combination with unitary state failure modes
 an expression for calculating the number of failure scenarios to
-check for in double failure analysis is expressed.
+check for in double failure analysis is presented.
 %
 % MOVE TO CH5 FMMD makes the claim that it can perform double simultaneous failure mode analysis without an undue
 % MOVE TO CH5 state explosion drawback.
@@ -126,7 +127,8 @@ The number of checks  to make to achieve this, gives an indication of the comple
 %It is desirable to be able to measure the complexity of an analysis task.
 %
 Comparison~complexity (or reasoning~distance) is defined as the count  of 
-paths between failure modes and components necessary to achieve {\XFMEA} for a given group 
+paths (and thus reasoning checks applied) between failure modes and components 
+necessary to achieve {\XFMEA} for a given group 
 of components $G$. %system or {\fg}.
 
 % (except its self of course, that component is already considered to be in a failed state!).
@@ -236,7 +238,7 @@ i.e. at the zeroth level of an FMMD hierarchy where $\alpha=0$,
 would have the superscript 0 and a subscript of 1: $FG^{0}_{1}$.
 %
 The {\fg} representing the potential divider in section~\ref{subsec:potdiv}
-has an $\alpha$ level of 0 (as it contains base components). 
+has an $\alpha$ level of 0 (as it contains only {\bcs}). 
 %
 The {\fg} with the potential divider and the operational amplifier has an $\alpha$ level of 1.
 %$$
@@ -968,7 +970,7 @@ are not included.
 %
 This threshold is called the cardinality constraint.
 %
-To indicate this, the cardinality constraint $\le cc$ is subscripted to the powerset symbol thus $\mathcal{P}_{\le cc}$.
+To indicate this, the cardinality constraint $\le cc$ is subscripted to the power-set symbol thus $\mathcal{P}_{\le cc}$.
 Consider the set $S = \{a,b,c\}$. 
 
 The power-set of S: 
@@ -1009,7 +1011,7 @@ from $1$ to $cc$ thus
 %
 %
 \begin{equation}
- |{\mathcal{P}_{cc}S}| = \sum^{cc}_{k=1} \frac{|{S}|!}{ cc! ( |{S}| - cc)!} . % was k in the frac part now cc
+ |{\mathcal{P}_{\le cc}S}| = \sum^{cc}_{k=1} \frac{|{S}|!}{ cc! ( |{S}| - cc)!} . % was k in the frac part now cc
  \label{eqn:ccps}
 \end{equation} 
 %
@@ -1059,8 +1061,8 @@ applying equation \ref{eqn:ccps} gives:
 %
 $$ | P_{\le 2} (fm(FG)) |  = \frac{5!}{1!(5-1)!} + \frac{5!}{2!(5-2)!}  = 15.$$
 %
-This is composed of ${5 \choose 1}$
-five single fault modes, and ${5 \choose 2}$ ten double fault modes.
+This is composed of ${5 \choose 1}$,
+five single fault modes, and ${5 \choose 2}$, ten double fault modes.
 %
 However the {\fms} are mutually exclusive within a component.
 %
@@ -1183,7 +1185,7 @@ reproduced below to verify this.
 {
 \begin{equation}
  |{\mathcal{P}_{\le cc}SU}| = {\sum^{cc}_{k=1}  \frac{|{SU}|!}{k!(|{SU}| - k)!}}
-- {{\sum^{j}_{j \in J}   \frac{|FM({C_j})|!}{2!(|FM({C_j})| - 2)!}}  } .
+- {{\sum_{j \in J}   \frac{|FM({C_j})|!}{2!(|FM({C_j})| - 2)!}}  } .
  %\label{eqn:correctedccps2}
 \end{equation}
 }
@@ -1452,14 +1454,16 @@ of functional groups. These are:
 \end{itemize}
 %
 If a deliberately `bad' {\fg} were chosen it would be found that,
-on analysis, the component failure modes would not converge to common 
+on analysis, the component failure modes would not aggregate--i.e. be collectable as---common
 symptoms. 
 %
-This would be because, with functionally adjacent
-components, their failures often cause non-common failure symptoms for the {\fg}.
+This would be because, with non-functionally adjacent
+components, their failures often cause non-common failure symptoms. % for the {\fg}.
 %
-With components that are not interacting, it is unlikely to see 
-convergence of symptoms.
+That is a well defined  module will typically have a larger number of component failures than failure symptoms.
+%
+With components that are not interacting, it is unlikely to see good
+aggregation of symptoms.
 %
 %
 This property could be of use in future automated FMMD tools