diff --git a/submission_thesis/CH2_FMEA/copy.tex b/submission_thesis/CH2_FMEA/copy.tex index 5bca417..9c2e7f8 100644 --- a/submission_thesis/CH2_FMEA/copy.tex +++ b/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 diff --git a/submission_thesis/CH5_Examples/copy.tex b/submission_thesis/CH5_Examples/copy.tex index 7b8d365..2d653dc 100644 --- a/submission_thesis/CH5_Examples/copy.tex +++ b/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. diff --git a/submission_thesis/CH7_Evaluation/copy.tex b/submission_thesis/CH7_Evaluation/copy.tex index eb3c98c..e124267 100644 --- a/submission_thesis/CH7_Evaluation/copy.tex +++ b/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