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

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Robin Clark 2013-09-18 11:19:21 +01:00
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2
submission_thesis/CH2_FMEA/copy.tex
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@ -979,7 +979,7 @@ deduced).
\paragraph{Reasoning distance.} \subsection{Reasoning distance.}
\label{reasoningdistance} \label{reasoningdistance}
\fmmdglossRD \fmmdglossRD
Reasoning distance, is the number of stages of logic and reasoning used Reasoning distance, is the number of stages of logic and reasoning used

20
submission_thesis/CH5_Examples/copy.tex
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@ -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. 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 floating.
Sense+ will be tied to Vcc and will thus be out of range. 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 This shorts ground to
both of the sense lines. both of the sense lines.
Both values will be out of range. 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. This shorts both sense lines to Vcc.
Both values will be out of range. 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. This shorts the sense+ to Vcc and the sense- to ground.
Both values will be out of range. 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. This shorts the sense+ to Vcc and the sense- to ground.
Both values will be out of range. 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. This shorts the sense+ and sense- to Vcc.
Both values will be out of range. 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. This shorts the sense+ to Vcc and causes sense- to float.
The sense+ value will be out of range. 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. This shorts the sense+ and sense- to Vcc.
Both values will be out of range. 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. This shorts the sense- to ground.
The sense- value will be out of range. 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. This shorts the sense+ and sense- to Vcc.
Both values will be out of range. Both values will be out of range.

32
submission_thesis/CH7_Evaluation/copy.tex
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@ -8,7 +8,8 @@ This chapter defines %begins by defining
a metric for the complexity of an FMEA analysis task. a metric for the complexity of an FMEA analysis task.
% %
This concept is called `comparison~complexity' and is a means to assess 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 \fmmdglossRD
% %
This metric is developed using set theory % formally 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 Using this in combination with unitary state failure modes
an expression for calculating the number of failure scenarios to 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 FMMD makes the claim that it can perform double simultaneous failure mode analysis without an undue
% MOVE TO CH5 state explosion drawback. % 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. %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 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}. of components $G$. %system or {\fg}.
% (except its self of course, that component is already considered to be in a failed state!). % (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: $FG^{0}_{1}$. would have the superscript 0 and a subscript of 1: $FG^{0}_{1}$.
% %
The {\fg} representing the potential divider in section~\ref{subsec:potdiv} 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. 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. 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 $S = \{a,b,c\}$. Consider the set $S = \{a,b,c\}$.
The power-set of S: The power-set of S:
@ -1009,7 +1011,7 @@ from $1$ to $cc$ thus
% %
% %
\begin{equation} \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} \label{eqn:ccps}
\end{equation} \end{equation}
% %
@ -1059,8 +1061,8 @@ applying equation \ref{eqn:ccps} gives:
% %
$$ | P_{\le 2} (fm(FG)) | = \frac{5!}{1!(5-1)!} + \frac{5!}{2!(5-2)!} = 15.$$ $$ | P_{\le 2} (fm(FG)) | = \frac{5!}{1!(5-1)!} + \frac{5!}{2!(5-2)!} = 15.$$
% %
This is composed of ${5 \choose 1}$ This is composed of ${5 \choose 1}$,
five single fault modes, and ${5 \choose 2}$ ten double fault modes. five single fault modes, and ${5 \choose 2}$, ten double fault modes.
% %
However the {\fms} are mutually exclusive within a component. However the {\fms} are mutually exclusive within a component.
% %
@ -1183,7 +1185,7 @@ reproduced below to verify this.
{ {
\begin{equation} \begin{equation}
|{\mathcal{P}_{\le cc}SU}| = {\sum^{cc}_{k=1} \frac{|{SU}|!}{k!(|{SU}| - k)!}} |{\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} %\label{eqn:correctedccps2}
\end{equation} \end{equation}
} }
@ -1452,14 +1454,16 @@ of functional groups. These are:
\end{itemize} \end{itemize}
% %
If a deliberately `bad' {\fg} were chosen it would be found that, 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. symptoms.
% %
This would be because, with functionally adjacent This would be because, with non-functionally adjacent
components, their failures often cause non-common failure symptoms for the {\fg}. components, their failures often cause non-common failure symptoms. % for the {\fg}.
% %
With components that are not interacting, it is unlikely to see That is a well defined module will typically have a larger number of component failures than failure symptoms.
convergence of 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 This property could be of use in future automated FMMD tools