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Go through Chris Garret CH6 note
First half CH7 notes, and remove allot of formal defs from CH7
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Robin Clark 2013-03-09 17:05:48 +00:00
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55
submission_thesis/CH2_FMEA/copy.tex
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@ -223,6 +223,12 @@ i.e.
\label{ros}
$$ fm(R) = \{ OPEN, SHORT \} . $$
%
% Mention tolerance here
%
% hmmmmmm
%
\subsection{Failure modes determination for generic operational amplifier}
\begin{figure}[h+]
@ -387,6 +393,10 @@ The EN298 pinouts failure mode technique cannot reveal failure modes due to inte
The FMD-91 entries for op-amps are not directly usable as
component {\fms} in FMEA or FMMD and require interpretation.
%For our OpAmp example could have come up with different symptoms for both sides. Cannot predict the effect of internal errors, for instance ($LOW_{slew}$)
%is missing from the EN298 failure modes set.
@ -569,12 +579,21 @@ get a balance between subjective and objective perspectives.
%for the the results of an FMEA line of reasoning.
\paragraph{Failure modes, observability criterion: detectable and undetectable.}
Often the effects of a failure mode may be easy to detect, and our equipment can react by raising an alarm or compensating for the resulting fault.
Some failure modes may cause undetectable failure, for instance a component that causes
a measured reading to change could have dire consequences yet not be obvious.
In fault diagnosis failures are said to be observable and unobservable~\cite{721666, ACS:ACS1297}.
\glossary{name={observability}, description={The property of a system failure in relation to a particular component failure mode, where it can bedetermined whether the readings/actions associated     with it are valid, or the by-product of a failure. If we cannot determine that there is a fault present, the system level failure is said to be unobservable.}}
\paragraph{Failure modes and their observability criterion: detectable and undetectable.}
Often the effects of a failure mode may be easy to detect,
and our equipment can react by raising an alarm or compensating for the resulting fault.
%
Some failure modes may cause undetectable failures, for instance a component that causes
a measured reading to change could have adverse consequences yet not be flagged as a failure.
This type of failure would not be flagged as a failure by the system, because
it has no way of knowing the reading is invalid.
%
The term observable has a specific meaning in the field of control engineering~\cite{721666, ACS:ACS1297};
systems submitted for FMEA are generally related to control systems,
and so to avoid confusion the terms `detectable' and `undetectable'
will be used for describing the observability of failure modes in this document.
\glossary{name={observability}, description={The property of a system failure in relation to a particular component failure mode, where it can be determined whether the readings/actions associated     with it are valid, or the by-product of a failure. If we cannot determine that there is a fault present, the system level failure is said to be unobservable.}}
\paragraph{Impracticality of Field Data for modern systems.}
@ -629,12 +648,12 @@ would give a reasoning distance of 3 * 100 * 99.
%{sfmeaforwardbackward}
\subsection{FMEA and the State Explosion Problem}
\paragraph{Rigorous Single Failure FMEA.}
\paragraph{Exhaustive Single Failure FMEA.}
FMEA for a safety critical certification~\cite{en298,en61508} will have to be applied
to all known failure modes of all components within a system.
To perform FMEA rigorously (i.e. to examine every possible interaction
To perform FMEA exhaustively (i.e. to examine every possible interaction
of a failure mode with all other components in a system). Or in other words,
---we would need to look at all possible failure scenarios.
%to do this completely (all failure modes against all components).
@ -650,13 +669,13 @@ $f$ is the number of failure modes per component.
\end{equation}
\paragraph{Rigorous Single Failure FMEA}
\paragraph{Exhaustive Single Failure FMEA}
This would mean an order of $O(N^2)$ number of checks to perform
to undertake a `rigorous~FMEA'. Even small systems have typically
to undertake an `exhaustive~FMEA'. Even small systems have typically
100 components, and they typically have 3 or more failure modes each.
$100*99*3=29,700$.
\paragraph{Rigorous Double Failure FMEA}
\paragraph{Exhaustive Double Failure FMEA}
For looking at potential double failure
scenarios\footnote{Certain double failure scenarios are already legal requirements---The European Gas burner standard (EN298:2003)---demands the checking of
double failure scenarios (for burner lock-out scenarios).}
@ -673,19 +692,25 @@ $100*99*98*3=2,910,600$ failure mode scenarios.
\paragraph{Reliance of experts for meaningful FMEA Analysis.}
Current FMEA methodologies cannot consider---for practical reasons---a rigorous approach.
We define rigorous FMEA as examining the effect of every component failure mode
Current FMEA methodologies cannot consider---for the reason of state explosion---an exhaustive approach.
We define exhaustive FMEA ({\XFMEA}) as examining the effect of every component failure mode
against the remaining components in the system under investigation.
%
Because we cannot perform rigorous FMEA,
Because we cannot perform XFMEA,
we rely on experts in the system under investigation
to perform a meaningful FMEA analysis.
%
In practise these experts have to select the areas they see as most critical for detailed FMEA analysis.
\subsection{Component Tolerance}
Component tolerances may need considered when determining if a component has failed.
Calculations for acceptable ranges to determine failure or acceptable conditions
must be made where appropriate.
An example of component tolerance considered for FMEA
is given in section~\ref{sec:resistortolerance}.
\section{FMEA in practise: Five variants}
\section{FMEA in current usage: Five variants}
\paragraph{Five main Variants of FMEA}
\begin{itemize}

24
submission_thesis/CH3_FMEA_criticism/copy.tex
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@ -35,15 +35,28 @@ This problem is compounded by the fact that traditional FMEA cannot integrate so
Traditional FMEA cannot ensure that each failure mode of all its
components are checked against any other components in the system which
it may affect, due to state explosion.
%
FMEA is therefore performed using heuristics to decide
which components to check the effect of a component failure mode on.
We could term the number of checks made for each failure mode
on aspects of the system to be the reasoning distance.
%
In practise FMEA may be performed by following the signal path
of the component failure mode to its system level effect. This is less than ideal
and it can easily miss interactions with adjacent components, that could cause
other system level symptoms.
%
Were we to compare the reasoning distance with the theoretical maximum, the sum of all failure
modes in a system, multiplied by the number of components in it, we could arrive at a comparison complexity figure.
This figure would mean we could compare the maximum number of checks (i.e. rigorous analysis)
with the number actually performed.
This figure would mean we could compare the maximum number of checks (i.e. exhaustive%rigorous
analysis) with the number actually performed.
\paragraph{The ideal of exhaustive FMEA (XFMEA)}
Obviously, exhaustively checking every component failure mode in a system,
against all other components is the ideal for finding all possible system level failures.
While this is impossible for all but trivial systems, it should be possible
for small groups of components that work together to provide a well defined function.
We could term such a group a `{\fg}'.
\section{Re-use of FMEA analysis}
@ -136,7 +149,8 @@ of the communications protocol used to transmit data, and the failure mode chara
of the communications physical layer.
%(figure~\ref{fig:distcon}
The failure reasoning paths for a distributed real time system, mean traditional FMEA
The failure reasoning paths for a distributed real time system, with its multiple passes of the hardware/software
interface mean traditional FMEA, for these systems,
is impossible to perform.
%
The base component failure mode to system failure paradigm is
@ -163,11 +177,11 @@ utterly anachronistic in the distributed real time system environment.
\begin{itemize}
\item FMEA type methodologies were designed for simple electro-mechanical systems of the 1940's to 1960's.
\item Reasoning Distance - component failure to system level symptom
\item State explosion - impossible to perform rigorously
\item State explosion - impossible to perform FMEA exhaustively %rigorously
\item Difficult to re-use previous analysis work
\item Very Difficult to model simultaneous failures.
\item Software and hardware models are separate.
\item Distributed real time systemsare very difficult to meaningfully analyse with FMEA.
\item Distributed real time systems are very difficult to meaningfully analyse with FMEA.
\end{itemize}
FMEA is no longer fit for purpose!

6
submission_thesis/CH4_FMMD/copy.tex
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@ -2207,9 +2207,9 @@ Ensuring this condition is described in section~\ref{sec:completetest}.
\paragraph{State explosion problem of FMEA solved by FMMD.}
%
Because FMMD considers failure modes within functional groups;
the traditional state explosion problem in FMEA where each failure
mode could be considered in the context of all other components in the system
disappears.
the traditional state explosion problem in FMEA where the ideal of exhaustive FMEA (XFMEA)---where each failure
mode could be considered in the context of all other components in the system---disappears.
FMMD applies XFMEA within {\fgs}.
%
This issue addressed formally in section~\ref{sec:cc}.

43
submission_thesis/CH5_Examples/copy.tex
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@ -2073,28 +2073,29 @@ Temperature range calculations and detailed calculations
on the effects of each test case are found in section \ref{Pt100range}
and \ref{Pt100temp}.
%\paragraph{Consideration of Resistor Tolerance}
%
%The separate sense lines ensure the voltage read over the Pt100 thermistor are not
%altered due to having to pass any significant current.
%The Pt100 element is a precision part and will be chosen for a specified accuracy/tolerance range.
%One or other of the load resistors (the one we measure current over) should also
%be of this accuracy.
%
%The \ohms{2k2} loading resistors may be ordinary, in that they would have a good temperature co-effecient
%(typically $\leq \; 50(ppm)\Delta R \propto \Delta \oc $), and should be subjected to
%a narrow temperature range anyway, being mounted on a PCB.
\paragraph{Consideration of Resistor Tolerance}
\label{sec:resistortolerance}
The separate sense lines ensure the voltage read over the Pt100 thermistor are not
altered due to having to pass any significant current.
The Pt100 element is a precision part and will be chosen for a specified accuracy/tolerance range.
One or other of the load resistors (the one we measure current over) should also
be of this accuracy.
The \ohms{2k2} loading resistors may be ordinary, in that they would have a good temperature co-effecient
(typically $\leq \; 50(ppm)\Delta R \propto \Delta \oc $), and should be subjected to
a narrow temperature range anyway, being mounted on a PCB.
%\glossary{{PCB}{Printed Circuit Board}}
%To calculate the resistance of the Pt100 element % (and thus derive its temperature),
%having the voltage over it, we now need the current.
%Lets use, for the sake of example $R_2$ to measure the current flowing in the temperature sensor loop.
%As the voltage over $R_3$ is relative (a design feature to eliminate resistance effects of the cables).
%We can calculate the current by reading
%the voltage over the known resistor $R2$.\footnote{To calculate the resistance of the Pt100 we need the current flowing though it.
%We can determine this via ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$,
%and then using $I$, we can calculate $R_{3} = \frac{V_{R3}}{I}$.}
%As these calculations are performed by ohms law, which is linear, the accuracy of the reading
%will be determined by the accuracy of $R_2$ and $R_{3}$. It is reasonable to
To calculate the resistance of the Pt100 element % (and thus derive its temperature),
having the voltage over it, we now need the current.
Lets use, for the sake of example $R_2$ to measure the current flowing in the temperature sensor loop.
As the voltage over $R_3$ is relative (a design feature to eliminate resistance effects of the cables).
We can calculate the current by reading
the voltage over the known resistor $R2$.\footnote{To calculate the resistance of the Pt100 we need the current flowing though it.
We can determine this via ohms law applied to $R_2$, $V=IR$, $I=\frac{V}{R_2}$,
and then using $I$, we can calculate $R_{3} = \frac{V_{R3}}{I}$.}
As these calculations are performed by ohms law, which is linear, the accuracy of the reading
will be determined by the accuracy of $R_2$ and $R_{3}$.
%It is reasonable to
%take the mean square error of these accuracy figures.
\paragraph{Range and $Pt100$ Calculations}

108
submission_thesis/CH6_Evaluation/copy.tex
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@ -15,7 +15,7 @@ complexity of applying FMEA to a group of components.
%
These formulae are then used for a hypothetical example, which is analysed by both FMEA and FMMD.
After analysing hypothetical examples, the FMMD examples from chapter~\ref{sec:chap5} are
compared against RFMEA.
compared against {\XFMEA}.
%
Following on from the formal definitions, `unitary state failure modes' are defined. In short these
ensure that component failure modes are mutually exclusive. % Using the unitary state failure mode definition
@ -93,14 +93,14 @@ side effects of failure may manifest due interaction with other components not o
The temptation with FMEA can be to follow direct lines of failure effect reasoning without considering
side effects.
%%
To perform FMEA rigorously
To perform FMEA exhaustively % rigorously
we could stipulate that every failure mode must be checked for effects
against all the components in the system.
%
This would mean we would be %looking
examining for all possible side effects that a base component failure could cause.
%
We could term this `rigorous~FMEA'~(RFMEA).
We could term this `exhaustive~FMEA'~({\XFMEA}).
The number of checks we have to make to achieve this, gives an indication of the complexity of the analysis task.
%
%This is described in section~\ref{sec:rd}, where the reasoning distance, or complexity to
@ -110,7 +110,7 @@ The number of checks we have to make to achieve this, gives an indication of the
%It is desirable to be able to measure the complexity of an analysis task.
%
We define comparison~complexity as the count of
paths between failure modes and components necessary to achieve RFMEA for a given group
paths 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!).
@ -145,11 +145,12 @@ we can represent the number of potential failure modes of a component $c$, to be
\paragraph{Indexing components with the group $G$.}
If we index all the components in the system under investigation $ c_1, c_2 \ldots c_{|G|} $ we can express
the number of checks required to rigorously examine every
the number of checks required to exhaustively % rigorously
examine every
failure mode against all the other components in a system.
%
Comparison Complexity can be represented by a function $CC$, with its domain as $G$, and
its range as the number of checks---or reasoning stages---to perform to satisfy a rigorous FMEA inspection.
its range as the number of checks---or reasoning stages---to perform to satisfy an XFMEA inspection.
Where $\mathcal{G}$ represents the set of all {\fgs} %, and $ \mathbb{Z}^{+} $,
$CC$ is defined by,
@ -244,7 +245,7 @@ We combine the potential divider with an op-amp which has four failure modes
to form a {\fg} with two components, one with four failure modes and the other (the potential divider) with two.
$$CC(invamp) = 2 \times 1 + 4 \times 1 = 6 $$
To analyse the inverting amplifier with FMMD we required 10 reasoning stages.
Using RFMEA we obtain $ 2 \times (3-1) + 2 \times (3-1) + 4 \times (3-1)$ = 16.
Using {\XFMEA} we obtain $ 2 \times (3-1) + 2 \times (3-1) + 4 \times (3-1)$ = 16.
\paragraph{Complexity Comparison for an hypothetical 81 component system.}
%Even considering a $example$
@ -254,22 +255,24 @@ having 3 failure modes each) we would have an $CC$ of
$$CC(example) = \sum_{n=1}^{81} |3|.(|80|) = 19440 .$$
Ensuring all component failure modes are checked against all other components in a system
-- applying FMEA rigorously -- could be termed
Rigorous FMEA (RFMEA).
The computational order for RFMEA would be polynomial ($O(N^2.K)$) (where $K$ is the variable number of failure modes).
-- applying FMEA exhaustively
%rigorously
-- could be termed
exhaustive FMEA ({\XFMEA}).
The computational order for {\XFMEA} would be polynomial ($O(N^2.K)$) (where $K$ is the variable number of failure modes).
%
This order may be acceptable in a computational environment. However, the choosing of {\fgs} and the analysis
process are by-hand/human activities. It can be seen that it is practically impossible to achieve
RFMEA for anything but trivial systems.
{\XFMEA} for anything but trivial systems.
%
% Next statement needs alot of justification
%
It is the author's belief that FMMD reduces the comparison complexity enough to make
rigorous checking feasible.
exhaustive checking (within {\fgs}) entirely feasible.
\pagebreak[4]
%\subsection{Using the concept of Complexity Comparison to compare RFMEA with FMMD}
%\subsection{Using the concept of Complexity Comparison to compare {\XFMEA} with FMMD}
% \begin{figure}
% \centering
@ -288,16 +291,16 @@ rigorous checking feasible.
\end{figure}
\subsection{Comparing FMMD and RFMEA comparison complexity}
\subsection{Comparing FMMD and {\XFMEA} comparison complexity}
Because components have variable numbers of failure modes,
and {\fgs} have variable numbers of components, it is difficult to
use the general formula for comparing the number of checks to make for
RFMEA and FMMD.
{\XFMEA} and FMMD.
%
If we were to create an example by fixing the number of components in a {\fg}
and the number of failure modes per component, we can derive formulae
to compare the number of checks to make from an FMMD hierarchy to RFMEA applied to
to compare the number of checks to make from an FMMD hierarchy to {\XFMEA} applied to
all components in a system.
Consider $k$ to be the number of components in a {\fg} (i.e. $k=|{\FG}|$),
@ -312,16 +315,16 @@ with equation~\ref{eqn:anscen}.
\end{equation}
The thinking behind equation~\ref{eqn:anscen}, is that for each level of analysis -- counting down from the top --
there are ${k}^{n}$ {\fgs} within each level; we need to apply RFMEA to each {\fg} on the level.
there are ${k}^{n}$ {\fgs} within each level; we need to apply {\XFMEA} to each {\fg} on the level.
%
The number of checks to make for RFMEA, is the number of components $k$ multiplied by the number of failure modes $f$
The number of checks to make for {\XFMEA}, is the number of components $k$ multiplied by the number of failure modes $f$
checked against the remaining components in the {\fg} $(k-1)$.
%
If, for the sake of example, we fix the number of components in a {\fg} to three and
the number of failure modes per component to three, an FMMD hierarchy
would look like figure~\ref{fig:three_tree}.
\subsection{RFMEA FMMD Comparison Example}
\subsection{{\XFMEA} FMMD Comparison Example}
Using the diagram in figure~\ref{fig:three_tree}, we have three levels of analysis.
%
@ -334,17 +337,17 @@ On the level below that, we have three {\fgs} each with
an identical number of checks, $3^1 \times 3 \times 2 \times 3 = 56$. %{\fg}
%
On the level below that we have nine {\fgs}, $3^2 \times 3\times2\times3=168$.
Adding these together gives $242$ checks to make to perform FMMD (i.e. RFMEA {\em{within the}}
Adding these together gives $242$ checks to make to perform FMMD (i.e. {\XFMEA} {\em{within the}}
{\fgs}).
If we were to take the system represented in figure~\ref{fig:three_tree}, and
apply RFMEA on it as a whole system, we can use equation~\ref{eqn:CC},
apply {\XFMEA} on it as a whole system, we can use equation~\ref{eqn:CC},
$CC(G) = \sum_{n=1}^{|G|} |fm(c_n)|.(|G|-1)$, where $|G|$ is 27, $fm(c_n)$ is 3
and $(|G|-1)$ is 26.
This gives:
$CC(G) = \sum_{n=1}^{27} |3|.(|27|-1) = 2106$.
In order to get general equations with which to compare RFMEA with FMMD,
In order to get general equations with which to compare {\XFMEA} with FMMD,
we can re-write equation~\ref{eqn:CC} in terms of the number of levels
in an FMMD hierarchy.
%
@ -367,8 +370,8 @@ or
%(N^2 - N).f
\end{equation}
We can now use equation~\ref{eqn:anscen} (FMMD) and \ref{eqn:CC} (RFMEA) to compare (for fixed sizes of $|G|$ and $|fm(c)|$)
the two approaches, for the work required to perform rigorous checking.
We can now use equation~\ref{eqn:anscen} (FMMD) and \ref{eqn:CC} ({\XFMEA}) to compare (for fixed sizes of $|G|$ and $|fm(c)|$)
the two approaches, for the work required to perform exhaustive checking.
For instance, having four levels
@ -396,11 +399,11 @@ $$
All the FMMD examples in chapters \ref{sec:chap5}
and \ref{sec:chap6} showed a marked reduction in comparison
complexity compared to the RFMEA worst case figures.
To calculate RFMEA comparison complexity equation~\ref{eqn:CC} is used.
complexity compared to the {\XFMEA} worst case figures.
To calculate {\XFMEA} comparison complexity equation~\ref{eqn:CC} is used.
%
%
Complexity comparison vs. RFMEA for the first three examples
Complexity comparison vs. {\XFMEA} for the first three examples
are presented in table~\ref{tbl:firstcc}.
%
%\usepackage{multirow}
@ -413,7 +416,7 @@ are presented in table~\ref{tbl:firstcc}.
\textbf{Level} & \textbf{Component} & \textbf{Comparison} & \textbf{of derived} \\
& & & \textbf{failure modes} \\
%\hline \hline
%\multicolumn{3}{ |c| }{Complexity Comparison against RFMEA for examples in Chapter~\ref{sec:chap5}} \\
%\multicolumn{3}{ |c| }{Complexity Comparison against {\XFMEA} for examples in Chapter~\ref{sec:chap5}} \\
%\hline \hline
@ -427,14 +430,14 @@ are presented in table~\ref{tbl:firstcc}.
0 & PD & 4 & 2 \\
1 & INVAMP & 8 & 3 \\
2 & Total for INVAMP: & 10 (FMMD) & \\
0 & Total for INVAMP: & 16 (RFMEA) & \\
0 & Total for INVAMP: & 16 ({\XFMEA}) & \\
% & $(3-1) \times (4 + 2 +2)$ & & \\
\hline \hline
\multicolumn{3}{ |c| } {Inverting Amplifier One stage FMMD Hierarchy: section~\ref{sec:invamp}} \\ \hline
0 & INVAMP & 16 & 3 \\
1 & Total for INVAMP: & 16 (FMMD) & \\
0 & Total for INVAMP: & 16 (RFMEA) & \\
0 & Total for INVAMP: & 16 ({\XFMEA}) & \\
\hline
\hline
@ -444,8 +447,8 @@ are presented in table~\ref{tbl:firstcc}.
0 & SEC\_AMP & 16 & 4 \\
3 & DiffAMP & 7 & 4 \\
3 & Total for DiffAMP & 33 (FMMD)& \\
0 & Total for DiffAMP: & 80 (RFMEA) & \\
% & Differencing Amplifier: & RFMEA 80-16 = 74 & \\
0 & Total for DiffAMP: & 80 ({\XFMEA}) & \\
% & Differencing Amplifier: & {\XFMEA} 80-16 = 74 & \\
% & & & \\
\hline
\hline
@ -459,7 +462,7 @@ are presented in table~\ref{tbl:firstcc}.
3 & FivePoleLP & 20 & 4 \\
3 & Total for FivePoleLP & 82 (FMMD)& \\
% & 20+48+10+4 & & \\
0 & Total for FivePoleLP & 384 (RFMEA) & \\
0 & Total for FivePoleLP & 384 ({\XFMEA}) & \\
% & $(13-1) \times (3 \times 4 + 10 \times 2)$ & & \\ \hline
\hline
@ -470,7 +473,7 @@ are presented in table~\ref{tbl:firstcc}.
The complexity comparison figures for the example circuits in chapter~\ref{sec:chap5} show
that for the non trival examples, as we
use more levels in the FMMD hierarchy, the performance
gain over RFMEA becomes apparent. %for increasing complexity the performance benefits from FMMD are apparent.
gain over {\XFMEA} becomes apparent. %for increasing complexity the performance benefits from FMMD are apparent.
@ -481,7 +484,7 @@ The Bubba oscillator example (see section~\ref{sec:bubba}) was chosen because it
signal path. It was also analysed twice, once by
{na\"{\i}vely} using the first {\fgs} identified, and secondly by de-composing
the circuit further.
We use these two analyses to compare the effect on comparison complexity (see table~\ref{tbl:bubbacc}) with that of RFMEA.
We use these two analyses to compare the effect on comparison complexity (see table~\ref{tbl:bubbacc}) with that of {\XFMEA}.
%
\begin{table}
\label{tbl:bubbacc}
@ -493,7 +496,7 @@ We use these two analyses to compare the effect on comparison complexity (see ta
\textbf{Level} & \textbf{Component} & \textbf{Comparison} & \textbf{of derived} \\
& & & \textbf{failure modes} \\
%\hline \hline
%\multicolumn{3}{ |c| }{Complexity Comparison against RFMEA for examples in Chapter~\ref{sec:chap5}} \\
%\multicolumn{3}{ |c| }{Complexity Comparison against {\XFMEA} for examples in Chapter~\ref{sec:chap5}} \\
%\hline \hline
@ -516,7 +519,7 @@ We use these two analyses to compare the effect on comparison complexity (see ta
2 & Total for BUBBA: & 328 (FMMD) & \\
% R&C OPAMPS
% 14 components so 13 \times ( (10*2) (4*4) )
0 & Total for BUBBA: & 468 (RFMEA) & \\
0 & Total for BUBBA: & 468 ({\XFMEA}) & \\
% & $(3-1) \times (4 + 2 +2)$ & & \\
\hline \hline
@ -538,7 +541,7 @@ We use these two analyses to compare the effect on comparison complexity (see ta
%Level 4: 2 == 2
%
1 & Total for BUBBA: & 37 (FMMD) & \\
0 & Total for BUBBA: & 468 (RFMEA) & \\
0 & Total for BUBBA: & 468 ({\XFMEA}) & \\
\hline
\hline
@ -567,7 +570,7 @@ by more than a factor of ten.
\textbf{Level} & \textbf{Component} & \textbf{Comparison} & \textbf{of derived} \\
& & & \textbf{failure modes} \\
%\hline \hline
%\multicolumn{3}{ |c| }{Complexity Comparison against RFMEA for examples in Chapter~\ref{sec:chap5}} \\
%\multicolumn{3}{ |c| }{Complexity Comparison against {\XFMEA} for examples in Chapter~\ref{sec:chap5}} \\
%\hline \hline
@ -594,7 +597,7 @@ by more than a factor of ten.
2 & Total for {\sd}: & 55 (FMMD) & \\
% R&C OPAMPS
% 14 components so (10-1) *
0 & Total for {\sd}: & 225 (RFMEA) & \\
0 & Total for {\sd}: & 225 ({\XFMEA}) & \\
\hline \hline
@ -1211,6 +1214,31 @@ We can express their probabilities as $P(B_4) = P(B_1 \cap B_3)$ and $P(B_5) = P
\subsection{Problems in choosing membership of functional groups}
The choice of components for {\fgs} is one to be made by the analyst.
The guiding principle it to choose components that are functionally adjacent
and try to create the smallest groups possible.
There are some mistakes that an analyst could make when choosing the members
of functional groups. These are
\begin{itemize}
\item Choosing components that are not functionally adjacent --- i.e. components that do not work together to perform a specific function,
\item Not including components that may have side effects on the {\fg}, but are not obviously connected.
\end{itemize}
If we were to deliberately choose a `bad' {\fg} we would find that,
on analysing it, the component failure modes would not converge to common
symptoms.
%
This would be because, with functionally adjacent
components, their failures often cause common failure symptoms for the {\fg}.
%
With components that are not interacting, we are unlikely to see
this convergence of symptoms.
%
%
This property could be of use in future automated FMMD tools
to warn of potentially poorly chosen {\fgs}.
\subsubsection{Side Effects: A Problem for FMMD analysis}
\label{sec:sideeffects}
A problem with modularising according to functionality is that we can have component failures that would % poss split infinitive

3
submission_thesis/CH7_Conclusion/copy.tex
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@ -132,7 +132,8 @@ failure statistics, we calculate the reliability of this circuit.
The formula for given in MIL-HDBK-217F\cite{mil1991}[9.2] for a generic fixed film non-power resistor
is reproduced in equation \ref{resistorfit}. The meanings
and values assigned to its co-efficients are described in table \ref{tab:resistor}.
\glossary{name={FIT}, description={Failure in Time (FIT). The number of times a particular failure is expected to occur in a $10^{9}$ hour time period.}}
\glossary{name={FIT}, description={Failure in Time (FIT). The number of times a particular
failure is expected to occur in a $10^{9}$ hour time period.}}
\fmodegloss

6
submission_thesis/style.tex
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@ -55,6 +55,12 @@
\newcommand{\irl}{in~real~life}
\newcommand{\enc}{\ensuremath{\stackrel{enc}{\longrightarrow}}}
\newcommand{\pin}{\ensuremath{\stackrel{pi}{\longleftrightarrow}}}
%
% OK after about 3 years its not rigorous FMEA (RFMEA) anymore, oh no, its Exhaustive FMEA
% but since the fuckers might change it yet again, I am making this a macro.
\newcommand{\XFMEA}{XFMEA}
%
%\newcommand{\pic}{\em pure~intersection~chain}
\newcommand{\pic}{\emp pair-wise~intersection~chain}
\newcommand{\wrt}{\emp with~respect~to}

2
submission_thesis/thesis.tex
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@ -64,7 +64,7 @@
% numbers at outer edges
\pagenumbering{arabic} % Arabic page numbers hereafter
\cfoot{Page \thepage\ of \pageref{LastPage}}
\lfoot{University of Brighton 2012} %% Year keeps fucking incrementing
\lfoot{University of Brighton} %% Year keeps fucking incrementing
\rfoot{R.P.Clark \today}
\lhead{Failure Mode Modular De-Composition}
\rhead{Ph.D Thesis}