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7
mybib.bib
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@ -7,6 +7,13 @@
YEAR = "1992" YEAR = "1992"
} }
@BOOK{scsh,
AUTHOR = "D. Smith",
TITLE = "Safety Critical Stystems Handbook, 3rd Ed. ISBN 978-0-08-096781-3",
PUBLISHER = "Butterworth HeinemannH",
YEAR = "2011"
}
@ARTICLE{embedsfmea, @ARTICLE{embedsfmea,
AUTHOR = "Peter L. Goddard", AUTHOR = "Peter L. Goddard",
TITLE = "Validating The Safety of Embedded Real-Time Control Systems using FMEA", TITLE = "Validating The Safety of Embedded Real-Time Control Systems using FMEA",

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submission_thesis/CH4_FMMD/cfg.dia
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submission_thesis/CH4_FMMD/copy.tex
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@ -63,22 +63,80 @@ description and re-factoring process using UML class models.
% This chapter defines the FMMD process and related concepts and calculations. % This chapter defines the FMMD process and related concepts and calculations.
FMMD is in essence a modularised variant of traditional FMEA~\cite{sccs}[pp.34-38]. FMMD is in essence a modularised variant of traditional FMEA~\cite{sccs}[pp.34-38].
% %
Rather than taking each component failure mode FMEA is a bottom-up, or forward search failure mode technique starting with
and extrapolating top level or system failure symptoms from it, base component failure modes~\cite{safeware}[p.341].
small groups of components are collected into {\fgs} and analysed.
%and then {\dcs} are used to represent the {\fgs}.
We analyse each {\fg} in order to determine its failure mode behaviour.
%of the {\fg}.
With the failure mode behaviour we can obtain a set of failure modes
for the {\fg}.
% %
Or in other words we determine how the {\fg}, as an entity can fail. %\subsection{FMMD Process in outline.}
% %
We can then create a new theoretical component to represent the {\fg}. In order to analyse from the bottom-up and apply a modular methodology, we need to take
small groups of components that naturally
work together to perform a simple function: we term these groups `{\fgs}'.
% %
We call this a {\dc}. The components to include in a {\fg} are chosen by hand.
%a human, the analyst.
%We can represent the `Functional~Group' as a class.
When we have a
{\fg} we can look at the components it contains,
and from this determine the failure modes of all the components that belong to it.
% %
This {\dc} has a set of failure modes: we can thus treat it as a `higher~level' component. Initial {\fgs} will consist of {\bcs}.
%
% and determine a failure mode model for that group.
%
% expand 21sep2010
%The `{\fg}' as used by the analyst is a collection of component failures modes.
%The analysts interest is in the ways in which the components within the {\fg}
%can fail.
%
All the failure modes of all the components within a {\fg} are collected.
%
As each component %mode holds
has a set of failure modes associated with it,
the {\fg} represents a set of sets of failure modes.
%
We convert this
into a flat set
of failure modes for use in analysis.
%
A flat set is a set containing just the failure modes and not sets of failure modes~\cite{joyofsets}[p.8].
%
%In practical term each component failure mode is considered as a `failure~scenario' or 'test~case'
%for the {\fg}.
%
Each of these failure modes %, and optionally combinations of them, are
%formed into failure~scenarios which
are
analysed for their effect on the failure mode behaviour of the `{\fg}'.
%
Once we have the failure mode behaviour of the {\fg}, we can determine its symptoms of failure.
%,
%or the failure modes of the {\dc}.
%for the {\fg}.
%
We view these symptoms as derived failure modes of the {\fg}.
%
Or in other words we can determine how the `{\fg}' can fail.
We can now consider the {\fg} as a {\dc} % sort of super component
with its own set of failure modes.
%
% Rather than taking each component failure mode
% and extrapolating top level or system failure symptoms from it,
% small groups of components are collected into {\fgs} and analysed.
%
%
% %and then {\dcs} are used to represent the {\fgs}.
% We analyse each {\fg} in order to determine its failure mode behaviour.
% %of the {\fg}.
% With the failure mode behaviour we can obtain a set of failure modes
% for the {\fg}.
% %
% Or in other words we determine how the {\fg}, as an entity can fail.
% %
% We can then create a new theoretical component to represent the {\fg}.
% %
% We call this a {\dc}.
% %
%This {\dc} has a set of failure modes: we can thus treat it as a `higher~level' component.
% %
Because a {\dc} has a set of failure modes we can use it in higher level {\fgs} Because a {\dc} has a set of failure modes we can use it in higher level {\fgs}
which in turn produce higher level {\dcs}. which in turn produce higher level {\dcs}.
@ -90,13 +148,16 @@ at the top of the hierarchy.
The failure modes of the final or top {\dc} The failure modes of the final or top {\dc}
are the failure modes of the system under investigation. are the failure modes of the system under investigation.
% %
Or in other words we take the traditional FMEA process, and modularise it from the bottom-up. That is, we take the traditional FMEA process and modularise it from the bottom-up.
%We break down each stage of reasoning %We break down each stage of reasoning
%into small manageable groups, and use the failure mode behaviour from them to create {\dcs} %into small manageable groups, and use the failure mode behaviour from them to create {\dcs}
%to build higher level groups. %to build higher level groups.
In this way we can incrementally analyse an entire system. %, with documented reasoning stages. In this way we can incrementally apply FMEA to an entire system. %, with documented reasoning stages.
% %This has advantages of concentrating %
% %effort in where modules interact, This has advantages of concentrating
effort in where modules interact (interfaces), of
being able to re-use work and a saving in the complexity of performing
FMEA.
%A notation is then described to index and classify objects created in FMMD hierarchical models. %A notation is then described to index and classify objects created in FMMD hierarchical models.
@ -427,9 +488,9 @@ In this way we can incrementally analyse an entire system. %, with documented re
%% %%
%% GARK BEGIN %% GARK BEGIN
To demonstrate the principles of FMMD, we use it to analyse a We demonstrate the principles of FMMD, by using it to analyse a
commonly used circuit, a non-inverting amplifier built from an op amp~\cite{aoe}[p.234] and commonly used circuit, a non-inverting amplifier built from an op amp~\cite{aoe}[p.234] and
two resistors, a circuit schematic for this is shown in figure \ref{fig:noninvamp}. two resistors; a circuit schematic for this is shown in figure \ref{fig:noninvamp}.
% %
\begin{figure}[h+] \begin{figure}[h+]
\centering \centering
@ -441,6 +502,7 @@ two resistors, a circuit schematic for this is shown in figure \ref{fig:noninvam
\end{figure} \end{figure}
% %
The function of the resistors in this circuit is to set the amplifier gain. The function of the resistors in this circuit is to set the amplifier gain.
%
The resistors act as a potential divider---assuming the op-amp has high impedance---and The resistors act as a potential divider---assuming the op-amp has high impedance---and
program the inverting input on the op-amp program the inverting input on the op-amp
to balance them against the positive input, giving the voltage gain ($G_v$) to balance them against the positive input, giving the voltage gain ($G_v$)
@ -449,7 +511,7 @@ defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
\paragraph{Analysing the failure modes of the Potential Divider.} \paragraph{Analysing the failure modes of the Potential Divider.}
\label{subsec:potdiv} \label{subsec:potdiv}
As the resistors work to provide a clearly defined function, that of a potential divider, Since the resistors work to provide a clearly defined function, that of a potential divider,
we can treat them as a collection of components with a specific functionality---which can be termed a `{\fg}'. we can treat them as a collection of components with a specific functionality---which can be termed a `{\fg}'.
This {\fg} has two members, $R1$ and $R2$. This {\fg} has two members, $R1$ and $R2$.
% %
@ -457,13 +519,13 @@ The potential divider circuit can be considered as a component
that provides the function of splitting two voltages into three, that provides the function of splitting two voltages into three,
the third voltage being a ratio defined by the values of the resistors. the third voltage being a ratio defined by the values of the resistors.
%Taken as an entity the potential divider can be viewed as a {\dc}. %Taken as an entity the potential divider can be viewed as a {\dc}.
That is to say we can treat the potential divider, comprised of two resistors %That is to say we can treat the potential divider, comprised of two resistors
to act as a {\dc}. %to act as a {\dc}.
% %
Using the EN298 specification for resistor failure~\cite{en298}[App.A], Using the EN298 specification for resistor failure~\cite{en298}[App.A],
we can assign failure modes of $OPEN$ and $SHORT$ to the resistors individually (assignment of failure modes we can assign failure modes of $OPEN$ and $SHORT$ to the resistors individually (assignment of failure modes
is discussed in more detail in section~\ref{sec:resistorfm}). is discussed in more detail in section~\ref{sec:resistorfm}).
%
We represent a resistor and its failure modes as a directed acyclic graph (DAG) We represent a resistor and its failure modes as a directed acyclic graph (DAG)
(see figure \ref{fig:rdag}). (see figure \ref{fig:rdag}).
\begin{figure}[h+] \begin{figure}[h+]
@ -495,28 +557,31 @@ and determine how they affect the operation of the potential~divider.
% %
Each resistor failure mode is a potential {\fc} in the potential~divider. Each resistor failure mode is a potential {\fc} in the potential~divider.
%%For this example we look at single failure modes only. %%For this example we look at single failure modes only.
For each failure mode in our {\fg} potential~divider For each failure mode in our {\fg}---potential~divider---we can assign a {\fc}
we can assign a {\fc}
number (see table \ref{tbl:pdfmea}). number (see table \ref{tbl:pdfmea}).
% %
Each {\fc} is analysed to determine the symptom of failure in Each {\fc} is analysed to determine %the symptom of
the potential~dividers' operation. For instance a failure in
the potential~dividers' operation.
%
For instance
if resistor $R_1$ were to become open, then the potential~divider would not be grounded and the if resistor $R_1$ were to become open, then the potential~divider would not be grounded and the
voltage output from it would float high (+ve). voltage output from it would float high (+ve).
This would mean the symptom of the failed potential~divider would be voltage high output.
% %
The failure symptom of a high potential~divider output is termed `HighPD', and This would mean the resulting failure of the potential~divider would be voltage high output.
%
The failure mode of a high potential~divider output is termed `HighPD', and
for it outputting a low voltage `LowPD'. % Andrew asked for this to be defined before the table. ... for it outputting a low voltage `LowPD'. % Andrew asked for this to be defined before the table. ...
%We can now consider the {\fg} %We can now consider the {\fg}
%as a component in its own right, and its symptoms as its failure modes. %as a component in its own right, and its symptoms as its failure modes.
%
{ \small { \small
\begin{table}[ht] \begin{table}[ht]
\caption{Potential Divider: Failure Mode Effects Analysis: Single Faults} % title of Table \caption{Potential Divider: Failure Mode Effects Analysis: Single Failures} % title of Table
\centering % used for centering table \centering % used for centering table
\begin{tabular}{||l|c|c|l||} \begin{tabular}{||l|c|c|l||}
\hline \hline \hline \hline
% FUCKING HATE HAVING TO REMOVE THE TERM FAILURE SCENARIO HERE.... % FIDDLINGING HATAR HAVING TO REMOVE THE TERM FAILURE SCENARIO HERE....
% GOOD ENOUGH FOR THE IET/IEEE, but then they live in the real % GOOD ENOUGH FOR THE IET/IEEE, but then they live in the real
% world don't they.... % world don't they....
%\textbf{Failure} & \textbf{Pot.Div} & \textbf{Symptom} \\ %\textbf{Failure} & \textbf{Pot.Div} & \textbf{Symptom} \\
@ -536,25 +601,31 @@ for it outputting a low voltage `LowPD'. % Andrew asked for this to be defined b
\label{tbl:pdfmea} \label{tbl:pdfmea}
\end{table} \end{table}
} }
%
%\vbox{ %\vbox{
From table \ref{tbl:pdfmea} we can see that the resistor From table \ref{tbl:pdfmea} we can see that the resistor
failures modes lead to some common symptoms of failure from the perspective of the {\fg}. failures modes lead to some common symptoms of failure from the perspective of the {\fg}.
%YOU FUCKING CUNTS, TELL ME TO USE THE TERM SYMPTOM AND THEN TELL ME TO FUCKING REMOVE IT A YEAR LATER> CUNTS %YOU FIDDLINGING FITTAS, TELL ME TO USE THE TERM SYMPTOM AND THEN TELL ME TO FIDDLINGING REMOVE IT A YEAR LATER> FITTAS
%symptoms. %symptoms.
These common symptoms of failure are an important concept for FMMD. %These common symptoms of failure are an important concept for FMMD.
It means that we can take multiple failure modes from {\fgs} components and resolve them Notice the many to one mapping from {\bc} failure modes to {\dc} failure mode;
to failure modes of the {\fg}. this is a typical effect of an FMMD analysis stage, and means that with each analysis stage we reduce
the number of failure modes to consider.
% %
This means that we simplify the FMEA analysis task for further stages. %This means that we can take multiple failure modes from {\fgs} components and resolve them
By drawing directed edges from the failure modes to the {\dc} failure modes, % symptoms, %to failure modes of the {\fg}.
we show the relationships between the component failure modes and %
{\dc} failure modes. % resultant symptoms. %This means that
We thus simplify the FMEA analysis task for further stages.
%
By drawing vertices for failure modes, % symptoms,
and edges for the relationships between them
%component failure modes and
%{\dc} failure modes. % resultant symptoms.
%The {\fg} can now be considered a derived component. %The {\fg} can now be considered a derived component.
This is represented in the DAG in figure \ref{fig:fg1adag}. we represent the analysis with the DAG in figure \ref{fig:fg1adag}.
%} %}
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -593,12 +664,11 @@ This is represented in the DAG in figure \ref{fig:fg1adag}.
\end{tikzpicture} \end{tikzpicture}
\caption{Failure symptoms of the `Potential Divider'} \caption{Failure mode graph of the Potential~Divider}
\label{fig:fg1adag} \label{fig:fg1adag}
\end{figure} \end{figure}
%
We now have % can now create % formulate
We can now create % formulate
a {\dc} to represent this potential divider: a {\dc} to represent this potential divider:
we name this \textbf{PD}. we name this \textbf{PD}.
This {\dc} will have two failure modes, $HighPD$ and $LowPD$. This {\dc} will have two failure modes, $HighPD$ and $LowPD$.
@ -607,10 +677,8 @@ This {\dc} will have two failure modes, $HighPD$ and $LowPD$.
% HTR 05SEP2012 The creation of the {\dc} \textbf{PD} is represented as a % HTR 05SEP2012 The creation of the {\dc} \textbf{PD} is represented as a
% HTR 05SEP2012 hierarchy diagram in figure~\ref{fig:dc1}. % HTR 05SEP2012 hierarchy diagram in figure~\ref{fig:dc1}.
% HTR 05SEP2012 We represent the {\dc} \textbf{PD}, as a DAG in figure \ref{fig:dc1dag}. % HTR 05SEP2012 We represent the {\dc} \textbf{PD}, as a DAG in figure \ref{fig:dc1dag}.
%We could represent it algebraically thus: $ \derivec(PotDiv) = %We could represent it algebraically thus: $ \derivec(PotDiv) =
% FUCKING HELL THIS IS to be REMOVED TOO : CUNTS % FIDDLINGING OVERSATTNING THIS IS to be REMOVED TOO : FITTAS
% \begin{figure}[h+] % \begin{figure}[h+]
% \centering % \centering
% \includegraphics[width=200pt,keepaspectratio=true]{./CH4_FMMD/dc1.png} % \includegraphics[width=200pt,keepaspectratio=true]{./CH4_FMMD/dc1.png}
@ -619,13 +687,10 @@ This {\dc} will have two failure modes, $HighPD$ and $LowPD$.
% manual process and from this the {\dc} is created.} % manual process and from this the {\dc} is created.}
% \label{fig:dc1} % \label{fig:dc1}
% \end{figure} % \end{figure}
% We can now represent the potential divider as a {\dc}. % We can now represent the potential divider as a {\dc}.
% Because we have its symptoms (or failure mode behaviour), % Because we have its symptoms (or failure mode behaviour),
% we can treat these as the failure modes of a new {\dc}. % we can treat these as the failure modes of a new {\dc}.
% We can represent this as a DAG (see figure \ref{fig:dc1dag}). % We can represent this as a DAG (see figure \ref{fig:dc1dag}).
% \begin{figure}[h+] % \begin{figure}[h+]
% \centering % \centering
% \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] % \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -650,11 +715,11 @@ This {\dc} will have two failure modes, $HighPD$ and $LowPD$.
% %We can consider this an an orthogonal WHAT???? Group ???? Collection ???? % %We can consider this an an orthogonal WHAT???? Group ???? Collection ????
We now have a {\dc} model for a generic potential divider, and can use it We now have a {\dc} model for a generic potential divider, and can use it
as a building block for other {\fgs} in the same way as we used the base components $R1$ and $R2$. as a building block for other {\fgs} in the same way as we used the base components $R1$ and $R2$.
%
%\clearpage %\clearpage
%
\paragraph{Failure Mode Analysis of a generic op-amp} \paragraph{Failure Mode Analysis of a generic op-amp.}
%
%\clearpage %\clearpage
Let us now consider the op-amp as a {\bc}. According to Let us now consider the op-amp as a {\bc}. According to
FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes %(with assigned probabilities): FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes %(with assigned probabilities):
@ -663,10 +728,10 @@ latch-down (l\_dn), where the output voltage is stuck low, %(6\%),
no-operation (noop), where the op-amp cannot drive the output, %(31.3\%), no-operation (noop), where the op-amp cannot drive the output, %(31.3\%),
and low~slew~rate (lowslew) where the op-amp cannot react quickly to changes on its inputs. %(50\%). and low~slew~rate (lowslew) where the op-amp cannot react quickly to changes on its inputs. %(50\%).
\nocite{mil1991} \nocite{mil1991}
%
%\ifthenelse {\boolean{dag}} %\ifthenelse {\boolean{dag}}
%{ %{
%
%\clearpage %\clearpage
We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}). We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
\begin{figure}[h+] \begin{figure}[h+]
@ -696,14 +761,14 @@ We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
\caption{DAG representing failure modes of an Op-amp} \caption{DAG representing failure modes of an Op-amp}
\label{fig:op1dag} \label{fig:op1dag}
\end{figure} \end{figure}
%
%} %}
%{ %{
%} %}
%\clearpage %\clearpage
%\paragraph{Modelling the OP amp with the potential divider.} %\paragraph{Modelling the OP amp with the potential divider.}
We now bring the op-amp and the {\dc} {\em PD} together to % andrew heavily critised this sentence but it made sense to Chris and I We now bring the op-amp and the {\dc} {\em PD} together to % andrew heavily critised this sentence but it made sense to Chris and I
form a {\fg} to represent the failure mode behaviour of the non-inverting amplifier. form a {\fg} to model the failure mode behaviour of the non-inverting amplifier.
% %
%We have the failure modes of the {\dc} for the potential divider, %We have the failure modes of the {\dc} for the potential divider,
%so we do not need to go back and consider the individual resistor failure modes that defined its behaviour. %so we do not need to go back and consider the individual resistor failure modes that defined its behaviour.
@ -715,8 +780,8 @@ The two components in this new {\fg}, the op-amp and the {\dc} {\em PD} have fa
as {\fcs} in table~\ref{tbl:ampfmea1}. as {\fcs} in table~\ref{tbl:ampfmea1}.
%Each of these failure modes will be given a {\fc} for analysis, %Each of these failure modes will be given a {\fc} for analysis,
%and this is represented in table \ref{tbl:ampfmea1}. %and this is represented in table \ref{tbl:ampfmea1}.
% CUNTS NOW I CANNOT USE THE TERM FAILURE SCENARIO---was first column of table below % FITTAS NOW I CANNOT USE THE TERM FAILURE SCENARIO---was first column of table below
%
%\clearpage %\clearpage
{\footnotesize {\footnotesize
\begin{table}[h+] \begin{table}[h+]
@ -724,7 +789,7 @@ as {\fcs} in table~\ref{tbl:ampfmea1}.
\centering % used for centering table \centering % used for centering table
\begin{tabular}{||l|c|c|l||} \begin{tabular}{||l|c|c|l||}
\hline \hline \hline \hline
%% FUCKING HATE HAVING TO REMOVE THE TERM FAILURE SCENARIO --- whats is this the fucking %% FIDDLINGING HATAR HAVING TO REMOVE THE TERM FAILURE SCENARIO --- whats is this the fucking
%%childrens version %%childrens version
%\textbf{Failure} & \textbf{Amplifier} & \textbf{Derived component} \\ %Symptom} \\ %\textbf{Failure} & \textbf{Amplifier} & \textbf{Derived component} \\ %Symptom} \\
% \textbf{Scenario} & \textbf{Effect} & \textbf{Failure Modes} \\ %Description} \\ % \textbf{Scenario} & \textbf{Effect} & \textbf{Failure Modes} \\ %Description} \\
@ -760,10 +825,10 @@ as {\fcs} in table~\ref{tbl:ampfmea1}.
\label{tbl:ampfmea1} \label{tbl:ampfmea1}
\end{table} \end{table}
} }
%
%
%
%
\begin{figure}[h+] \begin{figure}[h+]
\centering \centering
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep] \begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
@ -882,20 +947,21 @@ as {\fcs} in table~\ref{tbl:ampfmea1}.
%\node[annot,right of=s](dcl) {Derived Component}; %\node[annot,right of=s](dcl) {Derived Component};
\end{tikzpicture} \end{tikzpicture}
% End of code % End of code
\caption{Full DAG representing failure modes and symptoms of the Non Inverting Op-amp Circuit} \caption{Full DAG representing failure modes and {\bcs} of the Non Inverting Op-amp Circuit}
\label{fig:noninvdag1} \label{fig:noninvdag1}
\end{figure} \end{figure}
%
%Let us consider, for the sake of the example, that the voltage follower (very low gain of 1.0) %Let us consider, for the sake of the example, that the voltage follower (very low gain of 1.0)
%amplification characteristics from FS2 and FS6 can be considered as low output from the OPAMP for the application %amplification characteristics from FS2 and FS6 can be considered as low output from the OPAMP for the application
%in hand (say milli-volt signal amplification). %in hand (say milli-volt signal amplification).
%
For this amplifier configuration we have three {\dc} failure modes; {\em AMP\_High, AMP\_Low, LowPass}. % see figure~\ref{fig:fgampb}. For this amplifier configuration we have three {\dc} failure modes; {\em AMP\_High, AMP\_Low, LowPass}. % see figure~\ref{fig:fgampb}.
% HTR 05SEP2012 This model now has two stages of analysis hierarchy, as represented in figure~\ref{fig:dc2}. % HTR 05SEP2012
This model now has two stages of analysis, as represented in figure~\ref{fig:dc2}.
%
From the analysis in table \ref{tbl:ampfmea1} we can create the {\dc} {\em NONINVAMP}, which From the analysis in table \ref{tbl:ampfmea1} we can create the {\dc} {\em NONINVAMP}, which
represents the failure mode behaviour of the non-inverting amplifier. represents the failure mode behaviour of the non-inverting amplifier.
%
% HTR 05SEP2012 \begin{figure}[h] % HTR 05SEP2012 \begin{figure}[h]
% HTR 05SEP2012 % HTR 05SEP2012 \centering % HTR 05SEP2012 % HTR 05SEP2012 \centering
% HTR 05SEP2012 \includegraphics[width=225pt]{./CH4_FMMD/dc2.png} % HTR 05SEP2012 \includegraphics[width=225pt]{./CH4_FMMD/dc2.png}
@ -904,11 +970,13 @@ represents the failure mode behaviour of the non-inverting amplifier.
% HTR 05SEP2012 (i.e. two `$\derivec$' processes taking {\fgs} and creating {\dcs}) for the non-inverting amplifier} % HTR 05SEP2012 (i.e. two `$\derivec$' processes taking {\fgs} and creating {\dcs}) for the non-inverting amplifier}
% HTR 05SEP2012 \label{fig:dc2} % HTR 05SEP2012 \label{fig:dc2}
% HTR 05SEP2012 \end{figure} % HTR 05SEP2012 \end{figure}
%
%
We can represent the hierarchy as an Euler diagram, where the curves We can represent the analysis sstages of INVAMP as an Euler diagram,
define the components and {\dcs} used to form the INVAMP model, see figure~\ref{fig:eulerfmmd}. showing the choice of de-composition of the system into {\fgs}.}
%where the curves
%define the components and {\dcs} used to form the INVAMP model, see figure~\ref{fig:eulerfmmd}.
%
\begin{figure}[h] \begin{figure}[h]
\centering \centering
\includegraphics[width=300pt]{./CH4_FMMD/eulerfmmd.png} \includegraphics[width=300pt]{./CH4_FMMD/eulerfmmd.png}
@ -917,7 +985,7 @@ define the components and {\dcs} used to form the INVAMP model, see figure~\ref{
the components have been grouped into {\fgs} and then used as {\dcs} to build the analysis hierarchy.} the components have been grouped into {\fgs} and then used as {\dcs} to build the analysis hierarchy.}
\label{fig:eulerfmmd} \label{fig:eulerfmmd}
\end{figure} \end{figure}
%
We can now examine the failure mode relationships in the {\dc} {\em INVAMP} by drawing it as a DAG. We can now examine the failure mode relationships in the {\dc} {\em INVAMP} by drawing it as a DAG.
%expand the {\em PD} {\dc} and have a full FMMD failure %mode %expand the {\em PD} {\dc} and have a full FMMD failure %mode
%model %model
@ -926,23 +994,25 @@ failure modes
down to the base component failure modes, %leaves of the tree (the leaves being {\bc} failure modes), down to the base component failure modes, %leaves of the tree (the leaves being {\bc} failure modes),
and thus determine all possible causes for and thus determine all possible causes for
the three high level symptoms, i.e. the failure~modes of the non-inverting amplifier {\dc} {\em INVAMP}. the three high level symptoms, i.e. the failure~modes of the non-inverting amplifier {\dc} {\em INVAMP}.
Knowing all possible causes for a top level event/failure~mode
is extremely useful.
% %
Were a particular top level event to be classified as catastrophic for instance, Knowing all possible causes for a top level event/failure~mode
is extremely useful;
if a particular top~level/system~failure was classified as catastrophic for instance,
we could use this information we could use this information
to strengthen components that could cause that particular top level event/failure. to strengthen components that could cause that particular top level event/system~failure.
% %
Figure \ref{fig:noninvdag1} shows a DAG, Figure \ref{fig:noninvdag1} shows a DAG,
from which we can trace top level failure modes to the base component failure modes from which we can trace top level failure modes to the base component failure modes
that can cause them. that can cause them.
That is to say that we can trace failure mode effects That is, we can trace failure mode effects
from base component level to the top and vice versa. from base component level to the top and vice versa.
% %
Having a base component failure modes traceable to top event events, Having a failure mode graph/model where base component failure modes are traceable to top event events,
provides a a failure mode model, from which provides a forward search failure mode model.
we can derive information %
to assist in building models for FTA, FMEA, FMECA, FMEDA We can use this model to derive information
to assist in creating related models such as FTA~\cite{nucfta,nasafta},
traditional FMEA, FMECA~\cite{safeware}[p.344], FMEDA~\cite{scsh}
and other failure mode analysis methodologies. and other failure mode analysis methodologies.
@ -970,7 +1040,7 @@ and other failure mode analysis methodologies.
\clearpage %\clearpage
% When analysing a safety critical system using % When analysing a safety critical system using
% any form of Failure Mode Effects Analysis (FMEA), we need clearly defined failure modes for % any form of Failure Mode Effects Analysis (FMEA), we need clearly defined failure modes for
@ -982,69 +1052,65 @@ and other failure mode analysis methodologies.
\section{Defining terms} \section{Defining terms}
Here we define the terms as used in the worked example. % Here we define the terms as used in the worked example.
%
\begin{table}[h] % \begin{table}[h]
\center % \center
\begin{tabular}{||p{3cm}|p{10cm}||} % \begin{tabular}{||p{3cm}|p{10cm}||}
%
\hline \hline % \hline \hline
{\em Definition } & {\em Description} \\ \hline % {\em Definition } & {\em Description} \\ \hline
%
System & A product designed to % System & A product designed to
work as a coherent entity \\ \hline % work as a coherent entity \\ \hline
%
%
%
Base Component & An atomic building block used at the lowest level of an FMMD model. % Base Component & An atomic building block used at the lowest level of an FMMD model.
% \footnote{In the case of combinatorial packaged parts (such as a chip containing % % \footnote{In the case of combinatorial packaged parts (such as a chip containing
% four op-amps, each op-amp on the chip is considered as one atomic, or {\em{\bc}}).}. %% where did this footnote GO???? % % four op-amps, each op-amp on the chip is considered as one atomic, or {\em{\bc}}).}. %% where did this footnote GO????
% seems like its a bug in TeX 04JUN2012 % % seems like its a bug in TeX 04JUN2012
\\ % \\
{\em Constraint} & This object must have a defined set of failure~modes. \\ \hline % {\em Constraint} & This object must have a defined set of failure~modes. \\ \hline
%
%
Component & A building block, this may be a {\bc} or a {\dc}. \\%or manufacturers part. \\ % Component & A building block, this may be a {\bc} or a {\dc}. \\%or manufacturers part. \\
{\em Constraint} & This object must have a defined set of failure~modes. \\ \hline % {\em Constraint} & This object must have a defined set of failure~modes. \\ \hline
%
%
%
%Sub-system & A part of a system, sub-systems may contain sub-systems etc. \\ \hline % in FMMD terminology % %Sub-system & A part of a system, sub-systems may contain sub-systems etc. \\ \hline % in FMMD terminology
%this would be both a {\em{\dc}} and a {\fg}. \\ % %this would be both a {\em{\dc}} and a {\fg}. \\
%{\em Constraint} & This object must have a defined set of failure~modes. \\ \hline % %{\em Constraint} & This object must have a defined set of failure~modes. \\ \hline
%
%%A part failure mode is the way in which a component fails "functionally" on component level. Often a part has only a few failure modes. % %%A part failure mode is the way in which a component fails "functionally" on component level. Often a part has only a few failure modes.
Failure mode & A failure mode~\cite{sccs}[p.8] is the way in which a component may fail functionally (i.e. the way in which it can fail to perform % Failure mode & A failure mode~\cite{sccs}[p.8] is the way in which a component may fail functionally (i.e. the way in which it can fail to perform
its intended function). A component will typically have few failure modes. \\ \hline % its intended function). A component will typically have few failure modes. \\ \hline
%
Functional Grouping & A collection of % Functional Grouping & A collection of
components with a functional purpose. % components with a functional purpose.
\\ \hline % \\ \hline
%
% Symptom & A failure symptom of a {\fg}, caused by % WHICH MUST BE UNIQUE AND SEPARATE WITHIN THE \fg % % Symptom & A failure symptom of a {\fg}, caused by % WHICH MUST BE UNIQUE AND SEPARATE WITHIN THE \fg
% a combination of its component failure modes. \\ \hline % % a combination of its component failure modes. \\ \hline
%
%
Derived Component & A theoretical component, created to represent the failure % Derived Component & A theoretical component, created to represent the failure
mode behaviour of a {\fg}. \\ % mode behaviour of a {\fg}. \\
%
{\em Constraint} & This object must have a defined set of failure~modes. \\ \hline % {\em Constraint} & This object must have a defined set of failure~modes. \\ \hline
% UNITARY STATE NOT DISCUSSED HERE NOW...... % UNITARY STATE NOT DISCUSSED HERE NOW......
% Unitary State & A component with `unitary~state' failure modes, means that it cannot fail % Unitary State & A component with `unitary~state' failure modes, means that it cannot fail
% with more than one of its failure modes at a time.\\ \hline % with more than one of its failure modes at a time.\\ \hline
%%%% TOLD TO REMOVE THIS BUT FIDDLINGING HATAR TO HAVE TO DO IT
%%%% TOLD TO REMOVE THIS BUT FUCKING HATE TO HAVE TO DO IT
% Failure Scenario & A single failure mode (or a combination), used to % Failure Scenario & A single failure mode (or a combination), used to
% determine failure mode effects on a {\fg}. % determine failure mode effects on a {\fg}.
\\ %\\
% \hline
\hline % \end{tabular}
\end{tabular} % \caption{Failure Mode Modular De-composition: definitions and terms}
\caption{Failure Mode Modular De-composition: definitions and terms} % \label{tbl:fmmd_defs}
\label{tbl:fmmd_defs} % \end{table}
\end{table}
\paragraph{A discussion on the terms Parts, Components and Base Components.} \paragraph{A discussion on the terms Parts, Components and Base Components.}
@ -1063,18 +1129,20 @@ Geoffrey Hall, writing in Spacecraft Systems Engineering~\cite{scse}[p.619]
defines a `part' thus defines a `part' thus
``{{Part(definition)}---The lowest level of assembly, beyond which further disassembly irrevocably destroys the item''. ``{{Part(definition)}---The lowest level of assembly, beyond which further disassembly irrevocably destroys the item''.
% %
This definition of a `part' is useful, but consider parts, such as quad packaged op-amps: This definition %of a `part'
is useful, but consider parts, such as quad packaged op-amps:
in this case we have four op-amps on one chip.
% %
in this case, we have four op-amps on one chip. Using traditional FMEA methods~\cite{sccs}[p.34] we would consider each op-amp in the package Using traditional FMEA methods~\cite{sccs}[p.34] we would consider each op-amp in the package
as a separate building block for a circuit. For FMMD each of these four op-amps as a separate building block for a circuit. For FMMD each of these four op-amps
in the chip would be considered to be a separate {\bc}. in the chip would be considered to be a separate {\bc}.
% CAN WE FIND SUPPORT FOR THIS IN LITERATURE??? % CAN WE FIND SUPPORT FOR THIS IN LITERATURE???
% %
We, in fact, need to go a little further than the above definition of a part, We, need to go further than the above definition of a part defining an atomic entity. % used as a building block.
and say that we want to define an atomic entity. % used as a building block.
%The term component, in American English, can mean a building block or a part. %The term component, in American English, can mean a building block or a part.
%In British-English a component generally is given to mean the definition for part above. %In British-English a component generally is given to mean the definition for part above.
We define {\bc} to be the lowest level---an entity with which we begin our analysis---of component that we use as a building block. We define {\bc} to be the lowest level---an entity with which we begin our analysis---a component
that we use as a building block.
This is a choice made by the analyst, often guided by the standards to which the analysis is being performed. % to. This is a choice made by the analyst, often guided by the standards to which the analysis is being performed. % to.
% %
Both op-amps and transistors have published statistical failure rates and yet an op-amp is constructed from transistors. Both op-amps and transistors have published statistical failure rates and yet an op-amp is constructed from transistors.
@ -1091,7 +1159,7 @@ to which we are approving/analysing a system.
%and component to mean either a part or a sub-assembly. %and component to mean either a part or a sub-assembly.
%Definitions used in FMMD are lisfuckup mode or not?????ted in table~\ref{tbl:fmmd_defs} and discussed below. %Definitions used in FMMD are lisfuckup mode or not?????ted in table~\ref{tbl:fmmd_defs} and discussed below.
%% FUCKING STEREO SUB_SYSTEM EXAMPLE, THE FUCKING CHILDRENS SECTION %% FIDDLINGING STEREO SUB_SYSTEM EXAMPLE, THE FIDDLINGING CHILDRENS SECTION
\subsection{Definition of terms: sound system example.} \subsection{Definition of terms: sound system example.}
@ -1104,7 +1172,7 @@ A component can be viewed as a sub-system that is a part of some larger system.
% %
A modular system common to many homes is the sound separates audio system or stereo hi-fi. A modular system common to many homes is the sound separates audio system or stereo hi-fi.
% %
This is now used as an example to describe terms used in FMMD. This is used as an example to describe terms used in FMMD.
% %
For instance a stereo amplifier separate/slave is a component. For instance a stereo amplifier separate/slave is a component.
%The %The
@ -1115,13 +1183,13 @@ CD-player, tuner, amplifier~separate, loudspeakers and ipod~interface.
%and is the way in which FTA\cite{nucfta} analyses a System %and is the way in which FTA\cite{nucfta} analyses a System
%and breaks it down. %and breaks it down.
\paragraph{Functional Groupings and Components.} % {\fgs} and components.} \paragraph{Functional Groupings and Components.} % {\fgs} and components.}
Components can be composed of `components', recursively down to Components can be composed of components, recursively down to
the {\bcs}. the {\bcs}.
% %
However each `component' However each component
will have a fault/failure behaviour and it should will have a fault/failure behaviour and it should
always be possible to obtain a set of failure modes always be possible to obtain a set of failure modes
for each `component'. for each component.
%In FMMD terms a sub-system is a derived component. %In FMMD terms a sub-system is a derived component.
% %
If we look at the sound system example, If we look at the sound system example,
@ -1135,7 +1203,8 @@ we are presented with a problem: which initial collections of base components sh
% %
For instance in the CD~player example, if we start at the bottom, we are presented with For instance in the CD~player example, if we start at the bottom, we are presented with
a massive list of base~components, resistors, motors, user~switches, laser~diodes, etc. a massive list of base~components, resistors, motors, user~switches, laser~diodes, etc.
Clearly, working from the bottom~up, we need to pick small %Clearly,
Working from the bottom~up, we need to pick small
collections of components that work together in some way. collections of components that work together in some way.
These collections are termed `{\fgs}'. These collections are termed `{\fgs}'.
% %
@ -1147,15 +1216,17 @@ it performs a well defined function and it could be considered a design module.
\paragraph{Functional grouping to {\dc} process outline.} \paragraph{Functional grouping to {\dc} process outline.}
%In choosing the lowest level (base component) sub-systems we would look %In choosing the lowest level (base component) sub-systems we would look
%for the smallest `functional~groups' of components within a system. %for the smallest `functional~groups' of components within a system.
We can define a {\fg} as a set of components that interact We %can
define a {\fg} as a set of components that interact
to perform a specific function. to perform a specific function.
% %
When we have analysed the fault behaviour of a {\fg}, we can treat it as a `black box'. When we have analysed the fault behaviour of a {\fg}, we can treat it as a `black~box'.
% %
The {\fgs} fault behaviour will consist of a set of `symptoms' caused by combinations The {\fgs} fault behaviour will consist of a set of %
of its component failure modes. failure modes caused by combinations
of its component's failure modes.
% %
We can thus create a new `component' derived from analysing the {\fg} where We can thus create a new component derived from analysing the {\fg} where
% %
the symptoms of failure of the {\fg} are the failure modes of this new `{\dc}'. the symptoms of failure of the {\fg} are the failure modes of this new `{\dc}'.
@ -1174,13 +1245,7 @@ the symptoms of failure of the {\fg} are the failure modes of this new `{\dc}'.
%\footnote{Microchip sources give an FIT of 4 for their PIC18 series micro~controllers\cite{microchip}, The DOD %\footnote{Microchip sources give an FIT of 4 for their PIC18 series micro~controllers\cite{microchip}, The DOD
%1991 reliability manual\cite{mil1991} applies a FIT of 100 for this generic type of component} %1991 reliability manual\cite{mil1991} applies a FIT of 100 for this generic type of component}
Electrical components have data-sheets associated with them. The data sheets
supply detailed information on the component as supplied by the manufacturer.
%
Because they are design related they rarely show %clearly detail the
failure modes of the component, with environmental factors and MTTF~\cite{sccs}[p.165] statistics.
Given the growing usage of FMEA/FMEDA in industry this may change.
Currently, failure mode information is generally only available for generic component types~\cite{mil1991, fmd91}.
@ -1215,6 +1280,13 @@ failure rates)~\cite{mil1991,en298,fmd91}.
For instance, a simple resistor is generally considered For instance, a simple resistor is generally considered
to fail in two ways, it can go open circuit or it can short. to fail in two ways, it can go open circuit or it can short.
% %
Electrical components have data-sheets associated with them. The data sheets
supply detailed information on the component as supplied by the manufacturer.
%
Because they are design related they rarely show %clearly detail the
failure modes of the component, with environmental factors and MTTF~\cite{sccs}[p.165] statistics.
Given the growing usage of FMEA/FMEDA in industry this may change.
Currently, failure mode information is generally only available for generic component types~\cite{mil1991, fmd91}.
Thus we can associate a set of faults to this component $ResistorFaultModes=\{OPEN, SHORT\}$\footnote{The failure modes of the resistor Thus we can associate a set of faults to this component $ResistorFaultModes=\{OPEN, SHORT\}$\footnote{The failure modes of the resistor
are discussed in section~\ref{sec:resistorfm}.}. are discussed in section~\ref{sec:resistorfm}.}.
@ -1273,7 +1345,8 @@ each failure mode is referenced back to only one component. This constraint is d
%we are concerned with here.}, and will %we are concerned with here.}, and will
%not require a vendor reference, but must be named locally in the FMMD model. %not require a vendor reference, but must be named locally in the FMMD model.
We can term `modularising a system', to mean recursively breaking it into smaller sections for analysis. %We can term
By `modularising a system' we mean recursively breaking it into smaller sections for analysis.
% %
When modularising a system from the top~down, as in Fault Tree Analysis (FTA)~\cite{nasafta}\cite{nucfta} , When modularising a system from the top~down, as in Fault Tree Analysis (FTA)~\cite{nasafta}\cite{nucfta} ,
it is common to term the modules identified as sub-systems. it is common to term the modules identified as sub-systems.
@ -1330,10 +1403,13 @@ and is applied to specific failure modes in components and their probability of
Another top down methodology is to apply cost benefit analysis Another top down methodology is to apply cost benefit analysis
to determine which faults are the highest priority to fix~\cite{bfmea}. to determine which faults are the highest priority to fix~\cite{bfmea}.
% %
The aim of FMMD analysis is to produce complete failure The aim of FMMD analysis is to produce complete\footnote{Completeness dependent upon the completeness/correctness of the {\fms} supplied by the germane standard
for our {\bcs}.} failure
models of safety critical systems from the bottom-up, models of safety critical systems from the bottom-up,
starting where possible with known base~component failure~modes. starting where possible with known base~component failure~modes.
%
%
%
An advantage of working from the bottom up is that we can ensure that An advantage of working from the bottom up is that we can ensure that
all component failure modes must be considered. all component failure modes must be considered.
% %
@ -1341,58 +1417,6 @@ A top down approach
can miss individual failure modes of components~\cite{faa}[Ch.~9], can miss individual failure modes of components~\cite{faa}[Ch.~9],
especially where there are non-obvious top-level faults. especially where there are non-obvious top-level faults.
\subsection{FMMD Process in outline.}
In order to analyse from the bottom-up, we need to take
small groups of components that naturally
work together to perform a simple function.
%
The components to include in a {\fg} are chosen by hand.
%a human, the analyst.
%We can represent the `Functional~Group' as a class.
When we have a
`{\fg}' we can look at the components it contains,
and from this determine the failure modes of all the components that belong to it.
%
Initial {\fgs} will consist of {\bcs}.
%
% and determine a failure mode model for that group.
%
% expand 21sep2010
%The `{\fg}' as used by the analyst is a collection of component failures modes.
%The analysts interest is in the ways in which the components within the {\fg}
%can fail.
%
All the failure modes of all the components within a {\fg} are collected.
%
As each component %mode holds
has a set of failure modes associated with it,
the {\fg} represents a set of sets of failure modes.
%
We convert this
into a flat set
of failure modes for use in analysis.
%
A flat set is a set containing just the failure modes and not sets of failure modes~\cite{joyofsets}[p.8].
%
%In practical term each component failure mode is considered as a `failure~scenario' or 'test~case'
%for the {\fg}.
%
Each of these failure modes %, and optionally combinations of them, are
%formed into failure~scenarios which
are
analysed for their effect on the failure mode behaviour of the `{\fg}'.
%
Once we have the failure mode behaviour of the {\fg}, we can determine its symptoms of failure.
%,
%or the failure modes of the {\dc}.
%for the {\fg}.
%
We view these symptoms as derived failure modes of the {\fg}.
%
Or in other words we can determine how the `{\fg}' can fail.
We can now consider the {\fg} as a {\dc} % sort of super component
with its own set of failure modes.
\subsection{From functional group to newly derived component} \subsection{From functional group to newly derived component}
@ -1432,12 +1456,13 @@ with a known and traceable
fault behaviour. fault behaviour.
The UML representation (in figure \ref{fig:cfg}) shows a `{\fg}' having a one to one relationship with a derived~component. The UML representation (in figure \ref{fig:cfg}) shows a `{\fg}' having a one to one relationship with a derived~component.
%
The symbol $\derivec$ is used to indicate the analysis process that takes a The symbol $\derivec$ is used to indicate the analysis process that takes a
functional group and converts it into a new component. functional group and converts it into a new component.
\begin{definition} \begin{definition}
With $\mathcal{\FG}$ representing the set of all functional groups, and $\mathcal{{\DC}}$ the set of all derived components, With $\mathcal{\FG}$ representing the set of all functional groups (over all possible components),
this can be expressed as $$ \derivec : \mathcal{\FG} \rightarrow \mathcal{{\DC}} $$ . and $\mathcal{{\DC}}$ the set of all derived components,
we express the analysis process $\derivec$ as $$ \derivec : \mathcal{\FG} \rightarrow \mathcal{{\DC}} .$$
\end{definition} \end{definition}
\begin{figure}[h] \begin{figure}[h]
@ -1473,11 +1498,22 @@ represent the failure mode behaviour of the {\em INVAMP}.
% %
An analysis report is generated as part of the {\fg} to {\dc} An analysis report is generated as part of the {\fg} to {\dc}
process. %\footnote process. %\footnote
{By having an analysis report report for each analysis stage, i.e. {\fg} to {\dc}, By having an analysis report report for each analysis stage,
we add traceability to the reasoning applied to to the FMEA process.} %i.e. {\fg} to {\dc},
we add traceability to the reasoning applied to the FMEA process.
% %
Traditional FMEA has one large reasoning stage, that of component failure mode Consider that traditional FMEA has one large reasoning stage, that of component failure mode
directly to system level failure. directly to system level failure. The reasoning given is typically one line
on a spreadsheet entry~\cite{sccs}[p.38]. % (if we are lucky!).
%
FMMD typically has several reasoning stages from {\dc} {\fms} to system level failure modes.
Thus, each possible cause for a system {\fm} will have a collection of analysis reports associated with it.
%
These collections of analysis reports will provide a cause and effect
story for each possible scenario that could cause the system level failure.
%
This increases the traceability---or documented paper trail---for the understanding of the
failure event causes.
% %
We may now use the {\em INVAMP} {\dc} in even higher level {\fgs}. We may now use the {\em INVAMP} {\dc} in even higher level {\fgs}.
@ -1516,7 +1552,7 @@ a level 2 {\dc} ($\abslev=2$).
Because {\fgs} may include components at varying levels Because {\fgs} may include components at varying levels
of $\abslev$, having it quickly available as an attribute of $\abslev$, having it quickly available as an attribute
will be required in practical implementations will be required in practical implementations
to order the tree, and prevent recursion in the hierarchy. to order the tree, and assist in preventing recursion in the hierarchy.
The abstraction level concept is formally defined in section~\ref{sec:abstractionlevel}. The abstraction level concept is formally defined in section~\ref{sec:abstractionlevel}.
% \section{Set Theory Description} % \section{Set Theory Description}
@ -1541,55 +1577,55 @@ The abstraction level concept is formally defined in section~\ref{sec:abstractio
%%- the other parts were just fragments to illustrate points %%- the other parts were just fragments to illustrate points
%%- %%-
%%- %%-
\section{Complete UML Diagram} % \section{Complete UML Diagram}
%
In this section we examine the entities used in FMMD and their relationships. % In this section we examine the entities used in FMMD and their relationships.
We have been building parts of the data structure up until now, % We have been building parts of the data structure up until now,
and can now complete the picture. % and can now complete the picture.
For the complete UML data model we need to consider the system % For the complete UML data model we need to consider the system
as a data structure. % as a data structure.
%
%The `parts~list' is the %The `parts~list' is the
%key reference point and starting point. % in the data structure. %key reference point and starting point. % in the data structure.
%Our base components are kept here. %Our base components are kept here.
%
%From the {\bcs} the initial {\fgs} are formed, and from the first {\fgs}, %From the {\bcs} the initial {\fgs} are formed, and from the first {\fgs},
%the first {\dcs}. %the first {\dcs}.
\paragraph{Re-factoring the UML model to remove {\fgs}.}
While useful for describing the context of the FMMD analysis process,
it is desirable to remove the {\fg} from the UML diagram as this is by-product of the analysis process.
Figure~\ref{fig:cfg2} presents a final (and simpler) UML model for FMMD.
However, the analysis report, is a core feature of FMMD. Having an analysis
report associated with each incremental stage in the analysis is a strength
compared to traditional FMEA, where we only have one stage (possibly undocumented)
for each {\bc} {\fm} to system level event/failure mode.
The {\fg} and the analysis report have one to one relationships. We can therefore re-factor
these into an analysis report (which would list the components used to
make up and thus define the {\fg}) associated with the {\dc}.
% %
% Two other data types/entities are required % \paragraph{Re-factoring the UML model to remove {\fgs}.}
% however: we need to model environmental and operational states and % While useful for describing the context of the FMMD analysis process,
% where they fit into the data structure. % it is desirable to remove the {\fg} from the UML diagram as this is by-product of the analysis process.
% Figure~\ref{fig:cfg2} presents a final (and simpler) UML model for FMMD.
% However, the analysis report, is a core feature of FMMD. Having an analysis
% report associated with each incremental stage in the analysis is a strength
% compared to traditional FMEA, where we only have one stage (possibly undocumented)
% for each {\bc} {\fm} to system level event/failure mode.
% The {\fg} and the analysis report have one to one relationships. We can therefore re-factor
% these into an analysis report (which would list the components used to
% make up and thus define the {\fg}) associated with the {\dc}.
%
%
% % % %
% % Two other data types/entities are required
% % however: we need to model environmental and operational states and
% % where they fit into the data structure.
% \paragraph{UML Diagram Additional Objects.} % % %
% The additional objects System, Environment and Operational States %
% are added to UML diagram in figure \ref{fig:cfg} are represented in figure \ref{fig:cfg2}. %
%
\label{completeuml} % % \paragraph{UML Diagram Additional Objects.}
% % The additional objects System, Environment and Operational States
\begin{figure}[h] % % are added to UML diagram in figure \ref{fig:cfg} are represented in figure \ref{fig:cfg2}.
\centering %
\includegraphics[width=300pt,keepaspectratio=true]{./CH4_FMMD/master_uml.png} % \label{completeuml}
% cfg2.png: 702x464 pixel, 72dpi, 24.76x16.37 cm, bb=0 0 702 464 %
\caption{Complete UML diagram} % \begin{figure}[h]
\label{fig:cfg2} % \centering
\end{figure} % \includegraphics[width=300pt,keepaspectratio=true]{./CH4_FMMD/master_uml.png}
% % cfg2.png: 702x464 pixel, 72dpi, 24.76x16.37 cm, bb=0 0 702 464
% \caption{Complete UML diagram}
% \label{fig:cfg2}
% \end{figure}

2
submission_thesis/appendixes/algorithmic.tex
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@ -645,7 +645,7 @@ as a component with a known set of failure modes.
\paragraph{Enumerating abstraction levels} \paragraph{Enumerating abstraction levels}
\ref{sec:abstractionlevel} \label{sec:abstractionlevel}
We can assign an attribute of abstraction level $\abslev$ to We can assign an attribute of abstraction level $\abslev$ to
components, where $\abslev$ is a natural number, ($\abslev \in \mathbb{N}_0$). components, where $\abslev$ is a natural number, ($\abslev \in \mathbb{N}_0$).
For a base component, let the abstraction level be zero. For a base component, let the abstraction level be zero.

8
submission_thesis/style.tex
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@ -18,10 +18,10 @@
\usepackage{lastpage} \usepackage{lastpage}
\usetikzlibrary{shapes,snakes} \usetikzlibrary{shapes,snakes}
\newcommand{\tickYES}{\checkmark} \newcommand{\tickYES}{\checkmark}
%% FUCKING CUNTS \newcommand{\fc}{fault~scenario} %% \newcommand{\fc}{fault~scenario}
\newcommand{\fc}{fault~cause} \newcommand{\fc}{failure~cause}
%% FUCKING CUNTS \newcommand{\fcs}{fault~scenarios} %% \newcommand{\fcs}{fault~scenarios}
\newcommand{\fcs}{fault~causes} \newcommand{\fcs}{failure~causes}
% Page layout definitions to suit A4 paper % Page layout definitions to suit A4 paper
\setcounter{secnumdepth}{3} \setcounter{tocdepth}{4} \setcounter{secnumdepth}{3} \setcounter{tocdepth}{4}
\setlength{\topmargin}{0mm} \setlength{\topmargin}{0mm}