C Garret and J Howse proof readings

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@ -52,11 +52,13 @@
\section{Introduction}
This chapter
starts with %an overview of current failure modelling techniques, and then
a worked example using the new methodology,
considers %starts with %an overview of current failure modelling techniques, and then
a worked example to introduce % using
the new methodology,
Failure Mode Modular De-composition (FMMD).
This is followed by a discussion on the design of the FMMD methodology and then
an ontological description using UML class models.
This is followed by a discussion on the design of the FMMD methodology and then a
%an ontological
description using UML class models.
%A notation is then described to index and classify objects created in FMMD hierarchical models.
@ -459,7 +461,7 @@ commonly used circuit, the non-inverting op amp~\cite{aoe}[p.234], shown in fig
\begin{figure}[h+]
\centering
%\includegraphics[width=100pt,keepaspectratio=true]{../../noninvopamp/noninv.png}
\includegraphics[width=100pt,keepaspectratio=true]{./CH4_FMMD/noninv.png}
\includegraphics[width=300pt,keepaspectratio=true]{./CH4_FMMD/noninv.png}
% noninv.jpg: 341x186 pixel, 72dpi, 12.03x6.56 cm, bb=0 0 341 186
\caption{Standard non inverting amplifier configuration}
\label{fig:noninvamp}
@ -468,7 +470,8 @@ commonly used circuit, the non-inverting op amp~\cite{aoe}[p.234], shown in fig
The function of the resistors in this circuit is to set the amplifier gain.
They operate as a potential divider and program the minus input on the op-amp
They operate as a potential divider\footnote{The resistors act as a potential divider assuming the op-amp has high impedance.}
and program the inverting input on the op-amp
to balance them against the positive input, giving the voltage gain ($G_v$)
defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
@ -476,9 +479,10 @@ defined by $ G_v = 1 + \frac{R2}{R1} $ at the output.
\subsection{Potential Divider.}
\label{subsec:potdiv}
As the resistors work to provide a specific function, that of a potential divider,
we can treat them as a functional group. This functional group has two members, $R1$ and $R2$.
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 $R2$.
Using the EN298 specification for resistor failure~\cite{en298}[App.A],
we can assign failure modes of $OPEN$ and $SHORT$ to the resistors (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}).
We represent a resistor and its failure modes as a directed acyclic graph (DAG)
@ -503,29 +507,21 @@ We represent a resistor and its failure modes as a directed acyclic graph (DAG)
\end{figure}
Thus $R1$ has failure modes $\{R1\_OPEN, R1\_SHORT\}$ and $R2$ has failure modes $\{R2\_OPEN, R2\_SHORT\}$.
%
We look at each of these base component failure modes,
and determine how they affect the operation of the potential divider.
%Each failure mode scenario we look at will be given a test case number,
%which is represented on the diagram, with an asterisk marking
%which failure modes is modelling (see figure \ref{fig:fg1a}).
%
For this example we look at single failure modes only.
For each failure mode in our {\fg} `potential~divider',
we can assign a {\fc} number (see table \ref{tbl:pdfmea}).
Each {\fc} is analysed to determine the `symptom'
of the potential dividers' operation. For instance
if resistor $R_1$ was to go open, then the circuit 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).
This would mean the symptom of the failed potential divider would be that it
gives a high voltage output.%We can now consider the {\fg}
This would mean the symptom of the failed potential divider would be voltage high output.%We can now consider the {\fg}
%as a component in its own right, and its symptoms as its failure modes.
{ \small
@ -602,12 +598,14 @@ This is represented in the DAG in figure \ref{fig:fg1adag}.
\end{figure}
We can now make a `derived component' to represent this potential divider.
We can now formulate a `derived component' to represent this potential divider.
This can be named \textbf{PD}.
This {\dc} will have two failure modes.
We can use the symbol $\derivec$ to represent the process of taking the analysed
{\fg} and creating from it, a {\dc}. The creation of the {\dc} \textbf{PD} is
represented in figure~\ref{fig:dc1}.
We then represent the {\dc} as a DAG in figure \ref{fig:dc1dag}.
%We could represent it algebraically thus: $ \derivec(PotDiv) =
\begin{figure}[h+]
@ -617,7 +615,7 @@ represented in figure~\ref{fig:dc1}.
\caption{From functional group to derived component}
\label{fig:dc1}
\end{figure}
We then represent the {\dc} as a DAG in figure \ref{fig:dc1dag}.
% We can now represent the potential divider as a {\dc}.
% Because we have its symptoms (or failure mode behaviour),
@ -633,7 +631,7 @@ We then represent the {\dc} as a DAG in figure \ref{fig:dc1dag}.
\tikzstyle{failure}=[fmmde, fill=red!50];
\tikzstyle{symptom}=[fmmde, fill=blue!50];
\tikzstyle{annot} = [text width=4em, text centered]
\node[component] (PD) at (0,-0.8) {$PD$};
\node[component] (PD) at (0,-0.8) {{\em PD}};
\node[symptom] (PDHIGH) at (\layersep,-0) {$PD_{HIGH}$};
\node[symptom] (PDLOW) at (\layersep,-1.6) {$PD_{LOW}$};
\path (PD) edge (PDHIGH);
@ -655,11 +653,13 @@ We then represent the {\dc} as a DAG in figure \ref{fig:dc1dag}.
Let use 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):
latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
latch-up(12.5\%), latch-down(6\%), no-operation(31.3\%), low~slew~rate(50\%).
\nocite{mil1991}
%\ifthenelse {\boolean{dag}}
%{
\clearpage
We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
\begin{figure}[h+]
\centering
@ -694,8 +694,8 @@ We can represent these failure modes on a DAG (see figure~\ref{fig:op1dag}).
%}
%\clearpage
%\paragraph{Modelling the OP amp with the potential divider.}
We now merge the OP amp and the {\dc} $PD$, to
form a {\fg} to represent the non inverting amplifier.
We now merge the OP amp and the {\dc} {\em PD}, to
form a {\fg} to represent the non-inverting amplifier.
%
%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.
@ -730,10 +730,10 @@ and this is represented in table \ref{tbl:ampfmea1}.
FS4: $OPAMP$ & Low pass & LowPass \\
Low Slew & filtering & \\ \hline
FS5: $PD$ & Output High & AMPHigh \\
FS5: {\em PD} & Output High & AMPHigh \\
LowPD & & \\ \hline
FS6: $PD$ & Output Low & AMPLow \\
FS6: {\em PD} & Output Low & AMPLow \\
HighPD & Low Gain & \\ \hline
%TC7: $R_2$ OPEN & LOW & & LowPD \\ \hline
\hline
@ -871,9 +871,9 @@ and this is represented in table \ref{tbl:ampfmea1}.
%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).
For this amplifier configuration we have three failure modes; $AMPHigh, AMPLow, LowPass$.%see figure~\ref{fig:fgampb}.
For this amplifier configuration we have three failure modes; {\em AMP\_High, AMP\_Low, LowPass}.%see figure~\ref{fig:fgampb}.
This model now has two stages of analysis hierarchy, as represented in figure~\ref{fig:dc2}.
From the analysis in table \ref{tbl:ampfmea1} we can create the {\dc} $INVAMP$, 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.
\begin{figure}[h]
@ -884,11 +884,11 @@ represents the failure mode behaviour of the non-inverting amplifier.
\label{fig:dc2}
\end{figure}
We can now examine the {\dc} $INVAMP$ by drawing it as a DAG.
%expand the $PD$ {\dc} and have a full FMMD failure %mode
We can now examine the {\dc} {\em INVAMP} by drawing it as a DAG.
%expand the {\em PD} {\dc} and have a full FMMD failure %mode
%model
We can traverse this DAG, and thus determine all possible causes for
the three high level symptoms, i.e. the failure~modes of the non-inverting amplifier $INVAMP$.
the three high level symptoms, i.e. the failure~modes of the non-inverting amplifier {\em INVAMP}.
%
Figure \ref{fig:noninvdag1} shows a fully expanded DAG, from which we can derive information
to assist in building models for FTA, FMEA, FMECA and FMEDA failure mode analysis methodologies.
@ -952,7 +952,7 @@ Base Component & An atomic building block used at the lowest level of an FMMD mo
{\em Constraint} & This object must have a defined set of failure~modes. \\ \hline
Component & A building block, this may be a {\bc} or a sub-assembly. \\
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
@ -992,16 +992,18 @@ Failure Scenario & A single failure mode (or a combination), used to
\end{table}
\subsection{Parts, components and base components}
A component is anything we use to build a product or system.
It could be something quite complicated
like an integrated micro controller, or quite simple like the resistor.
\subsection{Parts, Components and Base Components.}
A component is anything we use to build %a product or
system.
It could be something %quite complicated
like an %integrated
micro-controller, or quite simple like the resistor.
%
We can define a
component by its name, a manufacturers' part number and perhaps
component by its name, a manufacturer's part number and perhaps
a vendor's reference number.
Geoffrey Hall, writing in Spacecraft Systems Engineering\cite{scse}[p.619]
Geoffrey Hall, writing in Spacecraft Systems Engineering~\cite{scse}[p.619]
defines a `part' thus
``{{Part(definition)}---The lowest level of assembly, beyond which further disassembly irrevocably destroys the item''.
@ -1018,14 +1020,15 @@ and say that we want to define an atomic entity. % used as a building block.
We define {\bc} to be the lowest level of component that we use as a building block.
This is a choice made by the analyst.
%
Both op-amps and transistors have published statistical failure rates and yet an op-amp is made out of transistors.
Both op-amps and transistors have published statistical failure rates and yet an op-amp is constructed from transistors.
%
However, a circuit designer would usually consider individual transistors and individual op-amps
as lowest level building blocks.
%
In fact any component with published failure modes could be considered to be a {\bc},
but this determination is the choice of the analyst, which may be influenced by the particular
standard~\cite{en298}~\cite{en61508}~\cite{en230} to which we are approving/analysing a system.
standard~\cite{en298}~\cite{en61508} %~\cite{en230}
to which we are approving/analysing a system.
%a lowest level of assembly `part' or an atomic entity, which ever is the smaller
%and component to mean either a part or a sub-assembly.
@ -1042,7 +1045,7 @@ A system, is any coherent entity that would be sold as a product. % safety criti
%
A component is a system that is a part of some larger system.
%
A modular system common in most 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.
%
@ -1074,7 +1077,7 @@ component failures (which can be missed in a top~down approach \cite{faa}[Ch.9])
we are presented with a problem. Which initial collections of base components should we choose?
%
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, all sorts!
a massive list of base~components, resistors, motors, user~switches, laser~diodes, etc.
Clearly, working from the bottom~up, we need to pick small
collections of components that work together in some way.
These collections are termed `{\fgs}'.
@ -1113,11 +1116,12 @@ 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
%1991 reliability manual\cite{mil1991} applies a FIT of 100 for this generic type of component}
Electrical components have detailed data-sheets associated with them. The data sheets
Electrical components have data-sheets associated with them. The data sheets
supply detailed information on the component as supplied by the manufacturer.
They rarely clearly detail the
%
Because they are design related they rarely rarely show %clearly detail the
failure modes of the component, with environmental factors and MTTF~\cite{sccs}[p.165] statistics.
Given the growing useage of FMEA/FMEDA in industry this may change.
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}.
@ -1167,7 +1171,7 @@ are discussed in section~\ref{sec:resistorfm}.}.
The UML class diagram in figure
\ref{fig:component} shows a component as a data
structure with its associated failure modes.
%
From this diagram we see that each component must have at least one failure mode.
To clearly show that the failure modes are mutually exclusive states, or unitary states associated with one component,
each failure mode is referenced back to only one component. This constraint is discussed in section~\ref{sec:unitarystate}.
@ -1233,7 +1237,7 @@ internally.
%
What we need to know are the symptoms of failure.
With these symptoms, we can trace their effects through the system under investigation
and determine outcomes.
and finally determine top-level failure events. % outcomes.
%
Different approval agencies may list different failure mode sets for the same generic components.
%
@ -1323,7 +1327,7 @@ Once we have the failure mode behaviour of the {\fg}, we can determine its sympt
We could term these symptoms the 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 sort of super component
We can now consider the {\fg} as a {\dc} % sort of super component
with its own set of failure modes.
@ -1337,15 +1341,15 @@ This
is dealt with in detail using an algorithmic description, in appendix \ref{sec:algorithmfmmd}.
% define difference between a \fg and a \dc
A {\fg} is a collection of components. A {\dc} is a new `theoretical'
component which has a set of failure modes,
corresponding to the failure symptoms from the {\fg} from which it was derived.
%
We now consider a {\dc} as a black box, or component
for use in further levels of analysis.
%, and in this case it would have a set of failure modes.
%Looking at the {\fg} in this way is seeing it as a {\dc}.
% % define difference between a \fg and a \dc
% A {\fg} is a collection of components. A {\dc} is a new `theoretical'
% component which has a set of failure modes,
% corresponding to the failure symptoms from the {\fg} from which it was derived.
% %
% We now consider a {\dc} as a black box, or component
% for use in further levels of analysis.
% %, and in this case it would have a set of failure modes.
% %Looking at the {\fg} in this way is seeing it as a {\dc}.
In terms of our UML model, the symptom abstraction process takes a {\fg}
and creates a new {\dc} from it.
@ -1360,7 +1364,8 @@ These failure modes are the failure mode behaviour---or symptoms---of the {\fg}
Because these new failure modes were derived from a {\fg}, we can call
these `derived~failure~modes'.
%It then creates a new derived~component object, and associates it to this new set of derived~failure~modes.
We thus have a `new' component, or system building block, but with a known and traceable
We thus have a `new' component, %or system building block, but
with a known and traceable
fault behaviour.
The UML representation (in figure \ref{fig:cfg}) shows a `{\fg}' having a one to one relationship with a derived~component.
@ -1374,7 +1379,7 @@ this can be expressed as $$ \derivec : \mathcal{\FG} \rightarrow \mathcal{{\DC
\begin{figure}[h]
\centering
\includegraphics[width=400pt,bb=0 0 712 286,keepaspectratio=true]{./CH4_FMMD/cfg.png}
\includegraphics[width=300pt,,keepaspectratio=true]{./CH4_FMMD/cfg.png}
% cfg.png: 712x286 pixel, 72dpi, 25.12x10.09 cm, bb=0 0 712 286
\caption{Basic UML Meta model for FMMD hierarchy}
\label{fig:cfg}
@ -1397,13 +1402,15 @@ The resistors are collected into a {\fg}, and the ${PD}$ derived component creat
As this derived component inherits the properties of a component, we may use
it in {\fg} higher in the hierarchy.
%
The $PD$ derived component is now placed into a {\fg}
The {\em PD} derived component is now placed into a {\fg}
with the op-amp.
%
This {\fg} is now analysed and a {\dc} created to
represent the failure mode behaviour of the $INVAMP$.
represent the failure mode behaviour of the {\em INVAMP}.
An analysis report is generated for each {\fg} to {\dc}
process.
%
We may now use the $INVAMP$ {\dc} in even higher level {\fgs}.
We may now use the {\em INVAMP} {\dc} in even higher level {\fgs}.
@ -1412,14 +1419,14 @@ We may now use the $INVAMP$ {\dc} in even higher level {\fgs}.
The UML meta model in figure \ref{fig:cfg}, shows the relationships
between the entities used in FMMD.
%
Note that because we can use derived components to build functional groups,
this model intrinsically supports % building a
hierarchy.
%
In use we will build a hierarchy of
objects, functional~groups formed with derived~components, and after symptom~abstraction creating
derived components yet higher up in the structure.
%
% Note that because we can use derived components to build functional groups,
% this model intrinsically supports % building a
% hierarchy.
% %
% In use we will build a hierarchy of
% objects, functional~groups formed with derived~components, and after symptom~abstraction creating
% derived components yet higher up in the structure.
% %
To keep track of the level in the hierarchy (i.e. how many stages of component
derivation `$\derivec$' have led to the current derived component)
we can add an attribute to the component data type.
@ -1433,8 +1440,14 @@ Derived~components take a level based on the highest level
component used to build the functional group it was derived from plus 1.
So a derived component built from base level components
would have an $\abslev$ value of 1.
%
In our example the resistors and op-amp are level zero ({\bcs}, $\abslev=0$), the {\em PD} a level 1 {\dc} ($\abslev=1$) and the {\em INVAMP}
a level 2 {\dc} ($\abslev=2$).
%\clearpage
Because {\fgs} may include components at varying levels
of $\abslev$, having it quickly available as an attribute
will be required in practical implementations
to order the tree, and prevent recursion in the hierarchy.
% \section{Set Theory Description}
@ -1464,84 +1477,40 @@ would have an $\abslev$ value of 1.
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,
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.
%The `parts~list' is the
%key reference point and starting point. % in the data structure.
%Our base components are kept here.
From the {\bcs} the initial {\fgs} are formed, and from the first {\fgs},
the first {\dcs}.
%
Two other data types/entities are required
however: we need to model environmental and operational states and
where they fit into the data structure.
%
A system will be expected to perform in a given environment.
%
Environment in the context of this study
means external influences under which the System could be expected to work. % under.
%
A typical data sheet for an electrical component will give
a working temperature range, for instance.
Mechanical components could be specified for stress and loading limits.
%From the {\bcs} the initial {\fgs} are formed, and from the first {\fgs},
%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}.
Systems may have distinct operational states. For instance, a safety critical controller
may have a LOCKOUT state where it has detected a serious problem and will not continue to operate until
authorised human intervention takes place.
A safety critical circuit may have a self test mode which could be operated externally.
%
Operational states and environmental conditions must be factored into the UML model.
\paragraph{Environmental Modelling.} The external influences/environment could typically be temperature ranges,
levels of electrical interference, high voltage contamination on supply
lines, radiation levels etc.
Environmental influences will affect specific components in specific ways.\footnote{A good example of a part
affected by environmental conditions, in this case temperature, is the opto-isolator~\cite{tlp181}
which is typically affected at around {60 \oc}. Most electrical components are more robust to temperature variations.}.
Environmental analysis is thus applicable to components.
Environmental influences, such as over stress due to voltage
can be eliminated by down-rating of components as discussed in section~\ref{sec:determine_fms}.
With given environmental constraints, we can therefore eliminate some failure modes from the model.
% 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{Operational states.}
Within the field of safety critical engineering, we often encounter
elements that include test or self-test facilities.
%
We also encounter degraded performance
(such as only performing functions in an emergency) and lockout/emergency conditions.
These can be broadly termed operational states. %, and apply to the
%functional groups.
%
We need to determine which UML class is most appropriate to hold a relationship
to operational states.
%
Consider for instance an electrical circuit that has a TEST line.
When the TEST line is activated, it supplies a test signal
which will validate the circuit. This circuit will have two operational states,
NORMAL and TEST mode.
%
It seems better to apply the operational states to {\fgs}.
%
Functional groupings by definition implement functionality, or purpose, and therefore are the best objects to model
operational states.% with.
\paragraph{Inhibit Conditions.}
A third data class may be required if modelling of inhibit conditions~\cite{nasatfa}[p.40] is desired.
Some failure modes may only be active given specific environmental conditions
or when other failures are already active.
To model this, an `inhibit' class has been added.
This is an optional attribute of
a failure mode. This inhibit class can be triggered
on a combination of environmental or failure modes.
\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}.
% \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}

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@ -3,7 +3,7 @@
#
# Place all .dia files here as .png targets
#
DIA =
DIA = master_uml_further_work.png
doc: $(DIA)
@ -20,5 +20,5 @@ doc: $(DIA)
copy:
copy: $(DIA)
echo $@

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@ -0,0 +1,86 @@
\section{Further Work}
\subsection{Environment, operational states and inhibit gates: additions to the UML model.}
FTA~\cite{nasafta,nucfta} models environmental, operational state and inhibit gates, and these can be incorporated into
the FMMD model.
A system will be expected to perform in a given environment.
%
Environment in the context of this study
means external influences under which the System could be expected to work. % under.
%
A typical data sheet for an electrical component will give
a working temperature range, for instance.
Mechanical components could be specified for stress and loading limits.
Systems may have distinct operational states. For instance, a safety critical controller
may have a LOCKOUT state where it has detected a serious problem and will not continue to operate until
authorised human intervention takes place.
A safety critical circuit may have a self test mode which could be operated externally.
%
Operational states and environmental conditions must be factored into the UML model.
\paragraph{Environmental Modelling.} The external influences/environment could typically be temperature ranges,
levels of electrical interference, high voltage contamination on supply
lines, radiation levels etc.
Environmental influences will affect specific components in specific ways.\footnote{A good example of a part
affected by environmental conditions, in this case temperature, is the opto-isolator~\cite{tlp181}
which is typically affected at around {60 \oc}. Most electrical components are more robust to temperature variations.}.
Environmental analysis is thus applicable to components.
Environmental influences, such as over stress due to voltage
can be eliminated by down-rating of components as discussed in section~\ref{sec:determine_fms}.
With given environmental constraints, we can therefore eliminate some failure modes from the model.
\paragraph{Operational states.}
Within the field of safety critical engineering, we often encounter
elements that include test or self-test facilities.
%
We also encounter degraded performance
(such as only performing functions in an emergency) and lockout/emergency conditions.
These can be broadly termed operational states. %, and apply to the
%functional groups.
%
We need to determine which UML class is most appropriate to hold a relationship
to operational states.
%
Consider for instance an electrical circuit that has a TEST line.
When the TEST line is activated, it supplies a test signal
which will validate the circuit. This circuit will have two operational states,
NORMAL and TEST mode.
%
It seems better to apply the operational states to {\fgs}.
%
Functional groupings by definition implement functionality, or purpose, and therefore are the best objects to model
operational states.% with.
\paragraph{Inhibit Conditions.}
A third data class may be required if modelling of inhibit conditions~\cite{nasatfa}[p.40] is desired.
Some failure modes may only be active given specific environmental conditions
or when other failures are already active.
To model this, an `inhibit' class has been added.
This is an optional attribute of
a failure mode. This inhibit class can be triggered
on a combination of environmental or failure modes.
\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{completeumlfurtherwork}
\begin{figure}[h]
\centering
\includegraphics[width=400pt,keepaspectratio=true]{./CH7_Conclusion/master_uml_further_work.png}
% cfg2.png: 702x464 pixel, 72dpi, 24.76x16.37 cm, bb=0 0 702 464
\caption{FMMD UML diagram, incorporating Environmental, Operational State and Inhibit gates}
\label{fig:cfg2}
\end{figure}

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@ -1,26 +0,0 @@
\section{Copy dot tex}
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@ -22,6 +22,6 @@ chapters_sub_make:
cd CH4_FMMD; make copy
cd CH5_Examples; make copy
cd CH6_Evaluation; make copy
cd CH7_Conculsion; make copy
cd CH7_Conclusion; make copy
#cd CH8_finsh_appendixes; make copy

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@ -40,7 +40,7 @@
\newcommand{\ohms}[1]{\ensuremath{#1\Omega}}
\newcommand{\fm}{\emp failure~mode}
\newcommand{\fms}{\emp failure~modes}
\newcommand{\FG}{\ensuremath{{G}}}
\newcommand{\FG}{\ensuremath{{FG}}}
\newcommand{\DC}{\ensuremath{{DC}}}
\newcommand{\fg}{\emp functional~grouping}
\newcommand{\fgs}{\emp functional~groupings}

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@ -69,7 +69,6 @@
\rhead{PhD Thesis}
%\begin{document}
%%% CH1_introduction CH2_FMEA CH3_FMEA_criticism CH4_FMMD CH5_Examples CH6_Evaluation CH7_Conculsion
%\typeout{>>--------------------->> introduction}
\chapter{Introduction}
\input{CH1_introduction/copy}
@ -90,7 +89,7 @@
\input{CH6_Evaluation/copy}
\chapter{Conclusion}
\input{CH7_Conculsion/copy}
\input{CH7_Conclusion/copy}
\appendix