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@ -391,51 +391,73 @@ and unused available zones.
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\section{Context, functional groups, failure modes and symptoms}
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\section{Context, functional groups, failure modes and symptoms}
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The intended application of these diagrams, is to model failure modes
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of collection of components, or {\fgs}. The aim is to
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create a derived component that represents the {\fg}.
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PLD diagrams are designed to aid this process.
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% Asterisks represent combinations of failure
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%modes. These are failure mode scenarios, or `test~cases'.
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\input{shortfg}
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\input{shortfg}
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\subsection{Symptom Collection}
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\subsection{Symptom Collection}
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\paragraph{Failure Mode Modular De-Composition (FMMD).}
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The methodology using these propositional logic diagrams is concerned with
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The methodology using these propositional logic diagrams is concerned with
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taking functional groups of components, analysing how the functional group
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taking functional groups of components, analysing how the functional group
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can fail, and then deriving a failure mode model for the functional group
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can fail, and then deriving a failure mode model for the functional group
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so that we can treat it as a component in its own right, or as a `derived component'
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so that we can treat it as a component in its own right, or as a `derived component'
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\paragraph{From component failure modes to {\fg} failure modes.}
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We represent the failure
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We represent the failure
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modes of the components within a {\fg} as contours in the diagram.
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modes of the components within a {\fg} as contours in the diagram.
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The test cases represent combinations of component failure modes
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The test cases represent combinations of component failure modes
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within the functional group.
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within the functional group. These are drawn as asterisks on the diagram.
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The test cases, when analysed can be grouped into $SMG$s.
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The SMG, Symptomatically merged group, is a collection of test
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cases where the failure symptom is the same.
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%
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%
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Each SMG
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The test cases, when analysed can be grouped into $SMG$s.
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The $SMG$, Symptomatically merged group, is a collection of test
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cases where their failure symptoms, from the perspective of the {\fg}, is the same.
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%
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Each $SMG$
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defines a failure mode behaviour of the functional group as though the
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defines a failure mode behaviour of the functional group as though the
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{\fg} were considered as a high level component.
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{\fg} were considered as a high level component.
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%
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%
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As we may be interested in treating the functional group
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As we may be interested in treating the functional group
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and a component to model higher levels of design, or failure mode abstraction,
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as a {\dc} to model higher levels of design, or failure mode abstraction,
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we can derive a new diagram from the $SMG$s. Each $SMG$ represents a failure
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we can derive a new diagram from the $SMG$s. Each $SMG$ represents a failure
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mode of the functional group, therefore in the higher level diagram
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mode of the functional group, therefore in the higher level diagram
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each SMG is represented by a contour.
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each $SMG$ is represented by a contour.
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{
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{
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\definition{
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\definition{
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\label{SMGderivation}
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\label{SMGderivation}
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%A diagram can be drawn to represent the collection of $SMG$s.
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%A diagram can be drawn to represent the collection of $SMG$s.
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The diagram $d$ represents $SMG$s as graphs of asterisks connected with joining lines.
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The diagram $d$ represents $SMG$s as graphs of asterisks connected with joining lines.
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A new diagram can be derived from this, replacing each SMG with a contour in the new diagram.
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A new diagram can be derived from this, replacing each $SMG$ with a contour in the new diagram.
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This diagram is at one higher level of failure~mode abstraction than the diagram that
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This diagram is at one higher level of failure~mode abstraction than the diagram that
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it was produced from.
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it was produced from.
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This diagram is the `symptom collection' diagram derived form $d$.
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This diagram is the `symptom collection' diagram derived form $d$.
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}
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}
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}
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}
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\subsection{Derived Component}
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\paragraph{Derived Component.}
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The diagram $d$ represents the failure modes of a functional group,
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The diagram $d$ represents the failure modes of a functional group,
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with the joining lines defining the its symptom collection.
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with the joining lines defining the its symptom collection.
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The `symptom collection' respresents the functional group
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The `symptom collection' represents the functional group
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at a higher level of failure mode abstraction. It represents the
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at a higher level of failure mode abstraction. That is to say,
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{\fg} as a higher level component, or {\textbf{derived component}}, with a defined set of failure modes.
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the contours in the new diagram represent the ways in which the {\fg} considered
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as an entity can fail. The new represents the
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{\fg} as a higher level component, or {\textbf{derived component}}, with its own set of failure modes.
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\ifthenelse {\boolean{paper}}
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{
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% ref symptom extraction process paper HERE
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}
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{
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Chapter \ref{chap:sympex} describes the symptom abstraction process, detailing algorithms and
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validation and consistency checks applied.
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}
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\section{Example Diagrams}
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\section{Example Diagrams}
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@ -503,7 +525,7 @@ sub-system failures, for instance two fuel shutdown safety valves failing to clo
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% reference gas shutoff valve closure example
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% reference gas shutoff valve closure example
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%
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%
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\clearpage
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%\clearpage
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\subsection { Logical XOR example }
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\subsection { Logical XOR example }
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\begin{figure}[h]
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\begin{figure}[h]
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@ -556,7 +578,7 @@ under analysis.
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\clearpage
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%\clearpage
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\subsection {Labels and usage}
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\subsection {Labels and usage}
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%In diagram \ref{fig:ld_meq} Z and W were labelled but were not necessary for the final expression
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%In diagram \ref{fig:ld_meq} Z and W were labelled but were not necessary for the final expression
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@ -624,7 +646,7 @@ of $ R = b \oplus c $.
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In failure analysis, this could be considered to be a functional~group with three failure states $a$,$b$ and $c$.
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In failure analysis, this could be considered to be a functional~group with three failure states $a$,$b$ and $c$.
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It has three SMG's Q,R and P. Thus there are three ways in which this functional~group is considered to fail.
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It has three SMG's Q,R and P. Thus there are three ways in which this functional~group is considered to fail.
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\clearpage
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%\clearpage
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@ -688,9 +710,10 @@ by the FMMD software tool.
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\clearpage
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%\clearpage
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\pagebreak[3]
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\subsection { Inhibit Failure }
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\subsection { Inhibit Failure }
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%
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%
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@ -914,6 +937,15 @@ The act of collecting common symptoms by joining lines is seen more intuitive
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than lists of logic equations. % seen as BY ME ! HA !
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than lists of logic equations. % seen as BY ME ! HA !
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It also neatly by-passes the problem of having test cases
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It also neatly by-passes the problem of having test cases
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which could inadvertently be placed into more than one $SMG$.
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which could inadvertently be placed into more than one $SMG$.
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\ifthenelse {\boolean{paper}}
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{
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% explain unitary state failure modes here? I'd rather not have to in the `paper' version.... 16MAR2011
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}
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{
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Having $SMG$s share test~cases would violate the concept of unitary state
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failure modes (see \ref{sec:unitarystate}).
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}
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Syntax checking (looking for contradictions and tautologies), as well as detecting
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Syntax checking (looking for contradictions and tautologies), as well as detecting
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errors of omission are automated in the FMMD tool.
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errors of omission are automated in the FMMD tool.
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@ -954,7 +986,7 @@ configuration is being termed \textbf{pair-wise intersection} of contours, in th
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A PLD editor can be set to ensure that each diagram has a test case for every
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A PLD editor can be set to ensure that each diagram has a test case for every
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double simultaneous failure instance.
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double simultaneous failure instance.
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\clearpage
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\pagebreak[3]
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\section{N Simultaneous Errors}
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\section{N Simultaneous Errors}
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There are systems where it may be necessary to model for N simultaneous failures.
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There are systems where it may be necessary to model for N simultaneous failures.
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@ -1013,4 +1045,5 @@ The test case AFE represents the condition where all four engines have failed \c
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%\theend
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%\theend
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%\pagebreak[4]
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\clearpage
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@ -23,8 +23,8 @@
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%\fancyfoot[LE,RO]{\thepage}
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%\fancyfoot[LE,RO]{\thepage}
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\cfoot{Page \thepage\ of \pageref{LastPage}}
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\cfoot{Page \thepage\ of \pageref{LastPage}}
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\rfoot{\today}
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\rfoot{\today}
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\lhead{Propositional Logic Diagram FMMD}
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\lhead{Propositional Logic Diagram }
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\rhead{FMMD - Failure Mode Modular De-Composition}
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% numbers at outer edges
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% numbers at outer edges
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\pagenumbering{arabic} % Arabic page numbers hereafter
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\pagenumbering{arabic} % Arabic page numbers hereafter
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\author{R.P.Clark}
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\author{R.P.Clark}
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@ -8,7 +8,7 @@ of components `functional groups'.
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%
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%
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For instance we may have a handful of components
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For instance we may have a handful of components
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brought together to perform a simple function
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brought together to perform a simple function
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like amplifying a signal or a power supply.
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like a `signal amplifier' or a `power supply'.
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%
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%
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The components in a {\fg} can be considered
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The components in a {\fg} can be considered
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to be `functionally~adjacent' to each other, in that
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to be `functionally~adjacent' to each other, in that
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