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%% What I have done
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%% What I have done
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%%
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%%
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This paper presents a simple two level Failure Mode Modular De-Composition (FMMD)
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This paper presents a simple two level Failure Mode Modular De-Composition (FMMD)
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model of a theoretical System.
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model of a theoretical system.
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Firstly a UML model is presented and the class relationships described.
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Firstly a UML model is presented and the class relationships described.
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Secondly the theoretical model is developed and analysed.
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Secondly the theoretical model is developed and analysed.
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This model is then represented as a Directed Acyclic Graph (DAG),
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This model is then represented as a Directed Acyclic Graph (DAG),
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@ -39,7 +39,7 @@ if they have multiple causes.
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This chapter
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This chapter
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presents a simple two stage FMMD % Failure Mode Modular De-Composition (FMMD)
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presents a simple two stage FMMD % Failure Mode Modular De-Composition (FMMD)
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model of a theoretical System.
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model of a theoretical system.
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The Analysis model is then represented as a Directed Acyclic Graph (DAG), of the {\fg}s
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The Analysis model is then represented as a Directed Acyclic Graph (DAG), of the {\fg}s
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components and failure modes represented in it.
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components and failure modes represented in it.
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@ -71,7 +71,7 @@ We can start with some base components, of types C and K say, $\{ C_1, C_2, C_3
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\input{./shortfm}
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\input{./shortfm}
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\paragraph{Determing Failure Mode collections.}
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\paragraph{Determining Failure Mode collections.}
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Thus applying the function $fm$ to any of the components
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Thus applying the function $fm$ to any of the components
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gives error modes identified by a or b.
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gives error modes identified by a or b.
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@ -109,18 +109,18 @@ the functional groups $FG^0_1$ and $FG^1_1$.
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Also note that the component type $K$ has been used by
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Also note that the component type $K$ has been used by
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two different functional groups.
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two different functional groups.
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For the sake of example let our temperature environment
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For the sake of example, let our temperature environment
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for the SYSTEM be ${{0}\oc}$ to ${{125}\oc}$, but let the component
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for the SYSTEM be ${{0}\oc}$ to ${{125}\oc}$, but let the component
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type `K' have a de-graded performance failure mode between
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type `K' have a de-graded performance failure mode between
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${{80}\oc}$ and ${{125}\oc}$\footnote{ A real world example of
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${{80}\oc}$ and ${{125}\oc}$\footnote{ A real world example of
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degraded performace with temperature is the isolating opto coupler.
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degraded performace with temperature is the isolating opto coupler.
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These can typically only cope with lower baud rate ranges
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These can typically only cope with lower baud rate ranges
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at high temperatures \cite{tlp181}.}. We can term this
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at high temperatures \cite{tlp181}.}. We can term this
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degraded performce of component `K' as failure mode `d'.
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degraded performance of component `K' as failure mode `d'.
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\paragraph{Symptom Extraction.}
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\paragraph{Symptom Extraction.}
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A processes of symptom extraction is now applied to the functional groups.
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A process of symptom extraction is now applied to the functional groups.
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Again for the sake of example, let us say that each functional
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Again for the sake of example, let us say that each functional
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group has one or two symptoms again subscripted by $a$ and $b$.
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group has one or two symptoms again subscripted by $a$ and $b$.
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@ -157,7 +157,7 @@ We must check this against all components used.
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For our example, we component `K' which has an extra
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For our example, we component `K' which has an extra
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failure mode for degraded performance `d'. Thus applying the function $fm$
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failure mode for degraded performance `d'. Thus applying the function $fm$
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to component type `K' under these temperature range conditions
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to component type `K' under these temperature range conditions
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give the foillowing failure modes, $fm{K} =\{ K_a, K_b, K_d \}$.
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gives the following failure modes, $fm{K} =\{ K_a, K_b, K_d \}$.
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Were our system specified for a ${{0}\oc}$ to ${{80}\oc}$ range
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Were our system specified for a ${{0}\oc}$ to ${{80}\oc}$ range
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we could say $fm{K} =\{ K_a, K_b \}$.
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we could say $fm{K} =\{ K_a, K_b \}$.
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@ -179,7 +179,7 @@ We can call these failures modes `symptoms'.
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As this is a theoretical example, we shall have to skip this step\footnote{
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As this is a theoretical example, we shall have to skip this step\footnote{
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In a real analysis this would involve evaluating the effect of each components failure mode, (or combinations of)
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In a real analysis this would involve evaluating the effect of each components failure mode, (or combinations of)
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on the performance of the {\fg}.}.
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on the performance of the {\fg}.}.
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The next stage is to collect the common symptoms, or the symtoms that
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The next stage is to collect the common symptoms, or the symptoms that
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are the same {\em from the perspective of a user of the {\fg}}.
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are the same {\em from the perspective of a user of the {\fg}}.
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We can define this stage as the function $\bowtie$ which has a set of failure modes as
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We can define this stage as the function $\bowtie$ which has a set of failure modes as
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its range and {\dc} as its domain.
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its range and {\dc} as its domain.
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@ -234,7 +234,7 @@ UML OBJECT MODEL OF DERIVED COMPONENT TOO
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\subsection{Using Derived Components in Functional Groups}
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\subsection{Using Derived Components in Functional Groups}
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HERE should how the hierarchy is built, how the inheritance works etc
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HERE show how the hierarchy is built, how the inheritance works etc
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HAVE an example. totally theoretical. HAVE Common mode failure detection AND Common dependency detection
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HAVE an example. totally theoretical. HAVE Common mode failure detection AND Common dependency detection
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\ifthenelse {\boolean{paper}}
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\ifthenelse {\boolean{paper}}
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{
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{
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\paragraph{Failure Mode function $fm$.}
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\paragraph{Failure Mode function $fm$.}
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We can definine a `failure modes' function $fm$ that has a functional group as its range
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We can define a `failure modes' function $fm$ that has a functional group as its range
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and returns a set of failure modes as its domain.
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and returns a set of failure modes as its domain.
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We now use this to determine the failure modes
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We now use this to determine the failure modes
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in our functional groups.
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in our functional groups.
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