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@ -112,8 +112,8 @@ two different functional groups.
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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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type `K' have a de-graded performance
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\footnote{ A real world example of
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degraded performace with temperature is the isolating opto coupler.
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\footnote{A real world example of
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degraded performance 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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at high temperatures \cite{tlp181}.}
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failure mode between
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@ -149,7 +149,7 @@ The UML model shows the relationships between data types (or classes) that
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are used in the FMMD process.
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The purpose of failure mode analysis, is to tie SYSTEM level failures
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to their possible causes in the base components.
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By doing this accurate statistics can be obtained for SYSTEM level
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By doing this, accurate statistics can be obtained for SYSTEM level
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failures, and an insight into how we can make the system safer
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can be determined.
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In order to do this, we need to be able to trace the component
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@ -157,7 +157,7 @@ failure modes from the functional groups, to the symptoms
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they cause, and to the failure modes in the {\dcs}.
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We can use graph theory to represent this.
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As it would make no sense for a derived component to
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derive failure modes form itsself, we can apply an acyclic constraint
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derive failure modes from itself, we can apply an acyclic constraint
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to the graph. This means the graph must be a Directed Acylic
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Graph (DAG).
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@ -174,7 +174,7 @@ Graph (DAG).
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Consider the SYSTEM environment with its temperature range of ${{0}\oc}$ to ${{125}\oc}$.
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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, 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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to component type `K' under these temperature range conditions
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gives the following failure modes, $fm(K) =\{ K^0_a, K^0_b, K^0_d \}$.
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@ -691,7 +691,7 @@ This is shown in the DAG in figure \ref{fig:dag3}.
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\node[annot,right of=s](dcl) {Derived Component};
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\end{tikzpicture}
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% End of code
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\caption{DAG representing failure modes and symptoms $FG^0_1 \rightarrow C^1_1$ and $FG^0_2 \rightarrow C^1_2$}
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\caption{DAG representing failure modes and symptoms $FG^0_1 \rightarrow C^1_1$, $FG^0_2 \rightarrow C^1_2$ and $FG^0_3 \rightarrow C^1_3$}
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\label{fig:dag3}
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\end{figure}
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@ -734,6 +734,7 @@ TO RACE BACK DOWN THE DAG
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\def\layersep{2.0cm}
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\begin{figure}
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@ -863,13 +864,55 @@ TO RACE BACK DOWN THE DAG
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\path (s8) edge (DC-3);
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\node[failure, right of=DC-1] (as1) {$a_{s1}$};
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\node[failure, below of=as1] (as2) {$a_{s2}$}; % will this overwrite ?
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\node[failure] (as1) at (\layersep*4,-2) {$a_{s1}$};
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\node[failure] (bs2) at (\layersep*4,-3) {$b_{s2}$};
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\path (DC-1) edge (as1);
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\path (DC-1) edge (as2);
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\path (DC-1) edge (bs2);
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\node[failure, above of=DC-2] (as3) {$a_{s3}$}; % will this overwrite ?
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\node[failure] (as3) at (\layersep*4,-5) {$a_{s3}$};
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\node[failure] (bs4) at (\layersep*4,-6) {$b_{s3}$};
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\node[failure] (cs5) at (\layersep*4,-7) {$c_{s3}$};
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\path (DC-2) edge (as3);
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\path (DC-2) edge (bs4);
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\path (DC-2) edge (cs5);
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\node[failure] (as6) at (\layersep*4,-12) {$a_{s6}$};
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\node[failure] (bs7) at (\layersep*4,-13) {$b_{s7}$};
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\node[failure] (cs8) at (\layersep*4,-14) {$c_{s8}$};
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\path (DC-3) edge (as6);
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\path (DC-3) edge (bs7);
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\path (DC-3) edge (cs8);
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\node[symptom] (s9) at (\layersep*5,-5) {s9};
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\node[symptom] (s10) at (\layersep*5,-10) {s10};
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\node[symptom] (s11) at (\layersep*5,-13) {s11};
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\path (bs2) edge (s9);
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\path (as1) edge (s10);
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\path (as3) edge (s10);
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\path (bs4) edge (s10);
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\path (as6) edge (s10);
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\path (bs7) edge (s10);
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% Single component failures causing same error in tree
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\path (cs5) edge (s11);
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\path (cs8) edge (s11);
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\node[component,right of=s10] (DC2-1) {$C^2_1$};
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\path (s9) edge (DC2-1);
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\path (s10) edge (DC2-1);
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\path (s11) edge (DC2-1);
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\node[failure] (as9) at (\layersep*7,-9) {$a_{s9}$};
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\node[failure] (as10) at (\layersep*7,-10) {$b_{s12}$};
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\node[failure] (as11) at (\layersep*7,-11) {$c_{s11}$};
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\path (DC2-1) edge (as9);
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\path (DC2-1) edge (as10);
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\path (DC2-1) edge (as11);
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% Connect every node in the hidden layer with the output layer
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%\foreach \source in {1,...,5}
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@ -879,10 +922,15 @@ TO RACE BACK DOWN THE DAG
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\node[annot,above of=C-1a, node distance=1cm] (hl) {Failure modes};
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\node[annot,left of=hl] {Base Components};
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\node[annot,right of=hl](s) {Symptoms};
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\node[annot,right of=s](dcl) {Derived Component};
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\node[annot,right of=s](dcl) {Derived Components};
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\node[annot,right of=dcl](dcf) {Derived Component Failure Modes};
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\node[annot,right of=dcf](S2s) {Symptoms};
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\node[annot,right of=S2s](DC2) {Derived Components};
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\node[annot,right of=DC2](dc2f) {Derived Component Failure Modes};
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\end{tikzpicture}
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% End of code
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\caption{DAG representing failure modes and symptoms $FG^0_1 \rightarrow C^1_1$ and $FG^0_2 \rightarrow C^1_2$}
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\caption{DAG representing failure modes and symptoms $FG^1_1 \rightarrow C^2_1$}
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\label{fig:dag3}
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\end{figure}
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@ -893,9 +941,26 @@ Show how the hierarchy can be represented as a DAG
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draw a dag
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\subsection{Inhibit Conditions represented in the DAG}
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Inhibit node type. Octagon (to follow example from FTA).
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a -> OCT
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inhibitcond--
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\subsection{Failure Mode Conjuction Conditions represented in the DAG}
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White filled node with an \& in it.
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\subsection{Traversing the datamodel}
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Show how we can find multiple causes for a SYSTEM level error
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Show how we can find multiple causes for a SYSTEM level error.
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Constrast this to the bottom-up approaches of FMEA, FMECA and FMEDA where
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without necessarily knowing complex interactions between
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functionally adjacent components, we must take each component failure
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mode and tie to to a SYSTEM level failure.
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\subsubsection{Common mode failure detection}
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