...
This commit is contained in:
Robin Clark
parent
bcd8de0d7e
commit
7d0532fdf2
@ -399,6 +399,125 @@ and let us say new symptom s5 can be caused by failure mode $\{K_{4 a} \}$.
|
||||
We can create a derived component $DC^1_2$ using
|
||||
$\bowtie fm(FG^0_2) = DC^1_2$.
|
||||
Applying $fm$ to our {\dcs} gives $fm(DC^1_2) = \{ s3,s4,s5 \}$.
|
||||
We can respresent this in the DAG in figure \ref{fig:dag2}.
|
||||
|
||||
|
||||
%
|
||||
% DAG INCLUDING DC^1_2
|
||||
%
|
||||
|
||||
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
|
||||
\tikzstyle{every pin edge}=[<-,shorten <=1pt]
|
||||
\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt]
|
||||
\tikzstyle{component}=[fmmde, fill=green!50];
|
||||
\tikzstyle{failure}=[fmmde, fill=red!50];
|
||||
\tikzstyle{symptom}=[fmmde, fill=blue!50];
|
||||
\tikzstyle{annot} = [text width=4em, text centered]
|
||||
|
||||
% Draw the input layer nodes
|
||||
%\foreach \name / \y in {1,...,4}
|
||||
% This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4}
|
||||
% \node[component, pin=left:Input \#\y] (I-\name) at (0,-\y) {};
|
||||
|
||||
\node[component] (C-1) at (0,-1) {$C^0_1$};
|
||||
\node[component] (C-2) at (0,-3) {$C^0_2$};
|
||||
\node[component] (C-3) at (0,-5) {$C^0_3$};
|
||||
\node[component] (K-4) at (0,-8) {$K^0_4$};
|
||||
%\node[component] (C-5) at (0,-10) {$C^0_5$};
|
||||
%\node[component] (C-6) at (0,-12) {$C^0_6$};
|
||||
%\node[component] (K-7) at (0,-15) {$K^0_7$};
|
||||
|
||||
% Draw the hidden layer nodes
|
||||
%\foreach \name / \y in {1,...,5}
|
||||
% \path[yshift=0.5cm]
|
||||
\node[failure] (C-1a) at (\layersep,-1) {a};
|
||||
\node[failure] (C-1b) at (\layersep,-2) {b};
|
||||
\node[failure] (C-2a) at (\layersep,-3) {a};
|
||||
\node[failure] (C-2b) at (\layersep,-4) {b};
|
||||
\node[failure] (C-3a) at (\layersep,-5) {a};
|
||||
\node[failure] (C-3b) at (\layersep,-6) {b};
|
||||
\node[failure] (K-4a) at (\layersep,-7) {a};
|
||||
\node[failure] (K-4b) at (\layersep,-8) {b};
|
||||
\node[failure] (K-4d) at (\layersep,-9) {d};
|
||||
|
||||
% Draw the output layer node
|
||||
|
||||
% Connect every node in the input layer with every node in the
|
||||
% hidden layer.
|
||||
%\foreach \source in {1,...,4}
|
||||
% \foreach \dest in {1,...,5}
|
||||
\path (C-1) edge (C-1a);
|
||||
\path (C-1) edge (C-1b);
|
||||
\path (C-2) edge (C-2a);
|
||||
\path (C-2) edge (C-2b);
|
||||
\path (C-3) edge (C-3a);
|
||||
\path (C-3) edge (C-3b);
|
||||
\path (K-4) edge (K-4a);
|
||||
\path (K-4) edge (K-4b);
|
||||
\path (K-4) edge (K-4d);
|
||||
|
||||
%\node[symptom,pin={[pin edge={->}]right:Output}, right of=C-1a] (O) {};
|
||||
\node[symptom, right of=C-1a] (s1) {s1};
|
||||
\node[symptom, right of=C-2a] (s2) {s2};
|
||||
\node[symptom, right of=C-3a] (s3) {s3};
|
||||
\node[symptom, right of=C-3b] (s4) {s4};
|
||||
\node[symptom, right of=K-4b] (s5) {s5};
|
||||
|
||||
|
||||
|
||||
\path (C-2b) edge (s1);
|
||||
\path (C-1a) edge (s1);
|
||||
|
||||
\path (C-2a) edge (s2);
|
||||
\path (C-1b) edge (s2);
|
||||
|
||||
\path (C-1a) edge (s3);
|
||||
\path (C-3b) edge (s3);
|
||||
\path (K-4b) edge (s3);
|
||||
|
||||
\path (C-1b) edge (s4);
|
||||
\path (C-3a) edge (s4);
|
||||
\path (K-4d) edge (s4);
|
||||
|
||||
\path (K-4a) edge (s5);
|
||||
|
||||
\node[component, right of=s1] (DC-1) {$C^1_1$};
|
||||
\node[component, right of=s4] (DC-2) {$C^1_2$};
|
||||
|
||||
\path (s1) edge (DC-1);
|
||||
\path (s2) edge (DC-1);
|
||||
|
||||
\path (s3) edge (DC-2);
|
||||
\path (s4) edge (DC-2);
|
||||
\path (s5) edge (DC-2);
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
% Connect every node in the hidden layer with the output layer
|
||||
%\foreach \source in {1,...,5}
|
||||
% \path (H-\source) edge (O);
|
||||
|
||||
% Annotate the layers
|
||||
\node[annot,above of=C-1a, node distance=1cm] (hl) {Failure modes};
|
||||
\node[annot,left of=hl] {Base Components};
|
||||
\node[annot,right of=hl](s) {Symptoms};
|
||||
\node[annot,right of=s](dcl) {Derived Component};
|
||||
\end{tikzpicture}
|
||||
% End of code
|
||||
\caption{DAG representing failure modes and symptoms $FG^0_1 \rightarrow DC^1_1$ and $FG^0_2 \rightarrow DC^1_2$}
|
||||
\label{fig:dag2}
|
||||
\end{figure}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\paragraph{Applying FMMD $\bowtie fm(FG^0_3) $ :}
|
||||
@ -410,16 +529,193 @@ We can create a derived component $DC^1_3$ using
|
||||
$\bowtie fm(FG^0_3) = DC^1_3$
|
||||
where $fm(DC^1_3) = \{ s6,s7,s8 \}$.
|
||||
|
||||
We can now represent the first stage of FMMD, all base component
|
||||
failure modes analysed and our first set of derived components determined.
|
||||
This is shown in the DAG in figure \ref{fig:dag3}.
|
||||
|
||||
\pagebreak[4]
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{tikzpicture}[shorten >=1pt,->,draw=black!50, node distance=\layersep]
|
||||
\tikzstyle{every pin edge}=[<-,shorten <=1pt]
|
||||
\tikzstyle{fmmde}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt]
|
||||
\tikzstyle{component}=[fmmde, fill=green!50];
|
||||
\tikzstyle{failure}=[fmmde, fill=red!50];
|
||||
\tikzstyle{symptom}=[fmmde, fill=blue!50];
|
||||
\tikzstyle{annot} = [text width=4em, text centered]
|
||||
|
||||
% Draw the input layer nodes
|
||||
%\foreach \name / \y in {1,...,4}
|
||||
% This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4}
|
||||
% \node[component, pin=left:Input \#\y] (I-\name) at (0,-\y) {};
|
||||
|
||||
\node[component] (C-1) at (0,-1) {$C^0_1$};
|
||||
\node[component] (C-2) at (0,-3) {$C^0_2$};
|
||||
\node[component] (C-3) at (0,-5) {$C^0_3$};
|
||||
\node[component] (K-4) at (0,-8) {$K^0_4$};
|
||||
\node[component] (C-5) at (0,-10) {$C^0_5$};
|
||||
\node[component] (C-6) at (0,-12) {$C^0_6$};
|
||||
\node[component] (K-7) at (0,-15) {$K^0_7$};
|
||||
|
||||
% Draw the hidden layer nodes
|
||||
%\foreach \name / \y in {1,...,5}
|
||||
% \path[yshift=0.5cm]
|
||||
\node[failure] (C-1a) at (\layersep,-1) {a};
|
||||
\node[failure] (C-1b) at (\layersep,-2) {b};
|
||||
\node[failure] (C-2a) at (\layersep,-3) {a};
|
||||
\node[failure] (C-2b) at (\layersep,-4) {b};
|
||||
\node[failure] (C-3a) at (\layersep,-5) {a};
|
||||
\node[failure] (C-3b) at (\layersep,-6) {b};
|
||||
\node[failure] (K-4a) at (\layersep,-7) {a};
|
||||
\node[failure] (K-4b) at (\layersep,-8) {b};
|
||||
\node[failure] (K-4d) at (\layersep,-9) {d};
|
||||
|
||||
|
||||
\node[failure] (C-5a) at (\layersep,-10) {a};
|
||||
\node[failure] (C-5b) at (\layersep,-11) {b};
|
||||
\node[failure] (C-6a) at (\layersep,-12) {a};
|
||||
\node[failure] (C-6b) at (\layersep,-13) {b};
|
||||
\node[failure] (K-7a) at (\layersep,-15) {a};
|
||||
\node[failure] (K-7b) at (\layersep,-16) {b};
|
||||
\node[failure] (K-7d) at (\layersep,-17) {d};
|
||||
|
||||
% Draw the output layer node
|
||||
|
||||
% Connect every node in the input layer with every node in the
|
||||
% hidden layer.
|
||||
%\foreach \source in {1,...,4}
|
||||
% \foreach \dest in {1,...,5}
|
||||
\path (C-1) edge (C-1a);
|
||||
\path (C-1) edge (C-1b);
|
||||
\path (C-2) edge (C-2a);
|
||||
\path (C-2) edge (C-2b);
|
||||
\path (C-3) edge (C-3a);
|
||||
\path (C-3) edge (C-3b);
|
||||
\path (K-4) edge (K-4a);
|
||||
\path (K-4) edge (K-4b);
|
||||
\path (K-4) edge (K-4d);
|
||||
|
||||
\path (C-5) edge (C-5a);
|
||||
\path (C-5) edge (C-5b);
|
||||
\path (C-6) edge (C-6a);
|
||||
\path (C-6) edge (C-6b);
|
||||
\path (K-7) edge (K-7a);
|
||||
\path (K-7) edge (K-7b);
|
||||
\path (K-7) edge (K-7d);
|
||||
|
||||
%\node[symptom,pin={[pin edge={->}]right:Output}, right of=C-1a] (O) {};
|
||||
\node[symptom, right of=C-1a] (s1) {s1};
|
||||
\node[symptom, right of=C-2a] (s2) {s2};
|
||||
|
||||
\node[symptom, right of=C-3a] (s3) {s3};
|
||||
\node[symptom, right of=C-3b] (s4) {s4};
|
||||
\node[symptom, right of=K-4b] (s5) {s5};
|
||||
|
||||
|
||||
\node[symptom, right of=C-5a] (s6) {s6};
|
||||
\node[symptom, right of=C-6b] (s7) {s7};
|
||||
\node[symptom, right of=K-7b] (s8) {s8};
|
||||
|
||||
\path (C-2b) edge (s1);
|
||||
\path (C-1a) edge (s1);
|
||||
|
||||
\path (C-2a) edge (s2);
|
||||
\path (C-1b) edge (s2);
|
||||
|
||||
\path (C-1a) edge (s3);
|
||||
\path (C-3b) edge (s3);
|
||||
\path (K-4b) edge (s3);
|
||||
|
||||
\path (C-1b) edge (s4);
|
||||
\path (C-3a) edge (s4);
|
||||
\path (K-4d) edge (s4);
|
||||
|
||||
\path (K-4a) edge (s5);
|
||||
|
||||
|
||||
|
||||
\path (C-5a) edge (s6);
|
||||
\path (C-6b) edge (s6);
|
||||
\path (K-7b) edge (s6);
|
||||
|
||||
\path (C-5b) edge (s7);
|
||||
\path (C-6a) edge (s7);
|
||||
\path (K-7d) edge (s7);
|
||||
|
||||
\path (K-7a) edge (s8);
|
||||
|
||||
|
||||
\node[component, right of=s1] (DC-1) {$C^1_1$};
|
||||
\node[component, right of=s4] (DC-2) {$C^1_2$};
|
||||
\node[component, right of=s7] (DC-3) {$C^1_3$};
|
||||
|
||||
\path (s1) edge (DC-1);
|
||||
\path (s2) edge (DC-1);
|
||||
|
||||
\path (s3) edge (DC-2);
|
||||
\path (s4) edge (DC-2);
|
||||
\path (s5) edge (DC-2);
|
||||
|
||||
\path (s6) edge (DC-3);
|
||||
\path (s7) edge (DC-3);
|
||||
\path (s8) edge (DC-3);
|
||||
|
||||
|
||||
% Connect every node in the hidden layer with the output layer
|
||||
%\foreach \source in {1,...,5}
|
||||
% \path (H-\source) edge (O);
|
||||
|
||||
% Annotate the layers
|
||||
\node[annot,above of=C-1a, node distance=1cm] (hl) {Failure modes};
|
||||
\node[annot,left of=hl] {Base Components};
|
||||
\node[annot,right of=hl](s) {Symptoms};
|
||||
\node[annot,right of=s](dcl) {Derived Component};
|
||||
\end{tikzpicture}
|
||||
% End of code
|
||||
\caption{DAG representing failure modes and symptoms $FG^0_1 \rightarrow DC^1_1$ and $FG^0_2 \rightarrow DC^1_2$}
|
||||
\label{fig:dag3}
|
||||
\end{figure}
|
||||
|
||||
|
||||
|
||||
|
||||
\clearpage
|
||||
%\pagebreak[4]
|
||||
\subsection{Using Derived Components in Functional Groups}
|
||||
|
||||
The DAG we have in figure \ref{fig:dag3} does not yet give us SYSTEM or `top~level'
|
||||
failure modes.
|
||||
We can apply $fm$ to the derived components and
|
||||
this returns the failure modes. We can notate
|
||||
these with $a$ and $b$ etc as before, but can give them
|
||||
a subscript representing the symptom they were sourced from thus:
|
||||
$$ fm(DC^1_1) = \{ a_{s1}, b_{s2} \}, $$
|
||||
$$ fm(DC^1_2) = \{ a_{s3}, b_{s4}, c_{s5} \}, $$
|
||||
$$ fm(DC^1_3) = \{ a_{s6}, b_{s7}, c_{s8} \}. $$
|
||||
|
||||
HERE show how the hierarchy is built, how the inheritance works etc
|
||||
In order to determine SYSTEM level symptoms, we need to
|
||||
use the derived components to form a higher level functional
|
||||
group and analyse that.
|
||||
|
||||
HAVE an example. totally theoretical. HAVE Common mode failure detection AND Common dependency detection
|
||||
For the sake of example, let us assume that we
|
||||
can use all three derived components to
|
||||
create a top~level functional group.
|
||||
|
||||
\subsection{Directed Acyclic Graph}
|
||||
Let
|
||||
$ FG^1_1 = \{ DC^1_1, DC^1_1, DC^1_1 \} $.
|
||||
|
||||
Applying $fm(FG^1_1) = \{ a_{s1}, b_{s2}, a_{s3}, b_{s4}, c_{s5}, a_{s6}, b_{s7}, c_{s8} \}$.
|
||||
To get our system level derived component we can apply $ \bowtie fm(FG^1_1) = DC^2_1 $.
|
||||
|
||||
NOW THINK ABOUT THIS
|
||||
|
||||
NEED INTERESTING FAULTS
|
||||
|
||||
TO RACE BACK DOWN THE DAG
|
||||
|
||||
|
||||
|
||||
\section{Directed Acyclic Graph}
|
||||
|
||||
Show how the hierarchy can be represented as a DAG
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user