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more work writing up dag

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inhibit and conjuction of failure modes needs
to be tackled here and in the PLD diagram.

Refs needs to be put in the design of methodology too
This commit is contained in:
Robin Clark 2010-12-02 15:33:46 +00:00
parent ea108b30a6
commit 56bd6c599d
2 changed files with 58 additions and 11 deletions
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42
fmmd_data_model/fmmd_data_model.tex
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@ -515,13 +515,6 @@ We can respresent this in the DAG in figure \ref{fig:dag2}.
\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};
@ -544,6 +537,13 @@ Let us say new symptom s6 can be caused by failure modes $\{C_{5 a}, C_{6 b}, K
, let us say new symptom s7 can be caused by failure modes $\{C_{5 b}, C_{6 a}, K_{7 d} \}$
and let us say new symptom s8 can be caused by failure mode $\{K_{7 a} \}$.
%xrightarrow{\hspace*{3cm}}
We can represent this using a relationship $\stackrel{Collect Symptoms}{\longrightarrow}$, thus:
$$ \{ C_{5 a}, C_{6 b}, K_{4 b} \} \stackrel{Collect Symptoms}{\longrightarrow} S6, $$
$$ \{ C_{5 b}, C_{6 a}, K_{7 d} \} \stackrel{Collect Symptoms}{\longrightarrow} S7, $$
$$ \{ K_{7 a} \} \stackrel{Collect Symptoms}{\longrightarrow} S8. $$
We can create a derived component $C^1_3$ using
$\bowtie fm(FG^0_3) = C^1_3$
where $fm(C^1_3) = \{ s6,s7,s8 \}$.
@ -698,7 +698,7 @@ This is shown in the DAG in figure \ref{fig:dag3}.
%\clearpage
\clearpage
%\pagebreak[4]
\subsection{Using Derived Components in Functional Groups}
@ -708,6 +708,9 @@ 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:
%$$ fm(C^1_1) = \{ a^0_{s1}, b^0_{s2} \}, $$
%$$ fm(C^1_2) = \{ a^0_{s3}, b^0_{s4}, c^0_{s5} \}, $$
%$$ fm(C^1_3) = \{ a^0_{s6}, b^0_{s7}, c^0_{s8} \}. $$
$$ fm(C^1_1) = \{ a_{s1}, b_{s2} \}, $$
$$ fm(C^1_2) = \{ a_{s3}, b_{s4}, c_{s5} \}, $$
$$ fm(C^1_3) = \{ a_{s6}, b_{s7}, c_{s8} \}. $$
@ -716,15 +719,32 @@ In order to determine SYSTEM level symptoms, we need to
use the derived components to form a higher level functional
group and analyse that.
%\clearpage
For the sake of example, let us assume that we
can use all three derived components to
create a top~level functional group.
Let
$ FG^1_1 = \{ C^1_1, C^1_1, C^1_1 \} $.
$ FG^1_1 = \{ C^1_1, C^1_2, C^1_3 \} $.
Applying $fm(FG^1_1) = \{ a_{s1}, b_{s2}, a_{s3}, b_{s4}, c_{s5}, a_{s6}, b_{s7}, c_{s8} \}$.
Applying $fm(FG_1) = \{ a_{s1}, b_{s2}, a_{s3}, b_{s4}, c_{s5}, a_{s6}, b_{s7}, c_{s8} \}$.
%Applying $fm(FG^1_1) = \{ a^1_{s1}, b^1_{s2}, a^1_{s3}, b^1_{s4}, c^1_{s5}, a^1_{s6}, b^1_{s7}, c^1_{s8} \}$.
Again for the sake of example let us determine `arbitary' common symptoms s9,s10 and s11 from
$fm(FG^1_1)$.
$$ \{ b_{s2} \} \stackrel{Collect Symptoms}{\longrightarrow} S9$$
%$$ \{ b^1_{s2} \} \stackrel{Collect Symptoms}{\longrightarrow} S9$$
$$ \{ a_{s3}, b_{s4}, a_{s6}, b_{s7} \} \stackrel{Collect Symptoms}{\longrightarrow} S10 $$
%$$ \{ a^1_{s3}, b^1_{s4}, a^1_{s6}, b^1_{s7} \} \stackrel{Collect Symptoms}{\longrightarrow} S10 $$
$$ \{ c_{s5}, c_{s8} \} \stackrel{Collect Symptoms}{\longrightarrow} S11 $$
%$$ \{ c^1_{s5}, c^1_{s8} \} \stackrel{Collect Symptoms}{\longrightarrow} S11 $$
To get our system level derived component we can apply $ \bowtie fm(FG^1_1) = C^2_1 $.
Thus applying $fm$ to our newly derived component $ C^2_1 $
gives its derived failure modes thus:
%$$ fm(C^2_1) = \{ a^1_{s9},b^1_{s10},c^1_{s11} \} .$$
$$ fm(C^2_1) = \{ a_{s9},b_{s10},c_{s11} \} .$$
This is represented in the DAG in figure \ref{fig:dag4}.
NOW THINK ABOUT THIS
@ -931,7 +951,7 @@ TO RACE BACK DOWN THE DAG
\end{tikzpicture}
% End of code
\caption{DAG representing failure modes and symptoms $FG^1_1 \rightarrow C^2_1$}
\label{fig:dag3}
\label{fig:dag4}
\end{figure}

27
latex_examples/mind_map.tex Normal file
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@ -0,0 +1,27 @@
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{mindmap,trees}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}
\path[mindmap,concept color=black,text=white]
node[concept] {Safety Engineering}
[clockwise from=0]
child[concept color=green!50!black] {
node[concept] {practical}
[clockwise from=90]
child { node[concept] {Certification } }
child { node[concept] {Maintenance} }
child { node[concept] {Staff Training} }
}
child[concept color=blue] {
node[concept] {applied}
[clockwise from=-30]
child { node[concept] {Standards} }
child { node[concept] {Insurance Liability} }
}
child[concept color=red] { node[concept] {Accident Investigation} }
child[concept color=orange] { node[concept] {theoretical} };
\end{tikzpicture}\end{document}