diff --git a/fmmd_data_model/fmmd_data_model.tex b/fmmd_data_model/fmmd_data_model.tex index f835e41..faa72ee 100644 --- a/fmmd_data_model/fmmd_data_model.tex +++ b/fmmd_data_model/fmmd_data_model.tex @@ -514,13 +514,6 @@ We can respresent this in the DAG in figure \ref{fig:dag2}. \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}; @@ -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} diff --git a/latex_examples/mind_map.tex b/latex_examples/mind_map.tex new file mode 100644 index 0000000..6ed4d51 --- /dev/null +++ b/latex_examples/mind_map.tex @@ -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} +