Inhibit and conjuction DAG and some text

fmmd_data_model/fmmd_data_model.tex

@@ -749,7 +749,8 @@ 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}.
+We now have all the SYSTEM level failures.
+This are represented on the r.h.s. of the DAG in figure \ref{fig:dag4}.
 
 NOW THINK ABOUT THIS
 
@@ -960,11 +961,96 @@ TO RACE BACK DOWN THE DAG
  \end{figure}
 
 
-\section{Directed Acyclic Graph}
 
-Show how the hierarchy can be represented as a DAG
+\section{Failure inhibition and conjunction}
 
-draw a dag
+\subsection{Inhibition}
+Failure inhibition is where a failure can only become active given a pre-condition.
+A component suseptible to a given temperature range 
+making a failure mode a possibility is an inhibit condition.
+for instance in electronics, a semi-conductor may begin to
+fail at an eleveted temperature range.
+Or in mechanical engineering a rubber seal may become brittle and leak
+at low temperatures.
+
+What we have is an inhibit condition, in this case the temperature 
+being in range makes the particular failure mode impossible.
+
+
+ \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{fmmdi}=[rectangle,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{inhibit}=[fmmdi, fill=grey!20];
+     \tikzstyle{conjunction}=[fmmde, fill=red!20];
+     \tikzstyle{annot} = [text width=4em, text centered]
+
+ 	\node[component] (C-1) at (0,-2) {$C^0_1$};
+ 	\node[fmmdi] (I-1) at (\layersep,-2) {$ > 80\oc$};
+        \path (C-1) edge (I-1);
+        \node[failure] (f) at (\layersep*2,-2)  {$a$}; 
+        \path (I-1) edge (f);
+
+ \end{tikzpicture}
+ % End of code
+ \caption{DAG representing inhibit condition ($ > 80\oc$) on failure mode $a$}
+ \label{fig:daginhibit}
+\end{figure}
+
+\subsection{Conjunction}
+
+Failure conjuction is simply considering, at the {\fg} analysis stage
+the possibility of two components failing within the same timeframe.
+We could for instance, looking at a fuel train to a burner/chemical~reactor;
+consider both shutoff valves failing at the same time.
+
+For high levels of safety or reliability, in critical sub-systems, all possible double
+simultaneous failures may have to be considered \cite{en298}. 
+
+
+ \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{fmmdi}=[rectangle,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{inhibit}=[fmmdi, fill=grey!20];
+     \tikzstyle{conjunction}=[fmmde, fill=red!20];
+     \tikzstyle{annot} = [text width=4em, text centered]
+
+ 	\node[component] (C-1) at (0,-2) {$C^0_1$};
+
+        \node[failure] (C-1a) at (\layersep,-1) {a}; 	
+        \node[failure] (C-1b) at (\layersep,-2) {b}; 	
+        \node[failure] (C-1c) at (\layersep,-3) {c}; 	
+	
+     \path (C-1) edge (C-1a);
+     \path (C-1) edge (C-1b);
+     \path (C-1) edge (C-1c);
+
+	\node[conjunction, right of=C-1b]  (CJ) {$\&$};
+
+     \path (C-1a) edge (CJ);
+     \path (C-1b) edge (CJ);
+     \path (C-1c) edge (CJ);
+
+ \end{tikzpicture}
+ % End of code
+ \caption{DAG representing conjuction condition on failure modes $a \wedge b \wedge c$}
+ \label{fig:dagconjuction}
+\end{figure}
+
+\subsection{Failure Mode Conjuction Conditions represented in the DAG}
+
+White filled node with an \& in it.
 
 \subsection{Inhibit Conditions represented in the DAG}
 
@@ -975,11 +1061,10 @@ a -> OCT
 inhibitcond--
 
 
-\subsection{Failure Mode Conjuction Conditions represented in the DAG}
+\section{Traversing the datamodel: Extracting Information from the Directed Acyclic Graph}
 
-White filled node with an \& in it.
 
-\subsection{Traversing the datamodel}
+\section{Determining the causes of SYSTEM level Failure modes}
 
 Show how we can find multiple causes for a SYSTEM level error.
 Constrast this to the bottom-up approaches of FMEA, FMECA and FMEDA where
@@ -987,6 +1072,9 @@ without necessarily knowing complex interactions between
 functionally adjacent components, we must take each component failure
 mode and tie to to a SYSTEM level failure. 
 
+
+
+
 \subsubsection{Common mode failure detection}
 
 Describe what a common mode failure is.

shortfm.tex

@@ -9,6 +9,7 @@ in our functional groups.
 We can overload this function to take a {\fg} as its range and 
 a set of failure modes  (being the failure modes of all the components in the {\fg})
 as its domain.
+
 }
 {
 Using the overloaded function $fm$ from chapter \ref{fmdef} we can determine the failure modes