From aa9f6755f66638fd9e1f0b61727e60822103e0e0 Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Thu, 2 Dec 2010 22:48:13 +0000 Subject: [PATCH] Inhibit and conjuction DAG and some text --- fmmd_data_model/fmmd_data_model.tex | 102 ++++++++++++++++++++++++++-- shortfm.tex | 1 + 2 files changed, 96 insertions(+), 7 deletions(-) diff --git a/fmmd_data_model/fmmd_data_model.tex b/fmmd_data_model/fmmd_data_model.tex index 54276c1..1d74865 100644 --- a/fmmd_data_model/fmmd_data_model.tex +++ b/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. diff --git a/shortfm.tex b/shortfm.tex index 3580ea7..2a6fc7a 100644 --- a/shortfm.tex +++ b/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