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fm function used

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Robin Clark 2011-05-31 09:11:47 +01:00
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fmmd_concept/System_safety_2011/submission.tex
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@ -54,8 +54,8 @@ failure mode of the component or sub-system}}}
%\innerfoot{{\small\bf R.P. Clark } } %\innerfoot{{\small\bf R.P. Clark } }
% numbers at outer edges % numbers at outer edges
\pagenumbering{arabic} % Arabic page numbers hereafter \pagenumbering{arabic} % Arabic page numbers hereafter
\author{R.P.Clark$^1$ , Andrew~Fish$^2$ , John~Howse$^2$ , Chris Garret$^2$ \\ \author{R.P.Clark$^\star$ , Andrew~Fish$^\dagger$ , John~Howse$^\dagger$ , Chris Garret$^\dagger$ \\
$^1${\em Energy Technology Control, Lewes,UK} \and $^2${\em University of Brighton, UK} $^\star${\em Energy Technology Control, Lewes,UK} \and $^\dagger${\em University of Brighton, UK}
} }
\title{Developing a rigorous bottom-up modular static failure mode modelling methodology} \title{Developing a rigorous bottom-up modular static failure mode modelling methodology}
@ -172,8 +172,8 @@ is $N \times K$. To examine the effect that one failure mode has on all
the other components\footnote{A base component failure will typically affect the sub-system the other components\footnote{A base component failure will typically affect the sub-system
it is part of, and create a failure effect at the SYSTEM level.} it is part of, and create a failure effect at the SYSTEM level.}
will be $(N-1) \times N \times K$, in effect a very large set cross product. will be $(N-1) \times N \times K$, in effect a very large set cross product.
If $E$ is the number of applied states or environmental conditions to consider If $E$ is the number of environmental conditions to consider
in a system, and $A$ the number of applied states, in a system, and $A$ the number of applied states (or modes of the SYSTEM),
the job of the bottom-up analyst is presented with two the job of the bottom-up analyst is presented with two
additional %cross product additional %cross product
factors, factors,
@ -194,12 +194,12 @@ The `reasoning~distance' $R_D$ can be calculated by summing the number of compon
involved, multiplied by the number of failure modes in each component, involved, multiplied by the number of failure modes in each component,
that must interact to reach the top level event. that must interact to reach the top level event.
Where $C$ represents the set of components in a failure mode causation chain, Where $C$ represents the set of components in a failure mode causation chain,
$c$ represents a component and $c_i$ represents a component in $C$ and
the function $fn$ returns the number of failure modes for a given component, equation the function $fm$ returns the failure modes for a given component, equation
\ref{eqn:complexity}, returns a value representing the complexity \ref{eqn:complexity}, returns a value representing the complexity
from the base component failure to the SYSTEM level event. from the base component failure to the SYSTEM level event.
\begin{equation} \begin{equation}
R_D = \sum_{i=1}^{|C|} {fn(c)} %\; where \; c \in C R_D = \sum_{i=1}^{|C|} |{fm(c_i)}| %\; where \; c \in C
\label{eqn:complexity} \label{eqn:complexity}
\end{equation} \end{equation}
@ -237,7 +237,9 @@ base our reasoning on, at each stage.
Development of the new methodology %Development of the new methodology
\section{An ontology of failure modes}
An ontology is developed of An ontology is developed of
failure modes and their relationship to environmental factors, failure modes and their relationship to environmental factors,
@ -291,9 +293,10 @@ mechanical and software elements in one integrated model.
% %
{ \tiny
\bibliographystyle{plain} \bibliographystyle{plain}
\bibliography{../vmgbibliography,../mybib} \bibliography{vmgbibliography,mybib}
}
\today \today
\end{document} \end{document}