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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 } }
% numbers at outer edges
\pagenumbering{arabic} % Arabic page numbers hereafter
\author{R.P.Clark$^1$ , Andrew~Fish$^2$ , John~Howse$^2$ , Chris Garret$^2$ \\
$^1${\em Energy Technology Control, Lewes,UK} \and $^2${\em University of Brighton, UK}
\author{R.P.Clark$^\star$ , Andrew~Fish$^\dagger$ , John~Howse$^\dagger$ , Chris Garret$^\dagger$ \\
$^\star${\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}
@ -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
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.
If $E$ is the number of applied states or environmental conditions to consider
in a system, and $A$ the number of applied states,
If $E$ is the number of environmental conditions to consider
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
additional %cross product
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,
that must interact to reach the top level event.
Where $C$ represents the set of components in a failure mode causation chain,
$c$ represents a component and
the function $fn$ returns the number of failure modes for a given component, equation
$c_i$ represents a component in $C$ and
the function $fm$ returns the failure modes for a given component, equation
\ref{eqn:complexity}, returns a value representing the complexity
from the base component failure to the SYSTEM level event.
\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}
\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
failure modes and their relationship to environmental factors,
@ -291,9 +293,10 @@ mechanical and software elements in one integrated model.
%
{ \tiny
\bibliographystyle{plain}
\bibliography{../vmgbibliography,../mybib}
\bibliography{vmgbibliography,mybib}
}
\today
\end{document}