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FM as function name to lower case

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Robin Clark 2010-08-31 20:21:17 +01:00
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1 changed files with 24 additions and 11 deletions
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fmmdset/fmmdset.tex
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@ -18,7 +18,20 @@ It is intended to be used to formally prove systems to meet EN and UL standards,
EN298, EN61508, EN12067, EN230, UL1998. EN298, EN61508, EN12067, EN230, UL1998.
\end{abstract} \end{abstract}
} }
{} {
This chapter describes a process for analysing safety critical systems, to formally prove how safe the
designs and built -in safety measures are. It provides
the rigourous method for creating a fault effects model of a system from the bottom up using {\bc} level fault modes.
Using symptom extraction, and taking {\fgs} of components, a fault behaviour
hierarchy is built, forming a fault model tree.
From the fault model trees,
modular re-usable sections of safety critical systems,
and accurate, statistical estimation for fault frequency can be derived automatically.
It provides the means to trace the causes of dangerous detected and dangerous undetected faults.
It is intended to be used to formally prove systems to meet EN and UL standards, including and not limited to
EN298, EN61508, EN12067, EN230, UL1998.
}
\section{Introduction} \section{Introduction}
@ -141,25 +154,25 @@ This analysis and symptom collection process is described in detail in the Sympt
\subsubsection{An algebraic notation for identifying FMMD enitities} \subsubsection{An algebraic notation for identifying FMMD enitities}
Each component $C$ is a set of failure modes for the component. Each component $C$ is a set of failure modes for the component.
We can define a function $FM$ that returns the We can define a function $fm$ that returns the
set of failure modes $F$ for the component $C$. set of failure modes $F$ for the component $C$.
Let the set of all possible components be $\mathcal{C}$ Let the set of all possible components be $\mathcal{C}$
and let the set of all possible failure modes be $\mathcal{F}$. and let the set of all possible failure modes be $\mathcal{F}$.
We can define a function $FM$ We can define a function $fm$
\begin{equation} \begin{equation}
FM : \mathcal{C} \mapsto \mathcal{P}\mathcal{F} fm : \mathcal{C} \mapsto \mathcal{P}\mathcal{F}
\end{equation} \end{equation}
defined by, where C is a component and F is a set of failure modes. defined by, where C is a component and F is a set of failure modes.
$$ FM ( C ) = F $$ $$ fm ( C ) = F $$
%$$ \mathcal{FM}(C) \rightarrow S $$ %$$ \mathcal{fm}(C) \rightarrow S $$
%$$ {FM}(C) \rightarrow S $$ %$$ {fm}(C) \rightarrow S $$
We can indicate the abstraction level of a component by using a superscript. We can indicate the abstraction level of a component by using a superscript.
Thus for the component $C$, where it is a `base component' we can assign it Thus for the component $C$, where it is a `base component' we can assign it
@ -210,11 +223,11 @@ $$ \bowtie( FG^0_1 ) = C^1_1 $$
to look at this analysis process in more detail. to look at this analysis process in more detail.
By way of exqample applying ${FM}$ to obtain the failure modes $f_N$ By way of exqample applying ${fm}$ to obtain the failure modes $f_N$
$$ {FM}(C^0_1) = \{ f_1, f_2 \} $$ $$ {fm}(C^0_1) = \{ f_1, f_2 \} $$
$$ {FM}(C^0_2) = \{ f_3, f_4, f_5 \} $$ $$ {fm}(C^0_2) = \{ f_3, f_4, f_5 \} $$
The analyst now considers failure modes $f_{1..5}$ in the context of the {\fg}. The analyst now considers failure modes $f_{1..5}$ in the context of the {\fg}.
@ -224,7 +237,7 @@ We can now create a {\dc} $C^1_1$ with this set of failure modes.
Thus: Thus:
$$ {FM}(C^1_1) = \{ s_6, s_7, s_8 \} $$ $$ {fm}(C^1_1) = \{ s_6, s_7, s_8 \} $$
We can represent this analysis process in a diagram see figure \ref{fig:onestage} We can represent this analysis process in a diagram see figure \ref{fig:onestage}