From 08d0c19b7c27133b2de13da23f285c1b49b0a66f Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Tue, 31 Aug 2010 20:21:17 +0100 Subject: [PATCH] FM as function name to lower case --- fmmdset/fmmdset.tex | 35 ++++++++++++++++++++++++----------- 1 file changed, 24 insertions(+), 11 deletions(-) diff --git a/fmmdset/fmmdset.tex b/fmmdset/fmmdset.tex index 99d54b4..41c004a 100644 --- a/fmmdset/fmmdset.tex +++ b/fmmdset/fmmdset.tex @@ -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. \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} @@ -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} 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 $C$. Let the set of all possible components be $\mathcal{C}$ 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} -FM : \mathcal{C} \mapsto \mathcal{P}\mathcal{F} +fm : \mathcal{C} \mapsto \mathcal{P}\mathcal{F} \end{equation} defined by, where C is a component and F is a set of failure modes. -$$ FM ( C ) = F $$ +$$ fm ( C ) = F $$ -%$$ \mathcal{FM}(C) \rightarrow S $$ -%$$ {FM}(C) \rightarrow S $$ +%$$ \mathcal{fm}(C) \rightarrow S $$ +%$$ {fm}(C) \rightarrow S $$ 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 @@ -210,11 +223,11 @@ $$ \bowtie( FG^0_1 ) = C^1_1 $$ 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 $f_N$ - $$ {FM}(C^0_1) = \{ f_1, f_2 \} $$ - $$ {FM}(C^0_2) = \{ f_3, f_4, f_5 \} $$ + $$ {fm}(C^0_1) = \{ f_1, f_2 \} $$ + $$ {fm}(C^0_2) = \{ f_3, f_4, f_5 \} $$ The analyst now considers failure modes $f_{1..5}$ in the context of the {\fg}. @@ -224,7 +237,7 @@ We can now create a {\dc} $C^1_1$ with this set of failure modes. 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}