From dee71ccf9233706c08d44d619d9ae6d20ec74b35 Mon Sep 17 00:00:00 2001 From: Robin Date: Mon, 3 May 2010 22:09:42 +0100 Subject: [PATCH] ~Bank Holiday Monday Edits --- .../component_failure_modes_definition.tex | 77 --------- statistics/Makefile | 17 ++ statistics/paper.tex | 27 +++ statistics/statistics.tex | 84 +++++++++ statistics/style.tex | 159 ++++++++++++++++++ 5 files changed, 287 insertions(+), 77 deletions(-) create mode 100644 statistics/Makefile create mode 100644 statistics/paper.tex create mode 100644 statistics/statistics.tex create mode 100644 statistics/style.tex diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex index cd02e29..d839167 100644 --- a/component_failure_modes_definition/component_failure_modes_definition.tex +++ b/component_failure_modes_definition/component_failure_modes_definition.tex @@ -394,81 +394,4 @@ The failure mode set for a given component or sub-system $F$ is therefore $$ F = \Omega(K) \backslash OK $$ -\clearpage -THIS SHOULD BE IN A DIFFERENT CHAPTER - -\section{Current Methods for Safety Critical Analysis} - - -\subsection{Deterministic Approach} -\paragraph{NOT WRITTEN YET PLEASE IGNORE} -No single component fault may lead to a dangerous condition. -EN298 En230 etc - -\subsection{Bayes Theorem} -\paragraph{NOT WRITTEN YET PLEASE IGNORE} -\label{bayes} -Describe application - likely hood of faults being the cause of symptoms - -probablistic approach - no direct causation paths to the higher~abstraction fault mode. -Often for instance a component in a module within a module within a module etc -that has a probability of causing a SYSTEM level fault. - -Used in FTA\cite{NASA}\cite{NUK}. -The idea being that probabilities can be assigned to components -failing, causing system level errors. - - Problems, difficult to get reliable stats -for probability to cause because of small sample numbers... - -FMMD approach can by traversing down the tree use known component failure figures -to get {\em accurate} probabilities and potential causes. -%$$ c1 \cap c2 \eq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \in U $$ - -%Thus if the failure~modes are pairwaise mutually exclusive they qualify for inclusion into the -%unitary~state set family. - -\subsection{ Saftey Integrity Level Analysis } -\paragraph{NOT WRITTEN YET PLEASE IGNORE} -\label{sil} -This technique looks at all components in the parts list -and asks what the effect of the component failing will be. -Note that particular failure modes of the compoent are not considered. -The component can fail in any of its failure modes from the perspective of this analysis. -The analyst has to make a choice between four conditions: - -\begin{itemize} -\item sd - A safe fault that is detected by an automated system -\item su - A safe fault that is undetected by an automated system -\item dd - A potentially dangerous fault that is detected by an automated system -\item du - A potentially dangerous fault that is not detected by an automated system -\end{itemize} -Actually this is almost how sil analysis is done, because -the base components are listed -and their failure result as either sd su dd du - -A formula is then applied according to the system architecture 1oo1 2oo3 3oo3 etc - -What is not done is the probability for all these conditions, the sil analysis -person simple has to decide which it is. -Another fault in this is that it is very difficult to -extract meaning ful stats -for how likely the detection systems are to pick the fault up, or even to introduce a fault of their own. - -\subsection{Tests of Hypotheses and Significance} -\paragraph{NOT WRITTEN YET PLEASE IGNORE} -Linked in with Bayes theorem -Accident analysis -plane crashes and faults etc -In high reliability systems the fauls are often logged - strange occurances - -processors resetting - what are the common factors - P values - -for instance very high voltage spikes can reset micro controllers - -but how do you corrollate that with unshielded suppressed contactors... - -Maybe looking at the equipment and seeing if there is a 5\% -level of the error being caused ? -i.e. using it to search for these conditions ? - - -Actually this could be used to refine the SIL method \ref{sil} -and give probabilities for the four conditions. diff --git a/statistics/Makefile b/statistics/Makefile new file mode 100644 index 0000000..e3c78b4 --- /dev/null +++ b/statistics/Makefile @@ -0,0 +1,17 @@ + +# +# Make the propositional logic diagram a paper +# + + +paper: paper.tex statistics.tex + #latex paper.tex + #dvipdf paper pdflatex cannot use eps ffs + pdflatex paper.tex + okular paper.pdf + + +# Remove the need for referncing graphics in subdirectories +# +statistics.tex: statistics.tex paper.tex + cat statistics.tex | sed 's/statistics\///' > statistics_paper.tex diff --git a/statistics/paper.tex b/statistics/paper.tex new file mode 100644 index 0000000..880efd4 --- /dev/null +++ b/statistics/paper.tex @@ -0,0 +1,27 @@ + +\documentclass[a4paper,10pt]{article} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{tikz} +\usepackage{amsfonts,amsmath,amsthm} +\input{style} + +%\newtheorem{definition}{Definition:} + +\begin{document} +\pagestyle{fancy} + +\outerhead{{\small\bf Statistical Basis for Current Static Analysis Methodologies}} +%\innerfoot{{\small\bf R.P. Clark } } + % numbers at outer edges +\pagenumbering{arabic} % Arabic page numbers hereafter +\author{R.P.Clark} +\title{Statistical Basis for Current Static Analysis Methodologies} +\maketitle +\input{statistics_paper} + +\bibliographystyle{plain} +\bibliography{vmgbibliography,mybib} + +\today +\end{document} diff --git a/statistics/statistics.tex b/statistics/statistics.tex new file mode 100644 index 0000000..0efad61 --- /dev/null +++ b/statistics/statistics.tex @@ -0,0 +1,84 @@ + +\abstract{ This chapter looks at current methodologies +for static analysis of safety critical systems +and looks at the statistical justifications for their application. +} + + +\section{Introduction} + + +\section{Current Methods for Safety Critical Analysis} + + +\subsection{Deterministic Approach} +\paragraph{NOT WRITTEN YET PLEASE IGNORE} +No single component fault may lead to a dangerous condition. +EN298 En230 etc + +\subsection{Bayes Theorem} +\paragraph{NOT WRITTEN YET PLEASE IGNORE} +\label{bayes} +Describe application - likely hood of faults being the cause of symptoms - +probablistic approach - no direct causation paths to the higher~abstraction fault mode. +Often for instance a component in a module within a module within a module etc +that has a probability of causing a SYSTEM level fault. + +Used in FTA\cite{NASA}\cite{NUK}. +The idea being that probabilities can be assigned to components +failing, causing system level errors. + + Problems, difficult to get reliable stats +for probability to cause because of small sample numbers... + +FMMD approach can by traversing down the tree use known component failure figures +to get {\em accurate} probabilities and potential causes. +%$$ c1 \cap c2 \eq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \in U $$ + +%Thus if the failure~modes are pairwaise mutually exclusive they qualify for inclusion into the +%unitary~state set family. + +\subsection{ Saftey Integrity Level Analysis } +\paragraph{NOT WRITTEN YET PLEASE IGNORE} +\label{sil} +This technique looks at all components in the parts list +and asks what the effect of the component failing will be. +Note that particular failure modes of the compoent are not considered. +The component can fail in any of its failure modes from the perspective of this analysis. +The analyst has to make a choice between four conditions: + +\begin{itemize} +\item sd - A safe fault that is detected by an automated system +\item su - A safe fault that is undetected by an automated system +\item dd - A potentially dangerous fault that is detected by an automated system +\item du - A potentially dangerous fault that is not detected by an automated system +\end{itemize} +Actually this is almost how sil analysis is done, because +the base components are listed +and their failure result as either sd su dd du + +A formula is then applied according to the system architecture 1oo1 2oo3 3oo3 etc + +What is not done is the probability for all these conditions, the sil analysis +person simple has to decide which it is. +Another fault in this is that it is very difficult to +extract meaning ful stats +for how likely the detection systems are to pick the fault up, or even to introduce a fault of their own. + +\subsection{Tests of Hypotheses and Significance} +\paragraph{NOT WRITTEN YET PLEASE IGNORE} +Linked in with Bayes theorem +Accident analysis +plane crashes and faults etc +In high reliability systems the fauls are often logged - strange occurances - +processors resetting - what are the common factors - P values - +for instance very high voltage spikes can reset micro controllers - +but how do you corrollate that with unshielded suppressed contactors... + +Maybe looking at the equipment and seeing if there is a 5\% +level of the error being caused ? +i.e. using it to search for these conditions ? + + +Actually this could be used to refine the SIL method \ref{sil} +and give probabilities for the four conditions. diff --git a/statistics/style.tex b/statistics/style.tex new file mode 100644 index 0000000..79082ab --- /dev/null +++ b/statistics/style.tex @@ -0,0 +1,159 @@ +% +%============= Definition of {asyoulikeit} page style ======================* +% +% Jonathan Burch This is the terse form - expanded, formatted, +% 20-Jan-1989 commented version in TEX$LATEX:ASYOULIKEIT.FULL +% +\catcode`\@=11\def\ps@asyoulikeit{\def\@oddhead{\hbox{}\lp@innerhead +\lp@headfill\lp@middlehead\lp@headfill\lp@outerhead}\def\@evenhead +{\hbox{}\lp@outerhead\lp@headfill\lp@middlehead\lp@headfill\lp@innerhead} +\def\@oddfoot{\hbox{}\lp@innerfoot\lp@footfill\lp@middlefoot\lp@footfill +\lp@outerfoot}\def\@evenfoot{\hbox{}\lp@outerfoot\lp@footfill\lp@middlefoot +\lp@footfill\lp@innerfoot}\def\sectionmark##1{}\def\subsectionmark##1{}} +\def\lp@innerhead{}\def\lp@middlehead{}\def\lp@outerhead{}\def\lp@innerfoot{} +\def\lp@middlefoot{ {\thepage} }\def\lp@outerfoot{}\def\lp@headfill{\hfil} +\def\lp@footfill{\hfil}\newcommand{\lp@linefill}{\leaders\hrule height 0.55ex +depth -0.5ex\hfill}\newcommand{\innerhead}[1]{\def\lp@innerhead{#1}} +\newcommand{\middlehead}[1]{\def\lp@middlehead{#1}}\newcommand{\outerhead}[1] +{\def\lp@outerhead{#1}}\newcommand{\innerfoot}[1]{\def\lp@innerfoot{#1}} +\newcommand{\middlefoot}[1]{\def\lp@middlefoot{#1}}\newcommand{\outerfoot}[1] +{\def\lp@outerfoot{#1}}\newcommand{\lineheadfill}{\def\lp@headfill +{\lp@linefill}}\newcommand{\linefootfill}{\def\lp@footfill{\lp@linefill}} +\newcommand{\blankheadfill}{\def\lp@headfill{\hfill}}\newcommand +{\blankfootfill}{\def\lp@footfill{\hfill}}\newcommand{\documentnumber}[1] +{\def\lp@docno{#1}\outerhead{\lp@docno}}\def\lp@docno{}\def\@maketitlet +{\newpage\null\vskip -14ex\hbox{}\hfill\lp@docno\vskip 13ex\begin{center} +{\LARGE\@title\par}\vskip 1.5em{\large\lineskip .5em\begin{tabular}[t]{c} +\@author\end{tabular}\par}\vskip 1em{\large\@date}\end{center}\par\vskip 3em} +\def\abstract{\if@twocolumn\section*{Abstract}\else\small\begin{center} +{\bf Abstract\vspace{-.5em}\vspace{0pt}}\end{center}\quotation\fi}\def +\endabstract{\if@twocolumn\else\endquotation\fi}\ps@asyoulikeit\catcode`\@=12 +% +%=========== End of {asyoulikeit} page style definition ====================* + +\DeclareSymbolFont{AMSb}{U}{msb}{m}{n} +\DeclareMathSymbol{\N}{\mathbin}{AMSb}{"4E} +\DeclareMathSymbol{\Z}{\mathbin}{AMSb}{"5A} +\DeclareMathSymbol{\R}{\mathbin}{AMSb}{"52} +\DeclareMathSymbol{\Q}{\mathbin}{AMSb}{"51} +\DeclareMathSymbol{\I}{\mathbin}{AMSb}{"49} +\DeclareMathSymbol{\C}{\mathbin}{AMSb}{"43} + + +% Page layout definitions to suit A4 paper +\setcounter{secnumdepth}{3} \setcounter{tocdepth}{4} +\setlength{\topmargin}{0mm} +\setlength{\textwidth}{160mm} \setlength{\textheight}{220mm} +\setlength{\oddsidemargin}{0mm} \setlength{\evensidemargin}{0mm} +% +% Local definitions +% ----------------- +\newcommand{\eg}{{\it e.g.}} +\newcommand{\etc}{{\it etc.}} +\newcommand{\ie}{{\it i.e.}} +\newcommand{\qv}{{\it q.v.}} +\newcommand{\viz}{{\it viz.}} +\newcommand{\degs}[1]{$#1^\circ$} % Degrees symbol +\newcommand{\mins}[1]{$#1^{\scriptsize\prime}$} % Minutes symbol +\newcommand{\secs}[1]{$#1^{\scriptsize\prime\prime}$} % Seconds symbol +\newcommand{\key}[1]{\fbox{\sc#1}} % Box for keys +\newcommand{\?}{\_\hspace{0.115em}} % Proper spacing for + % underscore +\newcommand{\rev}{PA5} +\newcommand{\etcdoc}{ HR222975 } +\newcommand{\wlc}{{Water~Level~Controller~Unit}} +\newcommand{\ft}{{\em 4 $\rightarrow$ 20mA } } +\newcommand{\tds}{TDS Daughterboard} +\newcommand{\oc}{$^{o}{C}$} +\newcommand{\adctw}{{${\mathcal{ADC}}_{12}$}} +\newcommand{\adcten}{{${\mathcal{ADC}}_{10}$}} +\newcommand{\ohms}[1]{\ensuremath{#1\Omega}} +%----- Display example text (#1) in typewriter font + +%\newcommand{\example}[1]{\\ \smallskip\hspace{1in}{\tt #1}\hfil\\ +% \smallskip\noindent} +% +%----- Enclose text (#2) in ruled box of given thickness (#1) + +\def\boxit#1#2{\vbox{\hrule height #1pt\hbox{\vrule width #1pt\hskip 5pt + \vbox{\vskip 5pt #2 \vskip 5pt}\hskip 5pt + \vrule width #1pt}\hrule height #1pt}} + +%----- Display boxed warning text (#1) + +\def\warning#1{\bigskip + \setbox1=\vbox{\tolerance=5000\parfillskip=0pt + \hsize=3in\noindent#1} + \centerline{\boxit{1.0}{\box1}} + \bigskip} + +%----- Definitions to aid display of help text +% (modelled on \item and \itemitem) + +\def\helpindent#1{\setbox2=\hbox to\parindent{{\it #1}\hfil} + \indent\llap{\box2}\ignorespaces} +\def\helpitem{\parindent=70pt\par\hang\helpindent} +\def\helpitemitem{\parindent=70pt\par\indent \parindent=80pt +\hangindent2\parindent \helpindent} + +%----- Tables and footnotes to tables +% +\newcommand{\spacerA}{\rule{0mm}{4mm}} +\newcommand{\spacerB}{\rule[-2mm]{0mm}{5mm}} +\footnotesep=5mm +\renewcommand{\footnoterule}{{\small Notes:}} + +%% Robin 01AUG2008 +%% + +\newcounter{examplec} +\newcounter{definitionc} +\newcounter{summaryc} + +%\@addtoreset{examplec}{chapter}\renewcommand\theexamplec{\thechapter.arabic{examplec}} +%\@addtoreset{definitionc}{chapter} +%\@addtoreset{summaryc}{chapter} + +%\renewcommand\examplec{\arabic{examplec}} + +%\newenvironment{example} +%{ +% \stepcounter{examplec} \vspace{10pt} \normalfont\bfseries Example:\normalfont\[{\arabic{chapter}.\arabic{examplec}}\] +% \normalfont \begin{quote}}{\end{quote}\par} +%\newenvironment{definition} +%\newenvironment{example} +%{ +% \stepcounter{examplec} \vspace{10pt} \normalfont\bfseries Example:\normalfont\[{\arabic{chapter}.\arabic{examplec}}\] +% \normalfont \begin{quote}}{\end{quote}\par} +\usepackage{amsthm} + +\newtheorem{example}{Example:} +\newtheorem{definition}{Definition:} +\newtheorem*{summary}{Summary:} + + +% +\newcommand{\Fam}{{\mathbb F}} +\newcommand{\Pow}{{\mathbb P}} +\newcommand{\Dis}{{\vee}} +\newcommand{\Con}{{\wedge}} +\newcommand{\FMEA}{{\bowtie}} +% +\newcommand{\Nat}{{\mathbb N}} +\newcommand{\Real}{{\mathbb R}} +\newcommand{\Complex} {{\mathbb C}} +\newcommand{\Rational} {{\mathbb Q}} +% +%\newenvironment{example} +%{ \stepcounter{examplec} \vspace{10pt} \normalfont\bfseries Example:(\arabic{chapter}.\arabic{examplec}) +% \normalfont \begin{quote}}{\end{quote}\par} + +% +%\newenvironment{definition} +%{ \stepcounter{definitionc} \vspace{10pt} \normalfont\bfseries Definition:(\arabic{chapter}.\arabic{definitionc}) +% \normalfont \begin{quote}}{\end{quote}\par} +% +%\newenvironment{summary} +%{ \vspace{10pt} \normalfont\bfseries Summary: +% \normalfont \begin{quote}}{\end{quote}\par} +%