From c47958816187c723fd0428d8ce9adadfa79b618f Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Sat, 20 Nov 2010 15:42:47 +0000 Subject: [PATCH] J. Howse comments -> changes From meeting on 19NOV2010 --- component_failure_modes_definition/cfg.dia | Bin 2515 -> 2456 bytes component_failure_modes_definition/cfg.jpg | Bin 22901 -> 20205 bytes .../component_failure_modes_definition.tex | 82 +++++++++++------- component_failure_modes_definition/paper.tex | 15 +++- 4 files changed, 65 insertions(+), 32 deletions(-) diff --git a/component_failure_modes_definition/cfg.dia b/component_failure_modes_definition/cfg.dia index 5cba712c7709f1e62e1540d073330f405a379d2b..222844fe6c84d5eb392103678e24606521878386 100644 GIT binary patch literal 2456 zcmV;J31{{niwFP!000021MOW~Z{s!^eb28DJa3DH;r%jhQnb66-G^PYK)cU@Y;zoK zWyz40Wb)GAz9c12e35c7O(!ZCAcL_&^N7^Z`7ZiM{qW5=e&-ce)z341FVnf6R66~mziViIlscsArLK0nT`bF0W}4KG%e^K& z{n&pu+O(}!rcp7!{`3?5)SOa#;Hj^!6YT}57il%mihUe2H+eG=7)Xq7!pBAn5<6ZEwAE=T$a){>I&E(bLOAHmh%Mz6F}DruWA{z29f6Y?AA)v(Jk9 zXx%>^r~BQjz-_Adh0b0GpU(oZ#NI~yKJUcFVJkeO;1m^ZL`alW_`EaYbT~T zv}3FtM4mqCs_p*gCo`S27r0fNB%RjT{rc0!oRpLQ>1o{#_P07MW@$A`E|Q}vE2+@7r6;hD~i4(`p?viwdd4A?mbWOoAg<)g3r$z-?p%A9{%%yYd)pcVqN zF@gY}E5Hu})45*UOv|d+cMpy=9tYu6WPeO+1rdNVxcNgpux@oWzpeYh2*6Zr{-DFa zR=4HDO^46;vO(;=c`u)sdN6g7FLjZ*&h}!{faJ9pmQQSqDS*tdmrxdxzn+8oa11t1 zo!X?Z6hmb2@A_N4L1ENV82eI~0xHEBtQJ6wM1txOOg%LEnFUot3ADef32pcp%!98xDw zjHttqr)5#x=wjwZ^X4&j2MYEKg`fup)aK$(m%As@m1}ygQ#&j(d*(8)_QZGnm*mzE zqZO>WbXkk!>95B1*c)fZcTxLYwEbPVpSsyOq2m};b_D8D29ddBBrta!3e=W$-`()2k7W?Z%v}0Nel#4BnQHc5E(sU015-h2cbrPi)s{HjXD?@ zwdf;jQFk(5_)5_QLV#Mgg{pvB3@D}_-y8fjt?HGLja7UY72GZCVPo_R2NKdjARm~@;Fda;=8dGQCRjHGQQIv)#O8(Vn05%?X*yLG*(nt~pNMb%5MFJpZ(86cX zx_B5hX?Q6#g#Bx|i855UfZ)(a!mljoCbWTJXzZSqn@<=}$-)+P`wlK9(oR_$i@eLw zF3iOsRGp*XIf)hswn+(NXO+VpLR#X>UE$J6hE)GFmwy>8ZtyUmhnLal4zMH*dDoxiQ2F+s9c1B1QwJ{d>pR*_2308m9osftRPrHYUkC06~36144n6V+tU~%m8vMVlW#`YcB_*Ssh?3%a5?Q6R)F87IuLr zYU4^i#snzpf>|a*uk!RA-3MH&4CPidi~mZ|tT+OpC1S`#4J>Rly9R$-0RHZ&9Mp+tO-X9;KhRy9xpg`EC zkQ6!)+H6Yd;!NWv1ukIo8`&!p{#)CH%8&_vWM}aRPZvJs){frgYvenxf^PWI!YH@j zi>*u&++q%6zn5I!>pc0Km`T%fT}4wH+SGQFGMd^UMgY`bp$KcpfP)GYY3v?{Z2SaC zVxB)LQXdJUAPrHF{P)OXMkG$KM_vol?veK$bQnHUl%(MKh)xg|WVGx9 ztSiF)JM|$zZIyKB)y2pr{#`+~WD*lTc1zj0a247@Q5<@|zRq!WuCS*Naody%iU(I# zgt^bQ^6#{6533{Wj)nO-30zmypx6bSc742LMn%n$VJzK?X7vO+W9@S=n$;n`JPP`6 zj3wMw8a(VfS}cl*T@k@S=2qUt`hRsw!?}!7Gd@mdOra1-_{HR#e}rM z6qZc!ut6KdoVkYyNMJE0fD>t`#R0((h2Al!f23Vy08Btg-0ngLr;9&M?m>FIGvMf{ zho7ox7n6^%^HsaifDFCw6;pQMN|SL=*0dsQ$btZ*SfKD5Uv&+$djTJ3Ub}is@2Y!! zGs{+H{8Qck=*dh4G0rW)iW4l2o!|$qPRxzW1$)kQ*y=#+vpR6+K16T6mzvLc`lzex Wv*v^Oomc7N`t1Mez{{8ki~s;D(ZALJ literal 2515 zcmV;^2`u&>iwFP!000021MOW+Z{s);z2{dL?%Tp<_$i9*Nd_~!=-tCEW`LPJ2a2tB zv?EJ~tR(Hr{PrzUauVBA;+Up88ZbbA$f5Z}>giRnR4o1QNRu)%7g79#V z7SnQ;74xg%e}Dfnj)y;9U;Hr3lF#sGUL}hGe4|+DqpRUvT`xahUOqlPqI|td>as$4 zc8^x+<)2BOCzsIZa(I0)7`*IYmeh&ngjwuhT)1EYhptZ8H61UX}O7Y}mAF z+fB>7tOgHBel`5`)%*-E+iotm`gx`AWin51t2FteyK4+TN*&YnGOc#IT`bF022JYq za<558Kl<+%ZQ52VXjIIvKmEi%HK){m@Z6W}L_0z1MN-YPVjl**(0S)7Vgyx%;`@3UFDdV^-$Z900oYnxrZHS4?W z4xO0hqa9;yAo66LR&Dn`Kbz@6dx2ZU86?v>d)OSkn3MAMf9bSt2m4!{6tkq74aS3? 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a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex index ce4ed04..cbd5bd6 100644 --- a/component_failure_modes_definition/component_failure_modes_definition.tex +++ b/component_failure_modes_definition/component_failure_modes_definition.tex @@ -30,7 +30,15 @@ Mathematical constraints and definitions are made using set theory. \section{Introduction} -This chapter describes the data types and concepts for the Failure Mode Modular De-composition (FMMD) method. +This +\ifthenelse {\boolean{paper}} +{ +paper +} +{ +chapter +} +describes the data types and concepts for the Failure Mode Modular De-composition (FMMD) method. When analysing a safety critical system using this methodology, we need clearly defined failure modes for all the components that are used to model the system. @@ -43,7 +51,7 @@ build hierarchical bottom-up models of failure mode behaviour. %When building a system from components, %we should be able to find all known failure modes for each component. %For most common electrical and mechanical components, the failure modes -%for a given type of part can be obtained from standard literature\cite{mil1991} +%for a given type of part can be obtained from standard literature~\cite{mil1991} %\cite{mech}. %The failure modes for a given component $K$ form a set $F$. @@ -62,8 +70,9 @@ build hierarchical bottom-up models of failure mode behaviour. \label{fig:component} \end{figure} -Let us first define a component. This is anything with which we use to build a -product or system. +Let us first define a component. +%This is anything with which we use to build a product or system. +This is anything we use to build a product or system. It could be something quite complicated like an integrated microcontroller, or quite simple like the humble resistor. We can define a @@ -72,7 +81,7 @@ a vendors' reference number. What these components all have in common is that they can fail, and fail in a number of well defined ways. For common components there is established literature for the failure modes for the system designer to consider (often with accompanying statistical -failure rates)\cite{mil1991}. For instance, a simple resistor is generally considered +failure rates)~\cite{mil1991}. For instance, a simple resistor is generally considered to fail in two ways, it can go open circuit or it can short. Thus we can associate a set of faults to this component $ResistorFaultModes=\{OPEN, SHORT\}$. The UML diagram in figure @@ -96,7 +105,7 @@ A product naturally consists of many components and these are traditionally kept in a `parts list'. For a safety critical product this is usually a formal document and is used by quality inspectors to ensure the correct parts are being fitted. The parts list is shown for -completeness here, as people involved with PCB and electronics production, verification +completeness here, as people involved with Printed Circuit Board (PCB) and electronics production, verification and testing would want to know where it lies in the model. The parts list is not actively used in the FMMD method. For the UML diagram in figure \ref{fig:componentpl} the parts list is simply a collection of components. @@ -119,7 +128,7 @@ we are concerned with here.}, and will not require a vendor reference, but must be named locally in the FMMD model. We can term `modularising a system', to mean recursively breaking it into smaller sections for analysis. -When modularising a system from the top~down, as in Fault Tree Analysis\cite{nasafta}\cite{nucfta} (FTA) +When modularising a system from the top~down, as in Fault Tree Analysis~\cite{nasafta}\cite{nucfta} (FTA), it is common to term the modules identified as sub-systems. When building from the bottom up, it is more meaningful to call them `derived~components'. @@ -128,23 +137,23 @@ When building from the bottom up, it is more meaningful to call them `derived~co %% Paragraph using failure modes to build from bottom up %% -\section{Fault Mode Analysis, \\ top down or bottom up?} +\section{Fault Mode Analysis, top down or bottom up?} Traditional static fault analysis methods work from the top down. They identify faults that can occur in a system, and then work down to see how they could be caused. Some apply statistical techniques to determine the likelihood of component failures -causing specific system level errors. For example, Bayes theorem \ref{bayes}, the relation between a conditional probability and its inverse, +causing specific system level errors. For example, Bayes theorem \ref{bayes}, the relation between a conditional probability and its reverse, can be applied to specific failure modes in components and the probability of them causing given system level errors. Another top down methodology is to apply cost benefit analysis -to determine which faults are the highest priority to fix\cite{bfmea}. +to determine which faults are the highest priority to fix~\cite{bfmea}. The aim of FMMD analysis is to produce complete failure models of safety critical systems from the bottom-up, starting, where possible with known base~component failure~modes. An advantage of working from the bottom up is that we can ensure that all component failure modes must be considered. A top down approach -can miss individual failure modes of components\cite{faa}[Ch.~9], +can miss individual failure modes of components~\cite{faa}[Ch.~9], especially where they are non obvious top-level faults. In order to analyse from the bottom-up, we need to take @@ -161,8 +170,12 @@ and from this determine the failure modes of all the components that belong to i % expand 21sep2010 %The `{\fg}' as used by the analyst is a collection of component failures modes. The analysts interest is the ways in which the components within the {\fg} -can fail. All the failure modes of all the components with an {\fg} are collected -into a flat set of failure modes. +can fail. All the failure modes of all the components within an {\fg} are collected. +As each component mode holds a set of failure modes, these set of sets of failure modes +is converted into +into a flat set +of failure modes +(i.e. a set containg just containg failure modes not sets of failure mosdes). % Each of these failure modes, and optionally combinations of them, are formed into `test cases' which are @@ -180,12 +193,19 @@ with its own set of failure modes. The process for taking a {\fg}, considering all the failure modes of all the components in the group, -and analysing it is called `symptom abstraction' and +and analysing it is called `symptom abstraction'. +\ifthenelse {\boolean{paper}} +{ +} +{ +This is dealt with in detail in chapter \ref{symptom_abstraction}. +} + % define difference between a \fg and a \dc A {\fg} is a collection of components, a {\dc} is a new `theorectical' component which has a set of failure modes, which -correspond to the failure modes of the {\fg} is was derived from. +correspond to the failure modes of the {\fg} it was derived from. We could consider a {\fg} as a black box, or component to use, and in this case it would have a set of failure modes. Looking at the {\fg} in this way is seeing it as a {\dc}. @@ -206,13 +226,13 @@ these `derived~failure~modes'. We thus have a `new' component, or system building block, but with a known and traceable fault behaviour. -The UML representation shows a `functional group' having a one to one relationship with a derived~component, -which we represent in the UML diagram in figure \ref{fig:cfg}. +The UML representation (in figure \ref{fig:cfg}) shows a `functional group' having a one to one relationship with a derived~component. The symbol $\bowtie$ is used to indicate the analysis process that takes a functional group and converts it into a new component. -This can be expresed as $ \bowtie ( FG ) \rightarrow DerivedComponent $ . +with $\mathcal{FG}$ represeting the set of all functional groups, and $\mathcal{DC}$ the set of all derived components, +this can be expresed as $ \bowtie : \mathcal{FG} \rightarrow \mathcal{DC} $ . \begin{figure}[h] @@ -224,7 +244,7 @@ This can be expresed as $ \bowtie ( FG ) \rightarrow DerivedComponent $ . \end{figure} -\subsection{Keeping track of the derived \\ components position in the hierarchy} +\subsection{Keeping track of the derived components position in the hierarchy} The UML meta model in figure \ref{fig:cfg}, shows the relationships between the classes and sub-classes. @@ -306,7 +326,7 @@ fm : \mathcal{FG} \rightarrow \mathcal{F} \end{equation} -\section{Unitary State Component \\ Failure Mode sets} +\section{Unitary State Component Failure Mode sets} \paragraph{Design Descision/Constraint} An important factor in defining a set of failure modes is that they @@ -325,7 +345,7 @@ within one package. This property, failure modes being mutually exclusive, is termed `unitary state failure modes' in this study. This corresponds to the `mutually exclusive' definition in -probability theory \cite{probstat}. +probability theory~\cite{probstat}. \begin{definition} @@ -342,7 +362,7 @@ the component failure modes in each of its members are unitary~state. Thus if the failure modes of a component $F$ are unitary~state, we can say $F \in \mathcal{U}$ is true. \end{definition} -\section{Component failure modes:\\ Unitary State example} +\section{Component failure modes: Unitary State example} An example of a component with an obvious set of ``unitary~state'' failure modes is the electrical resistor. @@ -397,7 +417,7 @@ with several modules that could all fail simultaneously, a process of reduction into smaller theoretical components will have to be made \footnote{A modern microcontroller will typically have several modules, which are configured to operate on pre-assigned pins on the device. Typically voltage inputs (\adcten / \adctw), digital input and outputs, -PWM (pulse width modulation), UARTs and other modules will be found on simple cheap microcontrollers \cite{pic18f2523}}. +PWM (pulse width modulation), UARTs and other modules will be found on simple cheap microcontrollers~\cite{pic18f2523}}. For instance the voltage reading functions which consist of an ADC multiplexer and ADC can be considered to be components inside the microcontroller package. @@ -410,14 +430,14 @@ in a {\fg} impractical due to the sheer size of the task. %%- Need some refs here because that is the way gastec treat the ADC on microcontroller on the servos -\section{Handling Simultaneous \\ Component Faults} +\section{Handling Simultaneous Component Faults} For some integrity levels of static analysis, there is a need to consider not only single failure modes in isolation, but cases where more then one failure mode may occur simultaneously. Note that the `unitary state' conditions apply to failure modes within a component. The scenarios presented here are where two or more components fail simultaneously. -It is an implied requirement of EN298 \cite{en298} for instance to +It is an implied requirement of EN298~\cite{en298} for instance to consider double simultaneous faults\footnote{This is under the conditions of LOCKOUT in an industrial burner controller that has detected one fault already. However, from the perspective of static failure mode analysis, this amounts @@ -460,7 +480,7 @@ $$ \mathcal{P}_{1} S = \{ \{a\},\{b\},\{c\} \} $$ A $k$ combination is a subset with $k$ elements. The number of $k$ combinations (each of size $k$) from a set $S$ -with $n$ elements (size $n$) is the binomial coefficient \cite{probstat} shown in equation \ref{bico}. +with $n$ elements (size $n$) is the binomial coefficient~\cite{probstat} shown in equation \ref{bico}. \begin{equation} C^n_k = {n \choose k} = \frac{n!}{k!(n-k)!} @@ -485,7 +505,7 @@ from $1$ to $cc$ thus -\subsection{Actual Number of combinations to check \\ with Unitary State Fault mode sets} +\subsection{Actual Number of combinations to check with Unitary State Fault mode sets} If all of the fault modes in $S$ were independent, the cardinality constrained powerset @@ -502,7 +522,7 @@ For example, say the cardinality constraint was 3, we would need to subtract both $|{n \choose 2}|$ and $|{n \choose 3}|$ for each component in the functional~group. -\subsubsection{Example: Two Component functional group \\ cardinality Constraint of 2} +\subsubsection{Example: Two Component functional group cardinality Constraint of 2} For example: suppose we have a simple functional group with two components R and T, of which $$fm(R) = \{R_o, R_s\}$$ and $$fm(T) = \{T_o, T_s, T_h\}$$. @@ -545,7 +565,7 @@ $$ \pagebreak[1] -\subsubsection{Establishing Formulae for unitary state failure mode \\ +\subsubsection{Establishing Formulae for unitary state failure mode cardinality calculation} The cardinality constrained powerset in equation \ref{eqn:ccps}, can be modified for % corrected for @@ -636,7 +656,7 @@ A recursive algorithm and proof is described in appendix \ref{chap:vennccps}. %% \pagebreak[1] -\section{Component Failure Modes \\ and Statistical Sample Space} +\section{Component Failure Modes and Statistical Sample Space} %\paragraph{NOT WRITTEN YET PLEASE IGNORE} A sample space is defined as the set of all possible outcomes. For a component in FMMD analysis, this set of all possible outcomes is its normal correct @@ -656,7 +676,7 @@ $$ F = \Omega(C) \backslash \{OK\} $$ The $OK$ statistical case is the largest in probability, and is therefore of interest when analysing systems from a statistical perspective. This is of interest for the application of conditional probability calculations -such as Bayes theorem \cite{probstat}. +such as Bayes theorem~\cite{probstat}. %%- diff --git a/component_failure_modes_definition/paper.tex b/component_failure_modes_definition/paper.tex index 1e593b9..abbeb88 100644 --- a/component_failure_modes_definition/paper.tex +++ b/component_failure_modes_definition/paper.tex @@ -4,6 +4,7 @@ \usepackage{fancyhdr} \usepackage{tikz} \usepackage{amsfonts,amsmath,amsthm} +\usepackage{lastpage} \usepackage{ifthen} \newboolean{paper} \setboolean{paper}{true} % boolvar=true or false @@ -14,13 +15,21 @@ \begin{document} \pagestyle{fancy} +\fancyhf{} +%\renewcommand{\chaptermark}[1]{\markboth{ \emph{#1}}{}} +\fancyhead[LO]{} +\fancyhead[RE]{\leftmark} +%\fancyfoot[LE,RO]{\thepage} +\cfoot{Page \thepage\ of \pageref{LastPage}} +\rfoot{\today} +\lhead{Definitions, Components, Functional Groups and Unitary State Failure Mode Sets} %\outerhead{{\small\bf Definitions, Components, Functional Groups and Unitary State Failure Mode Sets}} %\innerfoot{{\small\bf R.P. Clark } } % numbers at outer edges \pagenumbering{arabic} % Arabic page numbers hereafter \author{R.P.Clark} -\title{Definitions, Components, Functional Groups \\ and Unitary State Failure Mode Sets} +\title{Definitions, Components, Functional Groups and Unitary State Failure Mode Sets} \maketitle \input{component_failure_modes_definition_paper} @@ -29,3 +38,7 @@ \today \end{document} + + +\begin{document} +