git mix up... fixing I hope

fmmd_concept/System_safety_2011/submission.tex

@@ -57,6 +57,7 @@ failure mode of the component or sub-system}}}
 }
 
 \title{Developing a rigorous bottom-up modular static failure mode modelling methodology}
+%\nodate
 \maketitle 
 
 
@@ -74,13 +75,19 @@ These properties provide advantages in rigour and efficiency when compared to cu
 
 \section{Introduction}
 
-\subsection{Current methodologies} 
+This paper describes and criticises the four current failure mode methodologies,
+presents a table of the deficiencies and advantages, and then presents a new proposed
+methodology. A worked example is then provided, which models the failure mode
+behaviour of a non inverting op-amp.
+
+ 
+\paragraph{Current methodologies} 
 
 We briefly analyse the four current methodologies.
 
-\subsubsection{Fault Tree Analysis (FTA)}
+\paragraph{Fault Tree Analysis (FTA)}
 
-FTA is a top down methodology in which a diagram is drawn for
+FTA is a top down methodology in which a hierarchical diagram is drawn for
 each undesirable top level failure, presenting the conditions that must arise to cause
 the event. 
 %
@@ -88,14 +95,26 @@ It is suitable for large complicated systems with few undesirable top
 level failures and focuses on those events considered most important or most catastrophic.
 %
 Effects of duplication/redundancy of safety systems can be readily assessed. 
-It uses notations that are readily understood by engineers (logic symbols from digtal electroics and a fault hierarchy). 
+It uses notations that are readily understood by engineers (logic symbols from digital electronics and a fault hierarchy). 
 However, it cannot guarantee to model all base component failure modes 
 or be used to determine system level errors other than those modelled. 
-Each diagram is a separate model, creating duplication of modelled elements, 
+%
+Each FTA diagram models one top level event.
+This creates duplication of modelled elements, 
 and there is no facility to cross check between diagrams. It has limited 
 support for environmental and operational states.
 
 
+<<<<<<< HEAD
+\paragraph{Fault Mode Effects Analysis FMEA)} is used principally in manufacturing. 
+Each top level failure is assessed by its cost to repair and its frequency,%, using a 
+%failure mode ratio. 
+A list of failures and their cost is then calculated. 
+It is easy to identify single component failure to system failure scenarios 
+and an estimate of product reliability can be calculated. 
+%
+It cannot focus on 
+=======
 \subsection{Fault Mode Effects Analysis FMEA)}
 FMEA is used principally in manufacturing. 
 Each defect is assessed by its cost to repair and its frequency. %, using a 
@@ -110,32 +129,30 @@ self-checking safety elements or other in-built safety features or
 analyse how particular components may fail.
 
 
-\subsection{Failure Mode Criticality Analysis (FMECA)}
-FMECA is a refinement of FMEA, using 
+\paragraph{Failure Mode Criticality Analysis (FMECA)} is a refinement of FMEA, using 
 two extra variables: the probability of a component failure mode occurring 
 and the probability that this will cause a top level failure, and the perceived 
 criticallity. It gives better estimations of product reliability/safety and the 
 occurrence of particular system failure modes than FMEA but has similar deficiencies.
 
 
-\subsection{Failure Modes, Effects and Diagnostic Analysis (FMEDA)}
-
-FMEDA is a refinement of 
+\paragraph{Failure Modes, Effects and Diagnostic Analysis (FMEDA)} is a refinement of 
 FMEA and FMECA and models self-checking safety elements. It assigns two 
 attributes to component failure modes: detectable/undetectable and safe/dangerous.
  Statistical measures about the system can be made and used to classify a 
 safety integrity level. It allows designs with in-built safety features to be assessed. 
 Otherwise, it has similar deficiencies to FMEA but has limited support 
 for environmental and operational states in sub-systems or components, 
-via self checking statistical mitigation.
+via self checking statistical mitigation. FMEDA is the methodology associated with 
+the safety integrity standards IOC5108 and EN61508~\cite{en61508}.
 
 \subsection{Summary of Defeciencies in Current Methods}
 
-\subsubsection{Top Down approach: FTA} The top down technique FTA, introduces the possibility of missing base component
+\paragraph{Top Down approach: FTA} The top down technique FTA, introduces the possibility of missing base component
 level failure modes~\cite{faa}[Ch.9]. Since one FTA tree is drawn for each top level
 event, this leads to repeated work, with limited ability for cross checking/model validation.
 
-\subsubsection{Bottom-up approach: FMEA, FMECA, FMEDA}
+\subsection{Bottom-up approach: FMEA, FMECA, FMEDA}
 
 \paragraph{State Explosion problem}
 The bottom -up techniques all suffer from a problem of state explosion.
@@ -144,7 +161,7 @@ of a component failure against all other components. Adding environmental
 and operational states further increases this effect.
 
 Let N be the number of components in our system, and K be the average number of component failure modes
-(ways in which a component can fail). The total number of base component failure modes
+(ways in which a component can fail). The approximate total number of base component failure modes
 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
@@ -152,7 +169,7 @@ 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 environmental conditions to consider
 in a system, and $A$ the number of applied/operational states (or modes of the SYSTEM),
-the job of the bottom-up analyst is presented with two
+the bottom-up analyst is presented with two
 additional %cross product 
 factors, 
 $(N-1) \times N \times K \times E \times A$.
@@ -193,28 +210,30 @@ To look in detail at a half of a million test cases is obviously impractical.
 \paragraph{Multiple Events from one base component failure mode}
 A base component failure may potentially cause more than one
 SYSTEM level failure mode.
-It could be possible to identify one top level event associated with
+It would be possible to identify one top level event associated with
 a {\bcfm} and not investigate other possibilities. 
  
 %\section{Requirements for a new static failure mode Analysis methodology}
 
-\section{Desireable Criteria for a failure mode methodology}
-From the deficiencies outlined above, ideally  we can form a wish list for a better methodology.
+\section{Desireable Criteria for a failure mode methodology}.
+From the deficiencies outlined above, ideally  we can form a set of desirable criteria for a better methodology.
 { \small
-\begin{itemize}
+\begin{enumerate}
+%\begin{itemize}
 \label{fmmdreq}
-\item Address the state explosion problem.
-\item Ensure that all component failure modes be considered in the model.
-\item Be easy to integrate mechanical, electronic and software models \cite{sccs}[pp.287].
-\item Be re-usable, in that commonly used modules can be re-used in other designs/projects.
-\item It should have a formal basis, that is to say, be able to produce mathematical traceability
+\item Address the state explosion problem. % 1
+\item Ensure that all component failure modes be considered in the model. % 2
+\item Be easy to integrate mechanical, electronic and software models \cite{sccs}[pp.287]. %3
+\item Be re-usable, in that commonly used modules can be re-used in other designs/projects. %4
+\item It should have a formal basis, that is to say, be able to produce mathematical traceability %5
 for its results, such as  error causation trees.%, reliability and safety statistics.
 %\item It should be easy to use, ideally using a 
 %graphical syntax (as opposed to a formal symbolic/mathematical text based language).
 %\item From the top down, the failure mode model should follow a logical de-composition of the functionality
 %to smaller and smaller functional groupings \cite{maikowski}.
-\item Be able to model multiple (simultaneous) failure modes.% from the base component level up.
-\end{itemize}
+\item Be able to model multiple (simultaneous) failure modes.% 6 % from the base component level up.
+\end{enumerate}
+%\end{itemize}
 }
 
 % A new methodology must ensure that it represents all component failure modes and it therefore should be bottom-up,