\label{sec:chap1}

%\paragraph{Abstract} % : The Scope of this study.}{
{
%
Increasingly we rely on automation in everyday life.
Many % of the 
automated systems have the potential to cause harm or even death should they fail.
%
Safety assessment and certification is now required for %of
almost all potentially dangerous equipment.
%
As part of the assessment/certification process, we typically apply
a battery of tests, examining features such as resistance to extremes of environment, Electro Magnetic Compatibility (EMC),
endurance regimes and static testing. 
%
Static testing is at the theoretical, or design level, and involves
looking at failure scenarios and trying to predict how systems would react.
%
This thesis deals with one area of static testing, that of Failure Mode Effects Analysis (FMEA)~\cite{iec60812}, a commonly
used technique that is legally mandatory for a wide range of equipment certification.

The ability to assess the safety of man made equipment has been a concern 
since the dawn of the industrial age~\cite{usefulinfoengineers,steamboilers}.
%
The philosophy behind safety measures has progressed
with time and by World War Two we began to see concepts such as `no single component failure should cause
a dangerous system failure'~\cite{boffin} emerging~\cite{echoesofwar}[Ch.13]. 
%
Concepts such as these allow us to apply
objective criteria to safety assessment. We can extend the `no~single~failure' concept
to double or even multiple failures being unacceptable as the cause of dangerous states.
%
The concept of a double failure causing a dangerous condition being forbidden
can be found in the legally binding European standard EN298\footnote{EN298:2003 became
a legal requirement for all new forced draft industrial burner controllers in 2006 within
the European Union.} which 
came into force 
in 2006~\cite{en298}.
%
More sophisticated statistically based standards, i.e EN61508~\cite{en61508} and variants thereof,
are based on statistical thresholds for the frequency of dangerous failures.
%
We could state, for instance, that we can tolerate an `acceptable' maximum number of
dangerous failures per billion hours of operation. 
%
We can then broadly categorise ratings of failure rates into Safety Integrity Levels (SIL)~\cite{scsh}.
%
So for a maximum of 10 potentially dangerous failures per billion hours of operation we assign a SIL level of 4,
for 100 a SIL level of 3, and so on in powers of ten.
%
If we can determine a SIL rating,
we can match it against a risk. 
%
The more dangerous the consequences of failure
the higher SIL rating we can demand for it.
%
A band-saw with one operative may require a SIL rating of 1,
a nuclear power-station, with far greater consequences  on dangerous failure
may require a SIL rating of 4.
%
What we are saying is that while we may tolerate a low incidence of failure on a band-saw,
we will only tolerate extremely low incidences of failure in nuclear plant. 
SIL ratings give us another objective yardstick for the measurement of system safety.
%governing failure conditions and determining risk levels associated with systems.

All of these risk assessment techniques are based on variations of %on the theme of 
Failure Mode Effect Analysis (FMEA), which has its roots in the 1940's mass production industry
and was designed to save large companies money by prioritising the most financially
draining problems in a product. % first.
%
The FMEA of the 1940's has been refined and extended into four main variants.
%
This thesis describes the refinements and additions made to
FMEA to tailor them for military or statistically biased % commercial 
use.
It then reveals common flaws 
which make them unsuitable for the higher safety requirements of the 21st century.
%
Problems with state explosion in failure mode reasoning and the current difficulties %impossibility
of integrating software and hardware failure mode models~\cite{1372150} are the most obvious of these. %flaws.
%
The four current methodologies are described in chapter~\ref{sec:chap2} and %the advantages and drawbacks
%of each FMEA variant are examined 
critically assessed in chapter~\ref{sec:chap3}.
In chapter~\ref{sec:chap4}, a new methodology is proposed which addresses the state explosion problem
and, using contract programmed software, allows the modelling of integrated
software/electrical systems.
%
This is followed by two chapters showing examples of the new modular FMEA analysis technique (Failure Mode Modular De-Composition FMMD)
firstly looking at common electronic circuits and then at electronic/software hybrid systems.
}

\section{Motivation}
The motivation for this study came from two sources, one academic (my Software Engineering MSc project) and the other 
practical (as a practising embedded software engineer working with FMEA on safety critical burner systems). 
%
% AF does not think the paragraph below should be included 12JAN2013
\paragraph{MSc Project: Euler/Spider diagram Editor.}
I had recently completed an
MSc and my project was to create an Euler/Spider~Diagram~\cite{howse:spider} editor in Java.
This editor allowed the user to draw Euler/Spider diagrams, and could then 
represent these as abstract---i.e. mathematical---definitions.
%
The primary motive for writing the Spider diagram editor was to provide an alternative
to formal languages for software specification.
%
An added attraction for using spider diagrams was that they could be used in 
proving logic~\cite{stapleton:atpieds} and theorems~\cite{theoremflower,Fish200553} in an intuitive way.
%
Because of my daily work exposure to FMEA, 
I started thinking of ways to apply formal languages and spider diagrams to
failure mode analysis.
%
%
\paragraph{European Safety Requirements increase in scope and complexity.}
At work---which consisted of designing, testing, building and writing embedded `C' and assembly language code for safety critical
industrial burners---we were faced with a new and daunting requirement.
Conformance to the latest European standard, EN298~\cite{en298}. 
%
It appeared to ask for the impossible:
not only did it require the usual safety measures (self checking of ROM and RAM, watchdog processors with separate clock sources,  EMC and the
triple fail safe control of valves), it had one new clause in it that had far reaching consequences.
%
It stated that in the event of a failure, where the controller had gone into a `lockout~state'--- a state where the controller
applies all possible safety measures to stop fuel entering the burner---it was not permitted to % could not 
become dangerous should another fault occur.
%
In short this meant we had to be able to deal with double failures.
%
Any of the components that could, in failing, create a dangerous state were already
documented and approved using failure mode effects analysis (FMEA). 
%
This new requirement
effectively meant that all single and double component failures were
now required to be analysed. 
%
This, from a state explosion problem alone,
meant that it was going to be virtually impossible to perform.
%
To compound the problem, %state explosion problem
FMEA has a deficiency of repeated work, as each component failure is typically represented
by one line or entry in a spreadsheet~\cite{bfmea}; analysis on repeated sections of
circuitry (for instance repeated {\ft} outputs on a PCB) meant that
analysis of identical circuitry was performed many times.
%

%
\subsection{Modularising/De-Composing FMEA: Initial concepts.} % and augmenting this with concepts from Euler/Spider Diagrams.}
In the field of digital signal processing there is an algorithm that revolutionised 
access to frequency analysis of digital samples called the Fast Fourier transform (FFT)~\cite{fftoriginal}.
This took the discrete Fourier transform (DFT), and applied de-composition to its 
mesh of (often repeated) complex number calculations~\cite{fpodsadsp}[Ch.8].
%
By doing this it broke the computing order of complexity problem down from having a polynomial %n exponential
%order 
to logarithmic order~\cite{ctw}[pp.401-3].
I wondered if this thinking could be applied to the state explosion problems encountered in FMEA.
%
%Following the concept of de-composing a problem, and thus simplifying the state explosion---using the thinking behind
%the fast Fourier transform (FFT)~\cite{fpodsadsp}[Ch.8], which takes a complex intermeshed series of real and imaginary  number calculations
%and by de-composing them, simplifies the problem.
My reasoning was that if we analysed %were we to analyse 
the problem in small modules, from the bottom-up following the FFT example, we could apply
checking for all double failure scenarios.
%
Once these first modules were analysed---we now call them {\fgs}---we could determine the symptoms of failure for them.
Using the symptoms of failure, we could now treat these modules as components in their own right---or {\dcs}---and use them to build higher level
{\fgs}. Higher and higher levels of {\fgs} could be built until we had a hierarchy
representing a failure mode model for the system.
%
Because this is modular, we can apply double simultaneous failure mode checking; and as %because 
the number of components
in each {\fg} is typically small---we  avoid state explosion problems. % for the general case. % AF says `in the general case' here 12JAN2013
%
%
If we apply
double checking all the way up the hierarchy we can guarantee to have considered
every double simultaneous failure of all components in a system. 
%
This means, as a fortunate by-product, that many multiple as well as double
failures would be analysed, but because failure modes are traceable from the base components to the top level---or system---failure modes
these relationships can be  held in a traversable data structure.
%
If held in a traversable data structure we can apply automated methods to search for all the combinations of multiple failure modes
within the model that had been analysed. Because of this, it will not always %it may not 
be necessary to apply double checking
at all higher levels in the analysis hierarchy, to achieve complete double failure coverage.
%
The points at which it is possible to relax double failure checking can be verified automatically by traversing
the failure mode model.
%
\subsection{Initial direction: Application of Spider diagrams to FMEA.}

Because, Euler/Spider Diagrams~\cite{howse:spider}
could be used to model failure modes in components
it was thought that a diagrammatic notation would
be more user friendly than using formal logic.
%
For an FMEA Spider diagram, contours represent failure modes, and the Spider diagram 
`existential~points' represent instances of failure modes.
%
Overlapping contours could represent multiple failure modes.
%
By drawing a spider collecting existential points, a common failure symptom could 
be determined and from this a new diagram generated automatically to represent the {\dc}.
%
Each spider represented a derived failure mode.
The act of collecting common symptoms by drawing spiders
meant that the analyst was forced to associate one component failure mode with one symptom/derived~failure~mode of failure.
%
These concepts were presented at the ``Euler~2004''~\cite{Clark200519} conference held at the University of Brighton. % 
%
This defined the concepts for modularising FMEA using the formal visual notations from Spider diagrams.
This lead to work on rapidly calculating available zones in Euler diagrams~\cite{Clark_fastzone}.
%
The spider diagram notation was useful in defining the concepts and 
initial ideas, but a more traditional `spreadsheet' format has been used
for the analysis stages of the new methodology.
%
Euler diagrams have been used later in the thesis to describe the containment relationships
of derived components when building hierarchical analysis models with the modularised
variant of FMEA that this thesis proposes and defends.
%

%
\section{Objectives of the thesis.}
The primary objective of the work performed for this thesis is to present  a new modularised variant of
FMEA which solves the problems of:
\begin{itemize}
 \item State Explosion,
 \item Multiple failure mode modelling,
 \item Re-usability of pre-analysed modules,
 \item Inclusion of software in failure mode modelling.
\end{itemize}
To support this, worked examples using the new methodology were created and the work published and presented to
IET safety conferences. % in 2011~\cite{syssafe2011} and 2012~\cite{syssafe2012}.
%
The development of FMMD, starting with a critique of FMEA and a wish-list for a better methodology,
was presented to the IET System safety conference in 2011,~\cite{syssafe2011}.
%
FMEA, currently cannot integrate software models into its hardware failure mode models~\cite{sfmea,modelsfmea,embedsfmea,sfmeainterface}.
%
FMMD can use the existing structure of functional software, in conjunction
with contract programming, to model software and this concept was presented to the IET System safety conference in 2012~\cite{syssafe2012}.

\paragraph{Overview---quick guide to contents of the thesis.}
Chapter~\ref{sec:chap2} examines the current state of FMEA based methodologies, Chapter~\ref{sec:chap3}
examines the benefits and drawbacks of these methodologies
and proposes a detailed wish list for an ideal FMEA technique.
Chapter~\ref{sec:chap4} proposes Failure Mode Modular de-composition (FMMD)---a modularised variant
of FMEA designed to address the points in the detailed wish list.
Chapter~\ref{sec:chap5} provides worked examples using common electronic circuits.
Chapter~\ref{sec:chap6} gives two examples of integrated software and electronic systems analysed using FMMD.
Metrics and evaluation, along with an example showing double simultaneous failure analysis,
are provided in Chapter~\ref{sec:chap7}, with a conclusion and further work in Chapter~\ref{sec:chap8}.

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