\paragraph{Abstract}{
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 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 and static testing. 
%
Static testing is at the theoretical, or design level, and involves
looking a 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), a commonly
used technique that is legally mandatory for a wide range of equipment.

The ability to assess the safety of man made equipment has been a concern 
since the dawn of the industrial age~\cite{indacc01,usefulinfoengineers,steamboilers}.
The philosophy behind safety measure has progressed
with time, and by world war two~\cite{boffin} we begin to see concepts such as `no single component failure should cause
a dangerous system failure' emerging. 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 not being allowed to cause dangerous states.
%
The concept of a double failure causing a dangerous condition being unacceptable,
can be found in the legally binding European standard EN298 which became
a legal requirement 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 failure per billion hours of operation. 
We can then broadly separate these ratings failure rates into safety integrity levels (SIL).
So for a maximum of 10 failures per billion hours of operation we assign a SIL level of 4,
for 100 a sil level of 3 etc.
If we can determine a SIL rating
we can match it against the 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.
SIL ratings give us another objective yardstick to measure system safety.
%governing failure conditions and determining risk levels associated with systems.

All of these risk assessment techniques are based on variations 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 fixing the most financially
draining problems in a product first.

This thesis show that the refinements and additions made to
FMEA to tailor them for military or statistical commercial use, have 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 impossibility
of integrating software and hardware failure mode models are the most obvious of these. %flaws.
The methodologies are explained in chapter~\ref{sec:chap2} and the advantages and drawbacks
of each FMEA variant are examined in chapter~\ref{sec:chap3}.
In chapter~\ref{sec:chap4}, a new methodology is then 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 electronic circuits and then at electronic/software hybrid systems.
}

\section{Introduction}
The motivation for this study came form two sources, one academic and the other 
practical. 
\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.
\paragraph{European Safety Requirements increase in scope and complexity.}
At work, 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. 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
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 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 any all combinations of 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.
FMEA had 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 section of
circuitry (for instance repeated 4-20mA outputs on a PCB), meant that
analysis of identical circuitry was performed many times.
A desirable feature of a new methodology would be to be able to re-use
analysis for identical repeated modules. The development of this new methodology
was presented to the IET System safety conference in 2011~\cite{syssafe2011}.
FMEA, currently cannot integrate software into its failure mode models.
A modular variant of FMEA can use the existing structure of functional software, in conjunction
with contract programming, to model software~\cite{syssafe2012}.
%
\paragraph{Modularising FMEA and augmenting this with concepts from Euler/Spider Diagrams}
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 were I to analyse the problem in small modules, from the bottom-up following the FFT example, I could apply
checking for all double failure scenarios.
Once these first modules were analysed, I now call them {\fgs}, I could determine the symptoms of failure for them
Using the symptoms of failure, I could now treat these modules as components, now called {\dcs}, and use them to build higher level
modules. I could apply double simultaneous failure mode checking, because the number of components
in each module/{\fg} was quite small---thus avoiding state explosion problems, but I could apply
double checking all the way up the hierarchy. 
In fact this means, as a 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
and these are held in a data structure, we can apply automated methods to search all cardinalities of multiple failure modes
within the model.
%
Because, Euler/Spider Diagrams
could be used to model failure modes in components
it was thought that a diagrammatic notation would
be easier to demonstrate than using formal logic.
%

For an FMEA Spider diagram, contours represent failure modes, and the spider diagram 
`existential~points' 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 Brighton University.
This brought together concepts for modularising FMEA and the formal visual notations from Spider diagrams.
Euler diagrams have been used later in the thesis to describe the containment relationships
of derived components building hierarchical analysis models with the modularised
variant of FMEA that this thesis proposes and defends.

\paragraph{Objectives of the thesis}.
The primary objective of the work performed for this thesis is to propose a modularised variant of
FMEA that 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}


Chapter~\ref{chap2} examines the current state of FMEA based methodologies, Chapter~\ref{chap3}
examines the benifits and drawbacks of these these methodologies
and proposes a detailed wish list for an ideal FMEA technique.
Chapter~\ref{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{chap5} provides worked examples usin g common electronic circuits.
Chapter~\ref{chap6} gives two examples of integgrated software and electronic systems anyalysed using FMMD.
Metrics and evaluation, along with an example showing double simultaneous failure analysis
are dealt with in Chapter~\ref{chap7}



% \section{Case Study: Safety Critical Product Approval changes  for EN298:2003}
% 
% FMEA performed on selected areas perceived as critical
% by test house.
% Blanket measures, RAM ROM checks, EMC, electrical and environmental stress testing
% 
% \subsection{Practical limitations of testing for certification vs. rigorous approach}
% 
% State explosion problem considering a failure mode of a given component against
% all other components in the system i.e. an exponential ($2^N$) order of processing resource 
% rather than a polynomial i.e. $N^2$.
% 
% Impossible to perform double simultaneous failure analysis (as demanded by EN298~\cite{en298}).