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%% $$ \int_{0\-}^{\infty} f(t).e^{-s.t}.dt \; | \; s \in \mathcal{C}$$
This thesis describes the application of, mathematical (formal) techniques to
the design of safety critical systems.
The initial motivation for this study was to create a system
applicable to industrial burner controllers.
The methodology developed was designed to cope with
both the
deterministic
and
probablistic approaches.
\paragraph{Safety Critical Controllers, knowledge and culture sub-disiplines}
The maturing of the application of the programmable electronic controller (PEC)
for a wide range safety critical applications, has led to a fragmentation of subdisiplines
which speak imperfectly to one another.
The main three sub-disiplines are Electrical, Software and Mechanical engineering.
Additional disiplines are defined by application area of the PEC. These sub-displines
are in turn split into even finer units.
The practicioners of these fields tend to view a PEC in different ways.
Discoveries and culture in one field diffuse only slowly into the conciousness of a specialist in another.
Too often, one disipline's unproven assumptions or working methods, are treated as firm boundary conditions
for an overlapping field.
\paragraph{Safety Assessment/analysis of PEC's}
For a anyone responsible for ensuring or proving the safety of a PEC must be able
to understand the process being controlled, the mechanical and electrical
sensors and actuators and the software. Not only must the
safety engineer understand more than four potential disiplines, he/she
must be able to trace failure modes of components to SYSTEM levels failure modes,
and classify these according to their criticallity.
\paragraph{Desirability of a common failure mode notation}
Having a common failure mode notation accross all disciplines in a project
would allow all the specialists to prepare failure mode
analysis and then bring them together to model the PEC.
The visual notation developed was initially designed for electronic fault modelling.
However, it was realised that it could be applied to mechanical and software domains as well.
\paragraph{Scope of thesis}
This thesis describes the application of, a common notation mathematical notation to
describe the design of safety critical systems/PEC's.
The initial motivation for this study was to create a system
applicable to industrial burner controllers\footnote{Burner Controllers cover the disiplines of
combustion, high pressure steam and hot water, mechanical control, electronics and embedded software.}.
The methodology developed was designed to cope with
both the deterministic\footnote{Deterministic failure mode analysis traces failure mode effects} and probablistic approaches
\footnote{Probablistic failure mode analysis tries to determine the probability of given SYSTEM failure modes}.
\paragraph{Visual form of the notation}
The visual notation developed was initially designed for electronic fault modelling.
The notation deals with failure modes of components using a diagram derived from
Euler and Spider diagrams.
However, as the notation dealt with generic failure modes, it was realised that it could be applied to mechanical and software domains as well.
This changed the target for the study slightly to encompass these three domains in a common notation.
\section{Background}