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\newcommand{\fmmdgloss}{\glossary{name={FMMD},description={Failure Mode Modular De-Composition, a bottom-up methodolgy for incrementally building failure mode models, using a procedure taking functional groups of components and creating derived components representing them, and in turn using the derived components to create higher level functional groups, and so on, that are used to build a failure mode model of a SYSTEM}}}
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\lhead{Developing a rigorous bottom-up modular static failure mode modelling methodology}

%\outerhead{{\small\bf Developing a rigorous bottom-up modular static failure mode modelling methodology}}
%\innerfoot{{\small\bf R.P. Clark } }   
                                              % numbers at outer edges
\pagenumbering{arabic}                        % Arabic page numbers hereafter
\author{R.P.Clark$^1$ , Andrew~Fish$^2$ , John~Howse$^2$ , Chris Garret$^2$ \\
        $^1${\em Energy Technology Control, Lewes,UK} \and $^2${\em University of Brighton, UK}
}

\title{Developing a rigorous bottom-up modular static failure mode modelling methodology}
\maketitle 


\abstract{
The certification process of safety critical products for European and 
other international standards often involve environmental stress, 
endurance and EMC testing. Theoretical, or 'static testing',
is often also required to highlight modifications that must be made to
improve the product safety, or identify theoretical weaknesses in the design.
This paper proposes a new theoretical methodology for creating failure mode models of safety critical systems.
It has a common notation for mechanical, electronic and software domains and is modular and hierarchical.
These properties provide advantages in rigour and efficiency when compared to current methodologies.
% This paper proposes a methodology for
% creating failure mode models of safety critical systems, which
% has a common notation
% for mechanical, electronic and software domains and applies an
% incremental and rigorous approach.
% 
% The four main static failure mode analysis methodologies were examined and 
% in the context of newer European safety standards, assessed.
% Some of the deficiencies identified in these methodologies led to
% a wish list for a more rigorous methodology.
% %%
%% What I have found
%%
% From the wish list 
% %and considering some constraints determined from
% %the evaluation of the four established methodologies, 
% a new
% methodology is developed and proposed. 
% This has been named Failure Mode Modular De-Composition (FMMD).
% 
% %% Sell it
% %%
% In addition to addressing the traditional weaknesses of
% Fault Tree Analysis (FTA), Fault Mode Effects Analysis (FMEA), Failure Mode Effects Criticality Analysis (FMECA)
% and Failure Mode Effects and Diagnostic Analysis (FMEDA), FMMD provides the means to model multiple failure mode scenarios 
% as specified in newer European Safety Standards \cite{en298}.
% The proposed methodology is bottom-up and can guarantee to leave no component failure mode un-handled. 
% It is also modular, meaning that the results of analysed components may be re-used in other projects.
}

\section{Introduction}

\subsection{Current methodologies} 

We briefly analyse the four current methodologies.

\subsubsection{Fault Tree Analysis (FTA)}

FTA is a top down methodology in which a diagram is drawn for
each undesirable top level event, presenting the conditions that must arise to cause
the event. It is suitable for large complicated systems with few undesirable top
level events 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. 
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, 
and there is no facility to cross check between diagrams. It has limited 
support for environmental and operational states.


\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 
failure mode ratio. A list of failures and their cost is generated. 
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 
component interactions that cause system failure modes or determine potential 
problems from simultaneous failure modes. It does not consider environmental 
or operational states in sub-systems or components. It cannot model 
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 
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 
criticality. 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 
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.

\subsection{Summary of Defeciencies in Current Methods}

\paragraph{Top Down approach} The top down technique FTA, introduces the possibility of missing base component
level failure modes~\cite{faa}[Ch.9]. Also one FTA treee is drawn for each top level
event, leading to repreated work, with limitied ability for cross checking.

\paragraph{State Explosion problem}
The bottom -up techniques all suffer from a problem of state explosion.
To perform the analysis rigorously, we need to consider the effect
of a component failure agiaist 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 base~component can fail). The 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
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 applied states or environmental conditions to consider
in a system, and $A$ the number of applied states,
the job of the bottom-up analyst is presented with two
additional %cross product 
factors, 
$(N-1) \times N \times K \times E \times A$.
If we put some typical very small embedded system numbers\footnote{these figures would
be typical of a very simple temperature controller, with a micro-controller sensor 
and heater circuit.} into this, say $N=100$, $K=2.5$, $A=2$, and $E=10$
we have $99 \times 100 \times 2.5 \times 10 \times 2 = 495000 $.
To look in detail at a half of a million test cases is obviously impractical.
% Requirements for an improved methodology The deficiencies identified in the 
% current methodologies are used to establish criteria for an improved methodology.

\paragraph{Reasoning distance - complexity and reachability}
Tracing a component level failure up to a top level event, without rigour involving state explosion, involves
working heuistically. A base component failure will typically 
be concepually removed by several stages from a top level event.
The reasoning distance can be determined by the number of components
that must interact to reach the top level event.
% could have a chapter on this.
% take a circuit or system and follow all the interactions
% to the components that cause the system level event.

\paragraph{Multiple Events from one base component failure mode}
A base component failure may mpotentially cause more than one
SYSTEM level failure mode.
It could be possible to identify one top level event asssociated with
a {\bcfm} and not investigate other possibilities. 
 
\section{Requirements for a new static faiilure mode Analysis methodology}

A new methodology must ensure that it represents all component failure modes and it therefore should be bottom-up, 
starting with individual component failure modes. 

In order to control the state explosion problem, the process must be modular
and deal with small groups of components.


Components should be broken 
down into small functional groups to enable the examination of the effect of a
component failure mode on the other components in the group.
The functional group can now be considered as `derived component' with a known set 
of failure symptoms. We can use this `derived component' to build higher level 
functional groups.
This helps with the reasoning distance problem,
because we can trace failure modes back through complex interactions and have a structure to
base our reasoning on, at each stage.



Development of the new methodology 

An ontology is developed of 
failure modes and their relationship to environmental factors, 
operational states and the hierarchical nature inherent in product design, 
defining the relationships between the system as a whole, components, 
failure modes, operational and environmental states. 

DEVELOP UML MODELS



The ontology is used 
to determine the nature of a hierarchy modelling the system, and to which 
entities, various conditions/procedures are germane. From the ontology, 
we determine that environmental effects relate to components, and 
operational states to functional groups. A functional group can be 
analysed with respect to its component failure modes, operational 
states and environmental conditions and from this a set of failures 
modes, or symptoms for the functional group can be determined. A functional group 
can be treated as a derived component. Derived components can be 
used to build functional groups at a higher level. In this manner we 
can build a hierarchical model with each layer consisting of 
components derived from the functional groups of derived components.
From the ontology, a set of rules for simplifying the failure 
modes (collecting them into common symptoms) as we traverse up the 
hierarchy is developed. The hierarchical model can have layers added 
until it converges to a top level single functional group. On collecting 
symptoms from this, we are left with the top level, or system level, failure modes.
The model is presented in a diagrammatic notation that has been 
designed to be intuitive and understandable. It uses well tested 
visual techniques to represent the elements of the model and their 
relationships. Software support for the development of models in this 
notation has been designed and proof-of-concept tools have been implemented.



\section{Conclusion}

This new approach is called 
Failure Mode Modular De-Composition (FMMD) and is designed 
to be a superset of the current four approaches, that is to say, 
from an FMMD model, we should be able to 
derive models that the other four methodologies would have been 
able to create. As this approach is modular, many of the results of 
analysed components may be re-used in other projects, so 
test efficiency is improved.
FMMD is based on generic failure modes, so it is not constrained to a 
particular field. It can be applied to mechanical, electrical or software domains. 
It can therefore be used to analyse systems comprised of electrical,
mechanical and software elements in one integrated model.


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