robin/Robin_PHD
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

as sent to Andrew fish just now

Browse Source
This commit is contained in:
Robin Clark 2010-04-22 13:47:05 +01:00
parent e03e9acfe5
commit 7be8ef047b
1 changed files with 50 additions and 30 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

80
component_failure_modes_definition/component_failure_modes_definition.tex
View File

@ -2,7 +2,8 @@
\abstract{ This chapter defines what is meant by the terms
components, component fault modes and `unitary~state' component fault modes.
The application of Bayes theorem in current methodologies, and
the unsuitability of the `null hypothesis' or p value statistical approach.
the suitability of the `null hypothesis' or `P' value statistical approach
ar discussed.
Mathematical constraints and definitions are made using set theory.
}
@ -19,12 +20,12 @@ Using these failure modes we can build a `failure model' from the bottom-up.
Traditional static fault analysis methods work from the top down.
They identify faults that can occur in a system, and then work down
to see how they could be caused. Some apply statistical tequniques to
determine the likelyhood of component failures causing specific system level errors (see Bayes theorem \ref{bayes}).
determine the likelihood of component failures causing specific system level errors (see Bayes theorem \ref{bayes}).
Another top down technique is ato apply cost benifit analysis
to determine which faults are the highest priority to fix\cite{FMEA}.
The aim of this study is to produce complete failure
models of safety critical systems from the bottom-up
models of safety critical systems from the bottom-up,
starting, where possible with known component failure modes.
@ -33,7 +34,7 @@ starting, where possible with known component failure modes.
It is helpful here to define some terms, `system', `functional~group', `component', `base~component' and `sub-system'.
A System, is really any coherent entity that would be sold as a safety critical product.
A sub-system is a system that is part of some larger system.
A sub-system is a part of some larger system.
For instance a stereo amplifier separate is a sub-system. The
whole Sound System, consists perhaps of the following `sub-systems':
CD-player, tuner, amplifier~separate, loudspeakers and ipod~interface.
@ -43,18 +44,23 @@ CD-player, tuner, amplifier~separate, loudspeakers and ipod~interface.
%and breaks it down.
A sub-system will be composed of component parts, which
may themselves be sub-systems. However each `component part'
will have a fault/failure behaviour and it should
always be possible to obtain a set of failure modes
for each `component'.
may themselves be sub-systems.
Eventually by a recursive downwards process we would be able to identify
sub-systems built from base component parts.
Each `component part'
will have a known fault/failure behaviour.
That is to say, each base component has a set of known
ways in which it can fail.
If we look at the sound system again as an
example; the CD~player could fail in serveral distinct ways, no matter
what has happened to it or has gone wrong inside it.
A top down approach has an intrinsic problem in that we cannot guess
every possible failure mode at the SYSTEM level.
Using the reasoning that working from the bottom up forces the consideration of all possible
component failures (which can be missed in a top~down approach)
component failures (which could be missed in a top~down approach)
we are presented with a problem. Which initial collections of base components should we choose ?
For instance in the CD~player example; to start at the bottom; we are presented with
@ -92,8 +98,8 @@ Currently this sort of information is generally only available for generic comp
%At higher levels of analysis, functional~groups are pre-analysed sub-systems that interact to
%erform a given function.
\vspace{0.3cm}
%\begin{table}[p]
%\vspace{0.3cm}
\begin{table}[p]
\begin{tabular}{||l|l||} \hline \hline
{\em Definition } & {\em Description} \\ \hline
System & A product designed to \\
@ -113,10 +119,11 @@ Failure mode & of a `Failure Mode Group' \\ \hline
Base Component & Any bought in component, which \\
& hopefully has a known set of failure modes \\ \hline
\hline
\label{tab:def}
\end{tabular}
%\end{table}
\vspace{0.3cm}
\label{tab:def}
\end{table}
%\vspace{0.3cm}
\section{A UML Model of terms introduced}
@ -130,43 +137,54 @@ Base Component & Any bought in component, which \\
\end{figure}
The diagram in figure \ref{fig:fmmd_uml}
shows the relationships between the terms defined in table \ref{tab:def}.
shows the relationships between the terms defined in table \ref{tab:def} as classes in a UML model.
We can start with the functional group. This is a minimal collection
of components that perform a simple given function.
For our audio separates rig, this could be
the compoents that supply power to the laser diode.
From the `Functional Group we can now collect
all the `failure modes of the `components, and
produce a `Failure Mode Group. This
has a reference to the `Functional Group, and is a collection
From the `Functional~Group' we can now collect
all the `failure modes of the `components', and
produce a `Failure~Mode~Group'. This
has a reference to the `Functional~Group', and is a collection
of `failure modes.
By analysing the effects of the failure modes in the `Failure Mode Group'
By analysing the effects of the failure modes in the `Failure~Mode~Group'
we can determine the failure mode behaviour of the functional group.
This failure mode behaviour is a collection of derived failure modes.
We can now consider the Functional group as a component now, because
we have a set of failure modes for it.
We can term this set of failure modes a sub-system.
Note that this is recursive. We can build functional groups using sub-systems
\subsection{Sub-System Class Definition}
A sub-system can now be defined by the classes used to create it, and
its set of derived failure modes.
Note that the UML model is recursive. We can build functional groups using sub-systems
as components. This UML model naturally therefore, forms a hierarchy
of failure mode analysis, which has a one top level entry, that being the SYSTEM.
The TOP level entry will determine the failure modes
for the product/system under analysis.
\subsection{Refining the UML model to use inheritance}
We can refine this model a little by noticing that a system is merely the
top level sub-system. We can thus have System inherit sub-system.
A derived failure mode, is simply a failure mode at a higher level of analysis
it can therefore inherit `failure\_mode'.
The modified UML diagram using inheritance is figure \ref{fig:fmmd_uml2}
The modified UML diagram using inheritance is figure \ref{fig:fmmd_uml2}.
\begin{figure}[h]
\centering
\includegraphics[width=350pt,bb=0 0 680 500,keepaspectratio=true]{component_failure_modes_definition/fmmd_uml2.jpg}
% fmmd_uml.jpg: 680x500 pixel, 72dpi, 23.99x17.64 cm, bb=0 0 680 500
\caption{UML respresentation of Failure Mode Data types}
\includegraphics[width=350pt,bb=0 0 877 675,keepaspectratio=true]{./fmmd_uml2.jpg}
% fmmd_uml2.jpg: 877x675 pixel, 72dpi, 30.94x23.81 cm, bb=0 0 877 675
\caption{UML Representation of Failure Mode Data Types}
\label{fig:fmmd_uml2}
\end{figure}
%
% \begin{figure}[h]
% \centering
% \includegraphics[width=350pt,bb=0 0 680 500,keepaspectratio=true]{component_failure_modes_definition/fmmd_uml2.jpg}
% % fmmd_uml.jpg: 680x500 pixel, 72dpi, 23.99x17.64 cm, bb=0 0 680 500
% \caption{UML respresentation of Failure Mode Data types}
% \label{fig:fmmd_uml2}
% \end{figure}
\subsection{Unitary State Component Failure Mode sets}
@ -181,7 +199,7 @@ Having a set of failure modes where $N$ modes could be active simultaneously
would mean having to consider $2^N$ failure mode scenarios.
%
Should a component be analysed and simultaneous failure mode cases exit,
the combinations could be represented by a new failure modes, or
the combinations could be represented by new failure modes, or
the component should be considered from a fresh perspective,
perhaps considering it as several smaller components
within one package.
@ -239,7 +257,7 @@ the failure mode set is not unitary~state and does not exist in the family of se
\subsection{Component Failure Modes and Statistical Sample Space}
%\paragraph{NOT WRITTEN YET PLEASE IGNORE}
A sample space is defined as the set of all possible outcomes.
When dealing with failure modes, we are not interested in
the state where the compoent is working perfectly or `OK' (i.e. operating with no error).
@ -254,6 +272,7 @@ is therefore
$$ F = \Omega(K) \backslash OK $$
\subsection{Bayes Theorem}
\paragraph{NOT WRITTEN YET PLEASE IGNORE}
\label{bayes}
Describe application - likely hood of faults being the cause of symptoms -
probablistic approach - no direct causation paths to the higher~abstraction fault mode.
@ -271,6 +290,7 @@ to
%unitary~state set family.
\subsection{Tests of Hypotheses and Significance}
\paragraph{NOT WRITTEN YET PLEASE IGNORE}
Linked in with Bayes theorem
Accident analysis
plane crashes and faults etc