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edits from printout. added derived component class to uml diagram

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Robin 2010-05-01 22:38:01 +01:00
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component_failure_modes_definition/Makefile
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@ -13,5 +13,5 @@ paper: paper.tex component_failure_modes_definition_paper.tex
# Remove the need for referncing graphics in subdirectories # Remove the need for referncing graphics in subdirectories
# #
component_failure_modes_definition_paper.tex: component_failure_modes_definition.tex component_failure_modes_definition_paper.tex: component_failure_modes_definition.tex paper.tex
cat component_failure_modes_definition.tex | sed 's/component_failure_modes_definition\///' > component_failure_modes_definition_paper.tex cat component_failure_modes_definition.tex | sed 's/component_failure_modes_definition\///' > component_failure_modes_definition_paper.tex

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component_failure_modes_definition/cfg.dia
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component_failure_modes_definition/cfg.jpg
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component_failure_modes_definition/component_failure_modes_definition.tex
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@ -10,14 +10,16 @@ Mathematical constraints and definitions are made using set theory.
\section{Introduction} \section{Introduction}
This chapter describes the data types and concepts for the Failure Mode Modular De-composition (FMMD) method.
When analysing a safety critical system using the When analysing a safety critical system using the
FMMD technique, we need clearly defined failure modes for this technique, we need clearly defined failure modes for
all the components that are used to model the system. all the components that are used to model the system.
These failure modes have a constraint such that These failure modes have a constraint such that
the compoent failure modes must be mutually exclusive. the component failure modes must be mutually exclusive.
This and the definition of a component are When this constraint is complied with we can use the FMMD process to
described in this chapter. build hierarchical bottom-up models of failure mode behaviour.
%This and the definition of a component are
%described in this chapter.
%When building a system from components, %When building a system from components,
%we should be able to find all known failure modes for each component. %we should be able to find all known failure modes for each component.
%For most common electrical and mechanical components, the failure modes %For most common electrical and mechanical components, the failure modes
@ -104,8 +106,8 @@ We can term this a `Functional~Group'. When we have a
`Functional~Group' we can look at the failure modes of all the components `Functional~Group' we can look at the failure modes of all the components
in it and decide how these will affect the Group. in it and decide how these will affect the Group.
Or in other words we can determine the failure modes of the functional Or in other words we can determine the failure modes of the functional
group. These failure modes are derived from the functional group, as so we can call group. These failure modes are derived from the functional group, we can therefore call
them `derived failure modes'. these `derived failure modes'.
We now have something very useful, because We now have something very useful, because
we can now treat this functional group as a component with a known set of failure modes. we can now treat this functional group as a component with a known set of failure modes.
This newly derived component can be used as a higher level This newly derived component can be used as a higher level
@ -115,7 +117,7 @@ to form higher level functional groups.
This process can continue until have build a hierarcy that converges to a failure model of the entire system. This process can continue until have build a hierarcy that converges to a failure model of the entire system.
To differentiate the components derived from functional groups, we can To differentiate the components derived from functional groups, we can
add a new attribute to the class `Component', that of analysis add a new attribute to the class `Component', that of analysis
level. level. The UML representation shows a `functional group' having a one to one relationship with a derived component.
We can represet this in a UML diagram see figure \ref{fig:cfg} We can represet this in a UML diagram see figure \ref{fig:cfg}
\begin{figure}[h] \begin{figure}[h]
@ -125,8 +127,8 @@ We can represet this in a UML diagram see figure \ref{fig:cfg}
\caption{Components Derived from Functional Groups} \caption{Components Derived from Functional Groups}
\label{fig:cfg} \label{fig:cfg}
\end{figure} \end{figure}
\clearpage
\section{Set theory description} \section{Set Theory Description}
$$ System \stackrel{has}{\longrightarrow} PartsList $$ $$ System \stackrel{has}{\longrightarrow} PartsList $$
@ -312,7 +314,7 @@ It should not be possible for instance for
a component to have two or more failure modes active at once. a component to have two or more failure modes active at once.
Having a set of failure modes where $N$ modes could be active simultaneously Having a set of failure modes where $N$ modes could be active simultaneously
would mean having to consider $2^N$ failure mode scenarios. would mean having to consider $2^N-1$ failure mode scenarios.
% %
Should a component be analysed and simultaneous failure mode cases exit, Should a component be analysed and simultaneous failure mode cases exit,
the combinations could be represented by new failure modes, or the combinations could be represented by new failure modes, or
@ -348,10 +350,10 @@ A component with simple ``unitary~state'' failure modes is the electrical resist
Electrical resistors can fail by going OPEN or SHORTED. Electrical resistors can fail by going OPEN or SHORTED.
For a given resistor R we can assign it the failure mode by applying For a given resistor R we can apply the
the function $FM$ thus $ FM(R) = \{R_{SHORTED},R_{OPEN}\} $. the function $FM$ to find its set of failure modes thus $ FM(R) = \{R_{SHORTED},R_{OPEN}\} $.
Nothing can fail with both conditions open and short active at the same time ! The conditions A resistor cannot fail with both conditions open and short active at the same time ! The conditions
OPEN and SHORT are mutually exclusive. OPEN and SHORT are thus mutually exclusive.
Because of this the failure mode set $F=FM(R)$ is `unitary~state'. Because of this the failure mode set $F=FM(R)$ is `unitary~state'.
@ -370,7 +372,7 @@ $$ c1 \cap c2 \neq \emptyset | c1 \neq c2 \wedge c1,c2 \in C \wedge C \not\in U
That is to say that it is impossible that any pair of failure modes can be active at the same time That is to say that it is impossible that any pair of failure modes can be active at the same time
for the failure mode set $C$ to exists in the family of sets $U$ for the failure mode set $C$ to exists in the family of sets $U$
Note where that are more than two failure~modes, by banning pairs from happening at the same time Note where that are more than two failure~modes, by banning pairs from being active at the same time
we have banned larger combinations as well. we have banned larger combinations as well.