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Robin Clark 2011-11-03 09:21:24 +00:00
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opamp_circuits_C_GARRETT/opamps.tex
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@ -486,10 +486,10 @@ wihen it becomes a V2 follower).
\section{Basic Concepts Of FMMD} \section{Basic Concepts Of FMMD}
\paragraph{ Creating a fault hierarchy} \paragraph{ Creating a fault hierarchy.}
The main concept of FMMD is to build a hierarchy of failure behaviour from the {\bc} The main concept of FMMD is to build a hierarchy of failure behaviour from the {\bc}
level up to the top, or system level, with analysis stages between each transition to a higher level in the hierarchy. level up to the top, or system level, with analysis stages between each
transition to a higher level in the hierarchy.
The first stage is to choose The first stage is to choose
{\bcs} that interact and naturally form {\fgs}. The initial {\fgs} are collections of base components. {\bcs} that interact and naturally form {\fgs}. The initial {\fgs} are collections of base components.
@ -506,17 +506,22 @@ we can determine its symptoms of failure.
%In fact we can call these %In fact we can call these
%the symptoms of failure for the {\fg}. %the symptoms of failure for the {\fg}.
This new set of faults is the set of derived faults from the perspective of the {\fg}, and is thus at a higher level of With these Syptoms (a set of derived faults from the perspective of the {\fg})
fault~mode abstraction. We can now say that the {\fg} (as an entity in its own right) can fail in a number of well defined ways. % and is thus at a higher level of
%fault~mode abstraction.
We can now say that the {\fg} (as an entity in its own right) can fail in a number of well defined ways.
In other words we have taken a {\fg}, and analysed how it can fail according to the failure modes of its components. In other words we have taken a {\fg}, and analysed how
it can fail according to the failure modes of its components.
%These new failure~modes are derived failure modes. %These new failure~modes are derived failure modes.
%The ways in which the module can fail now becomes a new set of fault modes, the fault~modes %The ways in which the module can fail now becomes a new set of fault modes, the fault~modes
%being derived from the {\fg}. %being derived from the {\fg}.
\paragraph{Creating a derived component.}
We can now create a new `{\dc}' which has We can now create a new `{\dc}' which has
the failure symptoms of the {\fg} as its set of failure modes. the failure symptoms of the {\fg} as its set of failure modes.
This new {\dc} is at a higher `failure~mode~abstraction~level' than {\bcs}. This new {\dc} is at a higher `failure~mode~abstraction~level' than {\bcs}.
%
\paragraph{An example of a {\dc}.}
To give an example of this, we could look at the components that To give an example of this, we could look at the components that
form, say an amplifier. We look at how all the components within it form, say an amplifier. We look at how all the components within it
could fail and how that would affect the amplifier. could fail and how that would affect the amplifier.
@ -538,6 +543,7 @@ The components brought together in a specific way make it an amplifier !
%to represent the fault behaviour of the entire system. This can be seen as using the modules we have analysed %to represent the fault behaviour of the entire system. This can be seen as using the modules we have analysed
%as parts, parts which may now be combined to create new functional groups, %as parts, parts which may now be combined to create new functional groups,
%but as parts at a higher level of fault abstraction. %but as parts at a higher level of fault abstraction.
\paragraph{Building the Hierarchy.}
Applying the same process with {\dcs} we can bring {\dcs} Applying the same process with {\dcs} we can bring {\dcs}
together to form functional groups and create new {\dcs} together to form functional groups and create new {\dcs}
at even higher abstraction levels. Eventually we will have a hierarchy at even higher abstraction levels. Eventually we will have a hierarchy
@ -580,7 +586,7 @@ of components.
%We thus define $FG$ as a set of chosen components defining %We thus define $FG$ as a set of chosen components defining
%a {\fg}; all functional groups %a {\fg}; all functional groups
We can state that We can state that
$FG$ is a subset of the power set of all components, $ FG \in \mathcal{P} \mathcal{C}. $ $FG$ is a member of the power set of all components, $ FG \in \mathcal{P} \mathcal{C}. $
We can overload the $fm$ function for a functional group $FG$ We can overload the $fm$ function for a functional group $FG$
where it will return all the failure modes of the components in $FG$ where it will return all the failure modes of the components in $FG$