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

context.........

Browse Source
This commit is contained in:
Robin Clark 2011-03-15 14:36:17 +00:00
parent cab6906fb4
commit a734d0eae7
1 changed files with 20 additions and 8 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

28
logic_diagram/logic_diagram.tex
View File

@ -350,14 +350,14 @@ i.e. the contours $\mathcal{X}$ from the zone it inhabits.
{ {
\definition{ \definition{
Let $\mathcal{F_t}$ be a function mapping a test case $t \in T$, to a proposition / logical equation $p \in P$. Let $\mathcal{F}_{t}$ be a function mapping a test case $t \in T$, to a proposition / logical equation $p \in P$.
The test case $t$, inhabits the zone $\mathcal{Z}$ which is a collection of contours (the contours that enclose the test case). The test case $t$, inhabits the zone $\mathcal{Z}$ which is a collection of contours (the contours that enclose the test case).
We can express this as We can express this as
$$ \mathcal{F_t}:T \rightarrow P\;, $$ $$ \mathcal{F}_{t}:T \rightarrow P\;, $$
%$$ \mathcal{F}(t): p = \bigwedge_{c \in \mathcal{Z}} \Lambda c $$ %$$ \mathcal{F}(t): p = \bigwedge_{c \in \mathcal{Z}} \Lambda c $$
given by given by
$$ \mathcal{F_t}(t): p = \bigwedge_{c \in \mathcal{Z}} c \;. $$ $$ {F}_{t}(t): p = \bigwedge_{c \in \mathcal{Z}} c \;. $$
} }
} }
@ -378,7 +378,7 @@ $$ \mathcal{G}:SMG \rightarrow P. $$
The logic equation (using $oplus$ to represent exclusive-or) representing an SMG $p_{fmg}$ is given thus; The logic equation (using $oplus$ to represent exclusive-or) representing an SMG $p_{fmg}$ is given thus;
$$\mathcal{G}(fmg) = \bigoplus_{t \in fmg} (\; \mathcal{F_t} (t) \;) \; .$$ $$\mathcal{G}(fmg) = \bigoplus_{t \in fmg} (\; \mathcal{F}_{t} (t) \;) \; .$$
} }
} }
@ -396,10 +396,22 @@ and unused available zones.
\subsection{Symptom Collection} \subsection{Symptom Collection}
The methodology using these propositional logic diagrams is concerned with The methodology using these propositional logic diagrams is concerned with
taking functional groups of components, and representing the failure taking functional groups of components, analysing how the functional group
modes of those components as contours in the diagram. can fail, and then deriving a failure mode model for the functional group
The test cases, when analysed can be grouped into $SMG$s which so that we can treat it as a component in its own right, or as a `derived component'
define the failure mode behaviour of the functional group.
We represent the failure
modes of the components within a {\fg} as contours in the diagram.
The test cases represent combinations of component failure modes
within the functional group.
The test cases, when analysed can be grouped into $SMG$s.
The SMG, Symptomatically merged group, is a collection of test
cases where the failure symptom is the same.
%
Each SMG
defines a failure mode behaviour of the functional group as though the
{\fg} were considered as a high level component.
%
As we may be interested in treating the functional group As we may be interested in treating the functional group
and a component to model higher levels of design, or failure mode abstraction, and a component to model higher levels of design, or failure mode abstraction,
we can derive a new diagram from the $SMG$s. Each $SMG$ represents a failure we can derive a new diagram from the $SMG$s. Each $SMG$ represents a failure