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Going thourgh data model UML to DAG

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rough draft still
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Robin Clark 2010-11-25 20:55:26 +00:00
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fmmd_data_model/fmmd_data_model.tex
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@ -8,10 +8,13 @@
%% What I have done %% What I have done
%% %%
This paper presents a simple two stage Failure Mode Modular De-Composition (FMMD) This paper presents a simple two level Failure Mode Modular De-Composition (FMMD)
model of a theoretical System. model of a theoretical System.
The Analysis model is then represented as a Directed Acyclic Graph (DAG), of the {\fg}s Firstly a UML model is presented and the class relationships described.
components and failure modes represented in it. Secondly the theoretical model is developed and analysed.
This model is then represented as a Directed Acyclic Graph (DAG),
showing the data relationships between the {\fg}s
components and failure modes.
% What I have found % What I have found
%% %%
@ -22,12 +25,12 @@ can also be automatically determined.
%% Sell it %% Sell it
%% %%
By having a clear data model, we can not only produce results By having an FMMD data model, we can derive failure mode models
for the traditional methodologies, we can trace common mode and for the traditional methodologies (such as FMEA, FMECA, FMEDA and FTA).
component dependency failures as well.
Also, with statistical data, we can use the minimal cut set results Also, with statistical data, we can use the minimal cut set results
to determine the likelihood of particular system failures, even to determine the likelihood of particular system failures, even
if they have multiple causes. if they have multiple causes.
%
} % abstract } % abstract
} % ifthenelse } % ifthenelse
{ {
@ -49,9 +52,8 @@ can also be automatically determined.
%% Sell it %% Sell it
%% %%
By having a clear data model, we can not only produce results By having an FMMD data model, we can derive failure mode models
for the traditional methodologies, we can trace common mode and for the traditional methodologies (such as FMEA, FMECA, FMEDA and FTA).
component dependency failures as well.
Also, with statistical data, we can use the minimal cut set results Also, with statistical data, we can use the minimal cut set results
to determine the likelihood of particular system failures, even to determine the likelihood of particular system failures, even
if they have multiple causes. if they have multiple causes.
@ -62,18 +64,23 @@ if they have multiple causes.
\section{From UML Model to Object Model} \section{From UML Model to Object Model}
Let us consider a theoretical FMMD model. For the sake of simplicity Let us consider a theoretical FMMD model. For the sake of simplicity
consider that all components and functional groups have only two failure modes that consider that all base~components have %only
two failure modes that
we will label $a$ and $b$. we will label $a$ and $b$.
We can start with some base components, of types C and K say, $\{ C_1, C_2, C_3, K_4, C_5, C_6, K_7 \}$. We can start with some base components, of types C and K say, $\{ C_1, C_2, C_3, K_4, C_5, C_6, K_7 \}$.
\input{./shortfm}
\paragraph{Determing Failure Mode collections.}
Thus applying the function $fm$ to any of the components Thus applying the function $fm$ to any of the components
gives error modes identified by a or b. gives error modes identified by a or b.
For the sake of example, let us say that each component has two failure As each component has two failure
modes $a$ and $b$. So the function $fm$ applied to modes $a$ and $b$. So the function $fm$ applied to
$C_1$ yields $C_{1 a}$ and $C_{1 b}$: $C_1$ yields $C_{1 a}$ and $C_{1 b}$:
i.e. $fm(C_1) = \{ C_{1 a}, C_{1 b} \}$. i.e. $fm(C_1) = \{ C_{1 a}, C_{1 b} \}$.
HOW UML OBJECT MODEL OF COMPONENT AND ITS ERROR MODES %HOW UML OBJECT MODEL OF COMPONENT AND ITS ERROR MODES
\ifthenelse {\boolean{paper}} \ifthenelse {\boolean{paper}}
{ {
@ -89,17 +96,17 @@ $$ FG^0_1 = \{C_1, C_2\},$$
$$ FG^0_2 = \{C_1, C_3, K_4\},$$ $$ FG^0_2 = \{C_1, C_3, K_4\},$$
$$ FG^0_3 = \{C_5, C_6, K_7\}.$$ $$ FG^0_3 = \{C_5, C_6, K_7\}.$$
Note that in this model the base~component $C_1$ has been used in Note that in this model the base~component $C_1$ has been used in two separate functional groups.
two separate functional groups. This could be a component that they This could be a component that they
both commonly use. A real world example of a component included in both commonly use. A real world example of a component included in
more than one {\fg} could more than one {\fg} could
be a powersupply or DCDC\footnote{A DCDC (direct current to direct current) be a power-supply or DCDC\footnote{A DCDC (direct current to direct current)
converter, is a common feature in modern PCBs, used to provide isolation converter, is a common feature in modern PCBs, used to provide isolation
and/or voltage supplies at a different EMF from the source of power.} and/or voltage supplies at a different EMF from the source of power.}
converter shared to power converter shared to power
the functional groups $FG^0_1$ and $FG^1_1$. the functional groups $FG^0_1$ and $FG^1_1$.
Also that the component type $K$ has been used by Also note that the component type $K$ has been used by
two different functional groups. two different functional groups.
For the sake of example let our temperature environment For the sake of example let our temperature environment
@ -117,14 +124,15 @@ A processes of symptom extraction is now applied to the functional groups.
Again for the sake of example, let us say that each functional Again for the sake of example, let us say that each functional
group has one or two symptoms again subscripted by $a$ and $b$. group has one or two symptoms again subscripted by $a$ and $b$.
Applying symptom abstraction to $FG^0_1$ i.e. $\bowtie fm ( FG^0_1 ) = \{ FG^0_{1 a}, FG^0_{1 b} \} $ %Applying symptom abstraction to $FG^0_1$ i.e. $\bowtie fm ( FG^0_1 ) = \{ FG^0_{1 a}, FG^0_{1 b} \} $
We can now create a new derived component, $DC^1_1$, whose failure %We can now create a new derived component, $DC^1_1$, whose failure
modes are the symptoms of $FG^0_1 $ thus $ fm ( {DC}^1_1 ) = \{ FG^0_{1 a}, FG^0_{1 b} \} $. %modes are the symptoms of $FG^0_1 $ thus $ fm ( {DC}^1_1 ) = \{ FG^0_{1 a}, FG^0_{1 b} \} $.
\paragraph{Building the Object Model} \paragraph{Building the Object Model}
Using the UML model in figure \ref{fig:cfg2fmmd_data} we will apply FMMD analysis stages Using the UML model in figure \ref{fig:cfg2fmmd_data}, we apply FMMD analysis stages
to build a hierarchy representing the whole system, begining with the $FG^0$ level functional groups. to build a hierarchy representing the whole system.
We shall begin with the $FG^0$ level functional groups $ FG^0_1, FG^0_2 $ and $FG^0_3$ defined above.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
@ -147,22 +155,13 @@ to build a hierarchy representing the whole system, begining with the $FG^0$ lev
Consider the SYSTEM environment with its temperature range of ${{0}\oc}$ to ${{125}\oc}$. Consider the SYSTEM environment with its temperature range of ${{0}\oc}$ to ${{125}\oc}$.
We must check this against all components used. We must check this against all components used.
For our example, we component `K' which has an extra For our example, we component `K' which has an extra
failure mode for degraded performance `d'. failure mode for degraded performance `d'. Thus applying the function $fm$
to component type `K' under these temperature range conditions
give the foillowing failure modes, $fm{K} =\{ K_a, K_b, K_d \}$.
Were our system specified for a ${{0}\oc}$ to ${{80}\oc}$ range
\ifthenelse {\boolean{paper}} we could say $fm{K} =\{ K_a, K_b \}$.
{
We can definine a `failure modes' function $fm$ that has a functional group as its range
and returns a set of failure modes as its domain.
We now use this to determine the failure modes
in our functional groups.
}
{
Using the overloaded function $fm$ from chapter \ref{fmdef} we can determine the failure modes
in our functional groups.
}
\paragraph{Get the failure modes from the functional groups.}
Applying the function $fm$ to our functional groups, with the SYSTEM environmental Applying the function $fm$ to our functional groups, with the SYSTEM environmental
constraint applied to component type `K', yields constraint applied to component type `K', yields
@ -177,7 +176,9 @@ $$ fm(FG^0_3) = \{C_{5 a}, C_{5 b}, C_{6 a}, C_{6 b}, K_{7 a}, K_{7 b}, K_{7 d}\
The next stage is to look at the failure modes from the perspective of The next stage is to look at the failure modes from the perspective of
the functional groups, rather than the components. the functional groups, rather than the components.
We can call these failures modes `symptoms'. We can call these failures modes `symptoms'.
As this is a theoretical example, we shall have to skip this step. As this is a theoretical example, we shall have to skip this step\footnote{
In a real analysis this would involve evaluating the effect of each components failure mode, (or combinations of)
on the performance of the {\fg}.}.
The next stage is to collect the common symptoms, or the symtoms that The next stage is to collect the common symptoms, or the symtoms that
are the same {\em from the perspective of a user of the {\fg}}. are the same {\em from the perspective of a user of the {\fg}}.
We can define this stage as the function $\bowtie$ which has a set of failure modes as We can define this stage as the function $\bowtie$ which has a set of failure modes as
@ -229,7 +230,7 @@ UML OBJECT MODEL OF DERIVED COMPONENT TOO
\pagebreak[4]
\subsection{Using Derived Components in Functional Groups} \subsection{Using Derived Components in Functional Groups}

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shortfm.tex
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@ -1,5 +1,6 @@
\ifthenelse {\boolean{paper}} \ifthenelse {\boolean{paper}}
{ {
\paragraph{Failure Mode function $fm$.}
We can definine a `failure modes' function $fm$ that has a functional group as its range We can definine a `failure modes' function $fm$ that has a functional group as its range
and returns a set of failure modes as its domain. and returns a set of failure modes as its domain.
We now use this to determine the failure modes We now use this to determine the failure modes