diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex index a42152e..7a4f250 100644 --- a/component_failure_modes_definition/component_failure_modes_definition.tex +++ b/component_failure_modes_definition/component_failure_modes_definition.tex @@ -292,9 +292,10 @@ would have an $\alpha$ value of 1. Let the set of all possible components be $\mathcal{C}$ and let the set of all possible failure modes be $\mathcal{F}$ and $\mathcal{PF}$ is the powerset of -all $\mathcal{F}$.. +all $\mathcal{F}$. We can define a function $fm$ as equation \ref{eqn:fmset}. +\label{fmdef} \begin{equation} fm : \mathcal{C} \rightarrow \mathcal{P}\mathcal{F} @@ -763,6 +764,7 @@ operational states. The additional objects System, Environment and Operational States are added to UML diagram in figure \ref{fig:cfg} and represented in figure \ref{fig:cfg2}. +\label{completeuml} \begin{figure}[h] \centering diff --git a/fmmd_data_model/cfg2.dia b/fmmd_data_model/cfg2.dia new file mode 100644 index 0000000..fefc0ad Binary files /dev/null and b/fmmd_data_model/cfg2.dia differ diff --git a/fmmd_data_model/cfg2.jpg b/fmmd_data_model/cfg2.jpg new file mode 100644 index 0000000..2290552 Binary files /dev/null and b/fmmd_data_model/cfg2.jpg differ diff --git a/fmmd_data_model/fmmd_data_model.tex b/fmmd_data_model/fmmd_data_model.tex index e5bc015..b17225e 100644 --- a/fmmd_data_model/fmmd_data_model.tex +++ b/fmmd_data_model/fmmd_data_model.tex @@ -8,31 +8,53 @@ %% What I have done %% +This paper presents a simple two stage Failure Mode Modular De-Composition (FMMD) +model of a theoretical System. +The Analysis model is then represented as a Directed Acyclic Graph (DAG), of the {\fg}s +components and failure modes represented in it. -%% What I have found +% What I have found %% +From traversing the DAG, minimal cut sets (component level combinations +that cause system level failures) are revealed. +Common mode failure modes and same component dependencies +can also be automatically determined. %% Sell it %% -} -} +By having a clear data model, we can not only produce results +for the traditional methodologies, we can trace common mode and +component dependency failures as well. +Also, with statistical data, we can use the minimal cut set results +to determine the likelihood of particular system failures, even +if they have multiple causes. +} % abstract +} % ifthenelse { %%% CHAPTER INTO NEARLT THE SAME AS ABSTRACT \section{Introduction} This chapter +presents a simple two stage FMMD % Failure Mode Modular De-Composition (FMMD) +model of a theoretical System. +The Analysis model is then represented as a Directed Acyclic Graph (DAG), of the {\fg}s +components and failure modes represented in it. -%% What I have done +% What I have found %% - -%% What I have found -%% -%and considering some constraints determined from -%the evaluation of the four established methodologies, +From traversing the DAG, minimal cut sets (component level combinations +that cause system level failures) are revealed. +Common mode failure modes and same component dependencies +can also be automatically determined. %% Sell it %% - +By having a clear data model, we can not only produce results +for the traditional methodologies, we can trace common mode and +component dependency failures as well. +Also, with statistical data, we can use the minimal cut set results +to determine the likelihood of particular system failures, even +if they have multiple causes. } %{ \huge This might become a chapter in its own right after fmmdset } @@ -60,7 +82,7 @@ represents the FMMD hierarchy level, or $\alpha$ value, thus: } { We can organise these into functional groups (where the superscript -represents the $\alpha$ value, see section \ref{alpha}), thus: +represents the $\alpha$ value, or FMMD hierarchy level, see section \ref{alpha}), thus: } $$ FG^0_1 = \{C_1, C_2\},$$ @@ -68,10 +90,28 @@ $$ FG^0_2 = \{C_1, C_3, K_4\},$$ $$ FG^0_3 = \{C_5, C_6, K_7\}.$$ 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 +both commonly use. A real world example of a component included in +more than one {\fg} could +be a powersupply or DCDC\footnote{A DCDC (direct current to direct current) +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.} +converter shared to power +the functional groups $FG^0_1$ and $FG^1_1$. + Also that the component type $K$ has been used by two different functional groups. +For the sake of example let our temperature environment +for the SYSTEM be ${{0}\oc}$ to ${{125}\oc}$, but let the component +type `K' have a de-graded performance failure mode between +${{80}\oc}$ and ${{125}\oc}$\footnote{ A real world example of +degraded performace with temperature is the isolating opto coupler. +These can typically only cope with lower baud rate ranges +at high temperatures \cite{tlp181}.}. We can term this +degraded performce of component `K' as failure mode `d'. + + \paragraph{Symptom Extraction.} A processes of symptom extraction is now applied to the functional groups. Again for the sake of example, let us say that each functional @@ -81,6 +121,83 @@ Applying symptom abstraction to $FG^0_1$ i.e. $\bowtie fm ( FG^0_1 ) = \{ FG^0_{ 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} \} $. +\paragraph{Building the Object Model} + +Using the UML model in figure \ref{fig:cfg2fmmd_data} we will apply FMMD analysis stages +to build a hierarchy representing the whole system, begining with the $FG^0$ level functional groups. + +\begin{figure}[h] + \centering + \includegraphics[width=400pt,bb=0 0 702 464,keepaspectratio=true]{./fmmd_data_model/cfg2.jpg} + % cfg2.jpg: 702x464 pixel, 72dpi, 24.76x16.37 cm, bb=0 0 702 464 + \caption{UML Class model for FMMD} + \label{fig:cfg2fmmd_data} +\end{figure} + +% %\begin{figure}[h] +% \centering +% \includegraphics[width=400pt,keepaspectratio=true]{./fmmd_data_model/cfg2.jpg} +% % cfg2.jpg: 702x464 pixel, 72dpi, 24.76x16.37 cm, bb=0 0 702 464 +% \caption{Complete UML diagram} +% \label{fig:cfg2fmmd_data} +% \end{figure} + +\paragraph{Find Failure Modes} + +Consider the SYSTEM environment with its temperature range of ${{0}\oc}$ to ${{125}\oc}$. +We must check this against all components used. +For our example, we component `K' which has an extra +failure mode for degraded performance `d'. + + + +\ifthenelse {\boolean{paper}} +{ +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. +} + +Applying the function $fm$ to our functional groups, with the SYSTEM environmental +constraint applied to component type `K', yields + +%%//$$ FG^0_1 = \{C_1, C_2\},$$ +%%$$ FG^0_2 = \{C_1, C_3, K_4\},$$ +%%$$ FG^0_3 = \{C_5, C_6, K_7\}.$$ + +$$ fm(FG^0_1) = \{C_{1 a}, C_{1 b}, C_{2 a}, C_{2 b}\},$$ +$$ fm(FG^0_2) = \{C_{1 a}, C_{1 b}, C_{2 a}, C_{2 b}, K_{4 a}, K_{4 b}, K_{4 d}\},$$ +$$ fm(FG^0_3) = \{C_{5 a}, C_{5 b}, C_{6 a}, C_{6 b}, K_{7 a}, K_{7 b}, K_{7 d}\}.$$ + +The next stage is to look at the failure modes from the perspective of +the functional groups, rather than the components. +We can call these failures modes `symptoms'. +As this is a theoretical example, we shall have to skip this step. +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}}. +We can define this stage as the function $\bowtie$ which has a set of failure modes as +its range and {\dc} as its domain. + +For the sake of example let us determine some arbitary collections +into symptoms. Let us group the symptoms from $ FG^0_1 $ as the following +$ s1 = \{ C_{1 a}, C_{2 b} \}$ and $ s2 = \{ C_{1 b}, C_{2 a} \}$. +We can now create a new {\dc}. This will have an $\alpha$ value higher +than the {\fg} it was derived from. + +thus +$$ DC^1_1 = \bowtie fm(FG^0_1) .$$ + +Applying $fm$ to our new derived component will give us our symptoms from functional group $ FG^0_1 $ +thus + +$$ fm(DC^1_1) = \{s1, s2 \}.$$ + + UML OBJECT MODEL OF DERIVED COMPONENT TOO diff --git a/fmmd_data_model/paper.tex b/fmmd_data_model/paper.tex index 417a0c3..b9e042a 100644 --- a/fmmd_data_model/paper.tex +++ b/fmmd_data_model/paper.tex @@ -32,7 +32,7 @@ \author{R.P.Clark} \title{FMMD Data Model} \maketitle -\input{fmmd_data_model} +\input{fmmd_data_model_paper} \bibliographystyle{plain} \bibliography{../vmgbibliography,../mybib} diff --git a/style.tex b/style.tex index 3d40a3d..1c6d45b 100644 --- a/style.tex +++ b/style.tex @@ -66,7 +66,7 @@ %\newcommand{\wlc}{{Water~Level~Controller~Unit}} %\newcommand{\ft}{{\em 4 $\rightarrow$ 20mA } } %\newcommand{\tds}{TDS Daughterboard} -\newcommand{\oc}{$^{o}{C}$} +\newcommand{\oc}{\ensuremath{^{o}{C}}} \newcommand{\adctw}{{${\mathcal{ADC}}_{12}$}} \newcommand{\adcten}{{${\mathcal{ADC}}_{10}$}} \newcommand{\ohms}[1]{\ensuremath{#1\Omega}}