278 lines
8.4 KiB
TeX
278 lines
8.4 KiB
TeX
\documentclass{beamer}
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\title[Failure Mode Effects Analysis]{Failure Mode Effects Analysis\\A critical view}
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\usetheme{Warsaw}
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\usepackage[latin1]{inputenc}
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\author{Robin Clark -- Energy Technology Control Ltd}
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\institute{Brighton University}
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\setbeamertemplate{footline}[page number]
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\begin{document}
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\section{F.M.E.A.}
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\begin{frame}
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\begin{itemize}
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\pause \item Failure
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\pause \item Mode
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\pause \item Effects
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\pause \item Analysis
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\end{itemize}
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\end{frame}
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% % \begin{itemize}
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% \item Failure
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% \item Mode
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% \item Effects
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% \item Analysis
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% \end{itemize}
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\subsection{FMEA basic concept}
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\begin{frame}
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\begin{itemize}
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\pause \item \textbf{F - Failures of given component} Consider a component in a system
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\pause \item \textbf{M - Failure Mode} Look at one of the ways in which it can fail (i.e. determine a component `failure~mode')
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\pause \item \textbf{E - Effects} Determine the effects this failure mode will cause to the system we are examining
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\pause \item \textbf{A - Analysis} Analyse how much impact this symptom will have on the environment/people/the system its-self
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\end{itemize}
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\end{frame}
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\begin{frame}
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Example: Let us consider a system, in this case a milli-volt reader, consisting
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of instrumentation amplifiers connected to a micro-processor
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that reports its readings via RS-232.
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Let us perform an FMEA and consider how one of its resistors failing could affect
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it.
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For the sake of example let us choose a resistor in an OP-AMP
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reading the milli-volt source and that if it were to go open, we would have a gain
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of 1 from the amplifier.
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\begin{itemize}
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\pause \item \textbf{F - Failures of given component} The resistor could fail by going OPEN or SHORT (EN298 definition).
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\pause \item \textbf{M - Failure Mode} Consider the component failure mode OPEN
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\pause \item \textbf{E - Effects} This will disconnect the feedback loop in the amplifier causing a LOW READING
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\pause \item \textbf{A - Analysis} The reading will be out of normal range, and we will have an erroneous milli-volt reading
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\end{itemize}
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\end{frame}
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\begin{frame}
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Note here that we have had to look at the failure~mode
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in relation to the entire circuit.
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We have used intuition to determine the probable
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effect of this failure mode.
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We have not examined this failure mode
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against every other component in the system.
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Perhaps we should.... this would be a more rigorous and complete
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approach in looking for system failures.
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\end{frame}
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\begin{frame}
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Consider the analysis
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where we look at all the failure modes in a system, and then
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see how they can affect all other components within it.
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We need to look at a large number of failure scenarios
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to do this completely (all failure modes against all components).
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This is represented in equation~\ref{eqn:fmea_state_exp},
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where $N$ is the total number of components in the system, and
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$cfm$ is the number of failure modes per component.
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\begin{equation}
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\label{eqn:fmea_single}
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N.(N-1).cfm % \\
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%(N^2 - N).cfm
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\end{equation}
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This would mean an order of $N^2$ number of checks to perform
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to perform `rigorous~FMEA'. Even small systems have typically
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100 components, and they typically have 3 or more failure modes each.
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$100*99*3=29,700$.
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\end{frame}
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\begin{frame}
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For looking at potential double failure scenarios (two components
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failing within a given time frame) and the order becomes
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$N^3$.
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\begin{equation}
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\label{eqn:fmea_double}
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N.(N-1).(N-2).cfm % \\
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%(N^2 - N).cfm
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\end{equation}
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$100*99*98*3=2,910,600$.
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The European Gas burner standard (EN298:2003), demands the checking of
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double failure scenarios (for burner lock-out scenarios).
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\end{frame}
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\section{Production FMEA : 1940's to present}
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\begin{frame}
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Describe process, the probability times the cost
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\end{frame}
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\subsection{Production FMEA : Example Ford Pinto : 1975}
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\begin{frame}
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\end{frame}
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\subsection{FMEA and complexity of each failure scenario analysis}
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\begin{frame}
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Consider the FMEA type methodologies
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where we look at all the failure modes in a system, and then
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see how they can affect all other components within it,
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to determine its system level symptom or failure mode.
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We need to look at a large number of failure scenarios
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to do this completely (all failure modes against all components).
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This is represented in equation~\ref{eqn:fmea_state_exp},
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where $N$ is the total number of components in the system, and
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$cfm$ is the number of failure modes per component.
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\begin{equation}
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\label{eqn:fmea_state_exp}
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N.(N-1).cfm % \\
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%(N^2 - N).cfm
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\end{equation}
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The FMMD methodology breaks the analysis down into small stages,
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by making the analyst choose functional groups, and then when analysed the groups
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are treated as components to be used for a higher stage.
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This is designed to address the state explosion (where $O$ is order
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of complexity) $O=N^2$ inherent in equation~\ref{eqn:fmea_state_exp}.
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\end{frame}
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We can view the functional groups in FMMD as forming a hierarchy.
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If for the sake of example we consider each functional group to
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be three components, figure~\ref{fig:three_tree} shows
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how the levels work and converge to a top or system level.
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\begin{figure}
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\centering
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\includegraphics[width=300pt]{./three_tree.png}
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% three_tree.png: 780x226 pixel, 72dpi, 27.52x7.97 cm, bb=0 0 780 226
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\caption{Functional Group Tree example}
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\label{fig:three_tree}
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\end{figure}
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\clearpage
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We can represent the number of failure scenarios to check in an FMMD hierarchy
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with equation~\ref{eqn:anscen}.
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\begin{equation}
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\label{eqn:anscen}
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\sum_{n=0}^{L} {fgn}^{n}.fgn.cfm.(fgn-1)
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\end{equation}
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Where $fgn$ is the number of components in each functional group,
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and $cfm$ is the number of failure modes per component
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and L is the number of levels, the number of
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analysis scenarios to consider is show in equation~\ref{eqn:anscen}.
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So for a very simple analysis with three components forming a functional group where
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each component has three failure modes, we have only one level (zero'th).
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So to check every failure modes against the other components in the functional group
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requires 18 checks.
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\begin{equation}
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\label{eqn:anscen2}
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\sum_{n=0}^{0} {3}^{0}.3.3.(3-1) = 18
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\end{equation}
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\clearpage
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In other words, we have three components in our functional group,
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and nine failure modes to consider.
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So taking each failure mode and looking at how that could affect the functional group,
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we must compare each failure mode against the two other components (the `$fgn-1$' term).
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For the one `zero' level FMMD case we are doing the same thing as FMEA type analysis
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(but on a very simple small sub-system).
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We are looking at how each failure~mode can effect the system/top level.
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We can use equation~\ref{eqn:fmea_state_exp} to represent
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the number of checks to rigorously perform FMEA, where $N$ is the total
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number of components in the system, and $cfm$ is the number of failures per component.
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Where $N=3$ and $cfm=3$ we can see that the number of checks for this simple functional
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group is the same for equation~\ref{eqn:fmea_state_exp}
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and equation~\ref{eqn:anscen}.
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\clearpage
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\section{Example}
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To see the effects of reducing `state~explosion' we need to look at a larger system.
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Let us take a system with 3 levels and apply these formulae.
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Having three levels (in addition to the top zero'th level)
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will require 81 base level components.
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$$
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%\begin{equation}
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\label{eqn:fmea_state_exp}
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81.(81-1).3 = 19440 % \\
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%(N^2 - N).cfm
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%\end{equation}
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$$
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$$
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%\begin{equation}
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% \label{eqn:anscen}
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\sum_{n=0}^{3} {3}^{n}.3.3.(2) = 720
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%\end{equation}
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$$
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Thus for FMMD we needed to examine 720 failure mode scenarios, and for traditional FMEA
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type analysis methods 19440.
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% In practical example followed through, no more than 9 components have ever been required for a functional
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% group and the largest known number of failure modes has been 6.
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% If we take these numbers and double them (18 components per functional group
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% and 12 failure modes per component) and apply the formulas for a 4 level analysis
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% (i.e.
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\clearpage
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Note that for all possible double simultaneous failures the equation~\ref{eqn:fmea_state_exp} becomes
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equation~\ref{eqn:fmea_state_exp2} essentially making the order $N^3$.
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The FMMD case (equation~\ref{eqn:anscen2}), is cubic within the functional groups only,
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not all the components in the system.
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\begin{equation}
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\label{eqn:fmea_state_exp2}
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N.(N-1).(N-2).cfm % \\
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%(N^2 - N).cfm
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\end{equation}
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\begin{equation}
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\label{eqn:anscen2}
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\sum_{n=0}^{L} {fgn}^{n}.fgn.cfm.(fgn-1).(fgn-2)
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\end{equation}
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\end{document}
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