Made a presentations directory and moved

IET2011 to it.
Started on a general FMEA presentation.

presentations/fmea/fmea_pres.tex

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