Working on presentation while ill (have not eaten for 54+ hours)

presentations/fmea/Makefile

@@ -1,5 +1,5 @@
 
-DIAPNG= component.png  fmmd_env_op_uml.png  fmmd_exm_h.png  master_uml.png  mvampcircuit.png  mvamp.png  n_inv_dc.png  pd.png  pd_euler2.png  pd_euler.png
+DIAPNG= three_tree.png component.png  fmmd_env_op_uml.png  fmmd_exm_h.png  master_uml.png  mvampcircuit.png  mvamp.png  n_inv_dc.png  pd.png  pd_euler2.png  pd_euler.png
 
 %.png:%.dia
 	dia -t png $<

presentations/fmea/fmea_pres.tex

@@ -22,7 +22,9 @@
 \frametitle{FMEA}
 %\tableofcontents[currentsection]
 \end{frame}
-
+This talk introduces Failure Mode Effects Analysis, and the different ways it is applied.
+These techniques are discussed, and then
+a refinement is proposed, which is essentially a modularisation of the FMEA process.
 \begin{frame}
 \frametitle{FMEA}
 \begin{itemize}
@@ -129,13 +131,13 @@ 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 the equation below. %~\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.
+$f$ is the number of failure modes per component.
   
 
 \begin{equation}
   \label{eqn:fmea_single}
-  N.(N-1).cfm % \\
+  N.(N-1).f % \\
-  %(N^2 - N).cfm 
+  %(N^2 - N).f 
 \end{equation}
 \end{frame}
 
@@ -159,11 +161,14 @@ $N^3$.
 
 \begin{equation}
   \label{eqn:fmea_double}
-  N.(N-1).(N-2).cfm % \\
+  N.(N-1).(N-2).f % \\
-  %(N^2 - N).cfm 
+  %(N^2 - N).f 
 \end{equation}
 
 $100*99*98*3=2,910,600$.
+\pause
+
+.\\
 
 The European Gas burner standard (EN298:2003), demands the checking of 
 double failure scenarios (for burner lock-out scenarios).
@@ -438,6 +443,7 @@ against all safe and dangerous failure probabilities.
 Again this is usually expressed as a percentage.
 
 $$ SFF = \big( \Sigma\lambda_S + \Sigma\lambda_{DD} \big) / \big( \Sigma\lambda_S + \Sigma\lambda_D \big) $$
+\pause
 SFF determines how proportionately fail-safe a system is, not how reliable it is ! \pause
 Weakness in this philosophy; \pause adding extra safe failures (even unused ones) improves the SFF. 
 
@@ -577,12 +583,12 @@ judged to be in critical sections of the product.
 % 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.
+% $f$ is the number of failure modes per component.
 % 
 % \begin{equation}
 %   \label{eqn:fmea_state_exp}
-%   N.(N-1).cfm % \\
+%   N.(N-1).f % \\
-%   %(N^2 - N).cfm 
+%   %(N^2 - N).f 
 % \end{equation}
 
 
@@ -606,6 +612,8 @@ This creates an analysis hierarchy.
   \pause \item Collect Symptoms.
   \pause \item Create a '{\dc}', where its failure modes are the symptoms of the {\fg} from which it was derived.
   \pause \item The {\dc} is now available to be used in higher level {\fgs}.
+  \pause \item We can represent this process as a function which converts a {\fg} into a {\dc} and use the symbol $ \bowtie $ to represet it.
+  \pause \item i.e. $ \bowtie ( FunctionalGroup ) \rightarrow {DerivedComponent} $
 \end{itemize}
 \end{frame}
 
@@ -623,7 +631,7 @@ This creates an analysis hierarchy.
 We can return to the milli-volt amplifier as an example to analyse.
 \pause
 We can begin by looking for functional groups.\pause
-The resistors would together to perform a fairly common function in electronics, that of the potential divider.
+The resistors perform a fairly common function in electronics, that of the potential divider.
 So our first functional group is $\{ R1, R2 \}$.\pause
 We can now take the failure modes for the resistors (OPEN and SHORT EN298) and see what effect each of these failures will have on the {\fg} (the potential divider).
 
@@ -652,6 +660,7 @@ Resistor and its failure modes represented as a directed graph.
 \begin{table}
 \begin{tabular}{|| l | l | c | c | l ||} \hline
  \textbf{Failure Scenario} & &  \textbf{Pot Div Effect}  &   & \textbf{Symptom}          \\ 
+\textbf{ / test case     } & &  \textbf{              }  &   & \textbf{       }          \\ 
                \hline
      FS1: R1 SHORT    &  & $LOW$   &  &  $PDLow$                \\ \hline
     FS2: R1 OPEN      &  &  $HIGH$ &  &  $PDHigh$             \\ \hline
@@ -782,6 +791,7 @@ how the levels work and converge to a top or system level.
  \caption{Functional Group Tree example}
  \label{fig:three_tree}
 \end{figure}
+
 \end{frame}
  
  \begin{frame}
@@ -789,29 +799,42 @@ how the levels work and converge to a top or system level.
 The fact FMMD analyses small groups of components at a time, and organises them
 into a hierarchy
 addresses the state explosion problem. \pause
-Where $O$ is order
-of complexity $O(N^2)$ in the equation below.
 
+For FMEA where we check every component failure mode rigorously
+against all the other components (we could call this \textbf{RFMEA})
+Where $N$ is the number of components, we can determine the order
+of complexity $ O(N^2) $ thus.
+% % 
 \begin{equation}
   \label{eqn:fmea_single2}
-  N.(N-1).cfm % \\
+  N.(N-1).f 
-  %(N^2 - N).cfm 
 \end{equation}
+% 
+% %\end{frame}
+ \end{frame}
 
 
+
+\begin{frame}
+\frametitle{FMMD - comparing number of checks RFMEA $\ldots$ FMMD}
+%\end{frame}
+If we consider $c$ to be the number of components in a {\fg}, $f$ is the number of failure modes per component, and 
+$L$ to be the number of levels in the hierarchy of FMMD analysis.
+
+%\begin{frame}
 We can represent the number of failure scenarios to check in an FMMD hierarchy
 with equation~\ref{eqn:anscen}.
-
+\pause
 \begin{equation}
   \label{eqn:anscen}
-  \sum_{n=0}^{L} {fgn}^{n}.fgn.cfm.(fgn-1) 
+  \sum_{n=0}^{L} {c}^{n}.c.f.(c-1) 
 \end{equation}
-Where $fgn$ is the number of components in each functional group,
+% Where $c$ is the number of components in each functional group,
-and $cfm$ is the number of failure modes per component
+% and $f$ is the number of failure modes per component
-and L is the number of levels, the number of
+% and L is the number of levels, the number of
-analysis scenarios to consider.
+% analysis scenarios to consider.
 
-~\ref{eqn:fmea_state_exp}.
+%%~\ref{eqn:fmea_state_exp}.
 
 \end{frame}
 
@@ -833,18 +856,18 @@ analysis scenarios to consider.
 % 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).
+% we must compare each failure mode against the two other components (the `$c-1$' 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_exp44} 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.
+% number of components in the system, and $f$ 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 
+% Where $N=3$ and $f=3$ we can see that  the number of checks for this simple functional 
 % group is the same for equation~\ref{eqn:fmea_state_exp22}
 % and equation~\ref{eqn:anscen}.
 % \clearpage
@@ -855,7 +878,7 @@ analysis scenarios to consider.
 To see the effects of reducing `state~explosion' we can use an example.
 % with fixed numbers
 %for components in a functional group, and failure modes per component.
-Let us take a system with 4 levels (with a top/system 0 level),
+Let us take a system with 3 levels of FMMD analysis,
 with three components per functional group and three failure modes per component,
  and apply these formulae.
 Having 4 levels (in addition to the top zeroth level)
@@ -865,14 +888,14 @@ $$
 %\begin{equation}
   \label{eqn:fmea_state_exp22}
   81.(81-1).3 = 19440 % \\
-  %(N^2 - N).cfm 
+  %(N^2 - N).f 
 %\end{equation}
 $$
 
 $$
 %\begin{equation}
  % \label{eqn:anscen}
-  \sum_{n=0}^{4} {3}^{n}.3.3.(2) = 2178 
+  \sum_{n=0}^{3} {3}^{n}.3.3.(2) = 720
 %\end{equation}
 $$
 \end{frame}
@@ -884,10 +907,10 @@ $$
 
 
 \begin{itemize}
-  \pause \item Thus for FMMD we needed to examine 2178 failure~modes against functionally adjacent components, and for traditional FMEA
+  \pause \item Thus for FMMD we needed to examine 720 failure~modes against functionally adjacent components, and for traditional FMEA
 type analysis methods, the number rises to 19440.
    \pause \item 19440 `checks' is not practical
-   \pause \item 2178 checks is alot, but...
+   \pause \item 720 checks is quite alot, but...
   \pause \item Modules in FMMD can be re-used...
 \end{itemize}
 % In practical example followed through, no more than 9 components have ever been required for a functional
@@ -907,22 +930,31 @@ To determine  all possible double simultaneous failures for rigorous FMEA
 
 \begin{equation}
   \label{eqn:fmea_state_exp2}
-  N.(N-1).(N-2).cfm % \\
+  N.(N-1).(N-2).f % \\
-  %(N^2 - N).cfm 
+  %(N^2 - N).f 
 \end{equation}
+
+Or express in terms of the level
+
+\begin{equation}
+  \label{eqn:fmea_state_exp2}
+  c^{L+1}.(c^{L+1}-1).(c^{L+1}-2).f % \\
+  %(N^2 - N).f 
+\end{equation}
+
 \pause
 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:anscen2}
-  \sum_{n=0}^{L} {fgn}^{n}.fgn.cfm.(fgn-1).(fgn-2)
+  \sum_{n=0}^{L} {c}^{n}.c.f.(c-1).(c-2)
 \end{equation}
 \end{frame}
 
 \begin{frame}
 \frametitle{FMMD - Failure Mode Modular De-Composition}
 \textbf{Traceability}
-Because each reasoning stage contains associations ($FailureMode \mapsto Symptom$)
+Because each reasoning stage contains associations ($FailureMode \rightarrow Symptom$)
 we can trace the `reasoning' from base level component failure mode to top level/system
 failure, by traversing the tree/hierarchy. This is in effect providing a `framework' of the reasoning.