From a62f02591f9ba3adca7970f28dcd7a88b59295df Mon Sep 17 00:00:00 2001
From: "Robin P. Clark" <robin48gx@gmail.com>
Date: Tue, 2 Oct 2012 17:11:39 +0100
Subject: [PATCH] Copied from fmea_pres: first draft for the FMMD software
 presentation.

---
 presentations/System_safety_2012/Makefile     |   13 +
 .../System_safety_2012/component.dia          |  Bin 0 -> 1240 bytes
 .../System_safety_2012/fmmd_env_op_uml.dia    |  Bin 0 -> 2324 bytes
 .../System_safety_2012/fmmd_exm_h.dia         |  Bin 0 -> 1971 bytes
 .../System_safety_2012/fmmd_software_pres.tex | 1045 +++++++++++++++++
 .../System_safety_2012/master_uml.dia         |  Bin 0 -> 3529 bytes
 presentations/System_safety_2012/mvamp.dia    |  Bin 0 -> 2457 bytes
 .../System_safety_2012/mvampcircuit.dia       |  Bin 0 -> 1598 bytes
 presentations/System_safety_2012/n_inv_dc.dia |  Bin 0 -> 1386 bytes
 presentations/System_safety_2012/pd.dia       |  Bin 0 -> 1326 bytes
 presentations/System_safety_2012/pd_euler.dia |  Bin 0 -> 1229 bytes
 .../System_safety_2012/pd_euler2.dia          |  Bin 0 -> 1576 bytes
 .../System_safety_2012/three_tree.dia         |  Bin 0 -> 6455 bytes
 13 files changed, 1058 insertions(+)
 create mode 100644 presentations/System_safety_2012/Makefile
 create mode 100644 presentations/System_safety_2012/component.dia
 create mode 100644 presentations/System_safety_2012/fmmd_env_op_uml.dia
 create mode 100644 presentations/System_safety_2012/fmmd_exm_h.dia
 create mode 100644 presentations/System_safety_2012/fmmd_software_pres.tex
 create mode 100644 presentations/System_safety_2012/master_uml.dia
 create mode 100644 presentations/System_safety_2012/mvamp.dia
 create mode 100644 presentations/System_safety_2012/mvampcircuit.dia
 create mode 100644 presentations/System_safety_2012/n_inv_dc.dia
 create mode 100644 presentations/System_safety_2012/pd.dia
 create mode 100644 presentations/System_safety_2012/pd_euler.dia
 create mode 100644 presentations/System_safety_2012/pd_euler2.dia
 create mode 100644 presentations/System_safety_2012/three_tree.dia

diff --git a/presentations/System_safety_2012/Makefile b/presentations/System_safety_2012/Makefile
new file mode 100644
index 0000000..8abfb65
--- /dev/null
+++ b/presentations/System_safety_2012/Makefile
@@ -0,0 +1,13 @@
+
+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 $<
+
+all: $(DIAPNG)
+	pdflatex fmmd_software_pres
+	acroread fmmd_software_pres.pdf || evince fmmd_software_pres.pdf
+
+
+bib:
+	bibtex fmmd_software_pres
diff --git a/presentations/System_safety_2012/component.dia b/presentations/System_safety_2012/component.dia
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diff --git a/presentations/System_safety_2012/fmmd_env_op_uml.dia b/presentations/System_safety_2012/fmmd_env_op_uml.dia
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diff --git a/presentations/System_safety_2012/fmmd_software_pres.tex b/presentations/System_safety_2012/fmmd_software_pres.tex
new file mode 100644
index 0000000..42f3773
--- /dev/null
+++ b/presentations/System_safety_2012/fmmd_software_pres.tex
@@ -0,0 +1,1045 @@
+\documentclass{beamer}
+%\documentclass[handout]{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]
+
+
+\newcommand{\fg}{\em functional~group}
+\newcommand{\fgs}{\em functional~groups}
+\newcommand{\dc}{\em derived~component}
+\newcommand{\dcs}{\em derived~components}
+\newcommand{\bc}{\em base~component}
+\newcommand{\bcs}{\em base~components}
+\newcommand{\irl}{in~real~life}
+
+\begin{document}
+
+\section{F.M.E.A.}
+\begin{frame}
+\frametitle{FMEA}
+%\tableofcontents[currentsection]
+\end{frame}
+
+
+
+\begin{frame}
+\frametitle{FMEA}
+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{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 itsself
+\end{itemize}
+\end{frame}
+
+
+\begin{frame}
+ \frametitle{ FMEA Example: Milli-volt reader}
+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.
+\begin{figure}
+ \centering
+ \includegraphics[width=175pt]{./mvamp.png}
+ % mvamp.png: 561x403 pixel, 72dpi, 19.79x14.22 cm, bb=0 0 561 403
+\end{figure}
+
+
+\end{frame}
+
+
+\begin{frame}
+ \frametitle{FMEA Example: Milli-volt reader}
+Let us perform an FMEA and consider how one of its resistors failing could affect
+it.
+For the sake of example let us choose resistor R1 in the  OP-AMP gain circuitry.
+\begin{figure}
+ \centering
+ \includegraphics[width=175pt]{./mvamp.png}
+ % mvamp.png: 561x403 pixel, 72dpi, 19.79x14.22 cm, bb=0 0 561 403
+\end{figure}
+
+\end{frame}
+
+
+
+
+\begin{frame}
+ \frametitle{FMEA Example: Milli-volt reader}
+\begin{figure}
+ \centering
+ \includegraphics[width=80pt]{./mvamp.png}
+ % mvamp.png: 561x403 pixel, 72dpi, 19.79x14.22 cm, bb=0 0 561 403
+\end{figure}
+\begin{itemize}
+  \pause \item \textbf{F - Failures of given component} The resistor (R1) could fail by going OPEN or SHORT (EN298 definition).
+   \pause \item \textbf{M - Failure Mode} Consider the component failure mode SHORT
+   \pause \item \textbf{E - Effects} This will drive the minus input LOW causing a HIGH OUTPUT/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. \pause
+We have used intuition to determine the probable
+effect of this failure mode. \pause
+We have not examined this failure mode
+against every other component in the system. \pause
+Perhaps we should.... this would be a more rigorous and complete
+approach in looking for system failures.
+
+\end{frame}
+
+\subsection{Rigorous FMEA - State Explosion}
+\begin{frame}
+ \frametitle{Rigorous Single Failure FMEA}
+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.
+\end{frame}
+
+
+ \begin{frame}
+\frametitle{Rigorous Single Failure FMEA}
+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 
+$f$ is the number of failure modes per component.
+  
+
+\begin{equation}
+  \label{eqn:fmea_single}
+  N.(N-1).f % \\
+  %(N^2 - N).f 
+\end{equation}
+\end{frame}
+
+
+\begin{frame}
+\frametitle{Rigorous Single Failure FMEA}
+This would mean an order of $N^2$ number of checks to perform
+to undertake a `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}
+ \frametitle{Rigorous Double Failure FMEA}
+For looking at potential double failure scenarios (two components
+failing within a given time frame) and the order becomes
+$N^3$. \pause
+
+\begin{equation}
+  \label{eqn:fmea_double}
+  N.(N-1).(N-2).f % \\
+  %(N^2 - N).f 
+\end{equation}
+ \pause
+$100*99*98*3=2,910,600$.
+\pause
+
+.\\
+
+The European Gas burner standard (EN298:2003), demands the checking of 
+double failure scenarios (for burner lock-out scenarios).
+
+\end{frame}
+
+\begin{frame} 
+\frametitle{Four main Variants of FMEA}
+ \begin{itemize}
+ \pause \item \textbf{PFMEA - Production}  \pause Car Manufacture etc
+   \pause \item \textbf{FMECA - Criticallity}  \pause Military/Space
+   \pause \item \textbf{FMEDA - Statistical safety}   \pause EN61508/IOC1508 \pause Safety Integrity Levels
+  \pause \item \textbf{DFMEA - Design or static/theoretical}   \pause EN298/EN230/UL1998
+\end{itemize}
+\end{frame}
+
+
+
+
+\section{PFMEA - Production FMEA : 1940's to present}
+
+\begin{frame}
+ \frametitle{PFMEA}
+Production FMEA (or PFMEA), is FMEA used to prioritise, in terms of
+cost, problems to be addressed in product production.\pause
+
+It focuses on known problems, determines the 
+frequency they occur and their cost to fix.\pause
+This is multiplied together and called an RPN
+number.\pause
+Fixing problems with the highest RPN number
+will return most cost benefit.\pause
+
+\end{frame}
+
+
+\begin{frame}
+% benign example of PFMEA in CARS - make something up.
+\frametitle{PFMEA Example}
+
+{
+\begin{table}[ht]
+\caption{FMEA Calculations} % title of Table
+%\centering % used for centering table
+\begin{tabular}{|| l | l | c | c | l ||} \hline
+ \textbf{Failure Mode} &   \textbf{P}             & \textbf{Cost}        &  \textbf{Symptom} & \textbf{RPN} \\ \hline \hline
+      relay 1 n/c      & $1*10^{-5}$              &  38.0                & indicators fail   & 0.00038 \\ \hline
+        relay 2 n/c      & $1*10^{-5}$              &  98.0                & doorlocks fail   & 0.00098 \\ \hline
+%       rear end crash    &  $14.4*10^{-6}$         & 267,700              & fatal fire       &  3.855 \\
+%       ruptured f.tank   &                         &                      &                  &        \\ \hline
+
+
+\hline
+\end{tabular}
+\end{table}
+}
+
+%Savings: 180 burn deaths, 180 serious burn injuries, 2,100 burned vehicles. Unit Cost: $200,000 per death, $67,000 per injury, $700 per vehicle.
+%Total Benefit: 180 X ($200,000) + 180 X ($67,000) + $2,100 X ($700) = $49.5 million.
+%COSTS
+%Sales: 11 million cars, 1.5 million light trucks.
+%Unit Cost: $11 per car, $11 per truck.
+%Total Cost: 11,000,000 X ($11) + 1,500,000 X ($11) = $137 million.
+
+
+ 
+
+\end{frame}
+
+
+
+%\subsection{Production FMEA : Example Ford Pinto : 1975}
+\begin{frame}
+ \frametitle{PFMEA Example: Ford Pinto: 1975}
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt]{./ad_ford_pinto_mpg_red_3_1975.jpg}
+ % ad_ford_pinto_mpg_red_3_1975.jpg: 720x933 pixel, 96dpi, 19.05x24.69 cm, bb=0 0 540 700
+ \caption{Ford Pinto Advert}
+ \label{fig:fordpintoad}
+\end{figure}
+
+\end{frame}
+
+
+ \begin{frame}
+ \frametitle{PFMEA Example: Ford Pinto: 1975}
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=200pt]{./burntoutpinto.png}
+ % burntoutpinto.png: 376x250 pixel, 72dpi, 13.26x8.82 cm, bb=0 0 376 250
+ \caption{Burnt Out Pinto}
+ \label{fig:burntoutpinto}
+\end{figure}
+
+
+\end{frame}
+
+
+\begin{frame}
+ \frametitle{PFMEA Example: Ford Pinto: 1975}
+ {
+\begin{table}[ht]
+\caption{FMEA Calculations} % title of Table
+%\centering % used for centering table
+\begin{tabular}{|| l | l | c | c | l ||} \hline
+ \textbf{Failure Mode} &   \textbf{P}             & \textbf{Cost}        &  \textbf{Symptom} & \textbf{RPN} \\ \hline \hline
+      relay 1 n/c      & $1*10^{-5}$              &  38.0                & indicators fail   & 0.00038 \\ \hline
+        relay 2 n/c      & $1*10^{-5}$              &  98.0                & doorlocks fail   & 0.00098 \\ \hline
+       rear end crash    &  $14.4*10^{-6}$         & 267,700              & fatal fire       &  3.855 \\
+       ruptured f.tank   &                         &                      & allow               &        \\ \hline
+
+     rear end crash    &  $1$                      &  $11$             &    recall   &   11.0 \\
+       ruptured f.tank   &                         &                      & fix tank             &        \\ \hline
+
+\hline
+\end{tabular}
+\end{table}
+}
+
+ 
+ http://www.youtube.com/watch?v=rcNeorjXMrE
+ 
+\end{frame}
+
+
+
+
+\section{FMECA - Failure Modes Effects and Criticality Analysis}
+ 
+
+
+\begin{frame}
+\frametitle{ FMECA - Failure Modes Effects and Criticallity Analysis}
+\begin{figure}
+ \centering
+ %\includegraphics[width=100pt]{./military-aircraft-desktop-computer-wallpaper-missile-launch.jpg}
+ \includegraphics[width=100pt]{./A10_thunderbolt.jpg}
+ % military-aircraft-desktop-computer-wallpaper-missile-launch.jpg: 1024x768 pixel, 300dpi, 8.67x6.50 cm, bb=0 0 246 184
+ \caption{A10 Thunderbolt}
+ \label{fig:f16missile}
+\end{figure}
+Emphasis on determining criticality of failure.
+Applies some Bayesian statistics (probabilities of component failures and those thereby causing given system level failures).
+\end{frame}
+
+
+\begin{frame}
+\frametitle{ FMECA - Failure Modes Effects and Criticality Analysis}
+Very similar to PFMEA, but instead of cost, a criticality or
+seriousness factor is ascribed to putative top level incidents.\pause
+FMECA has three probability factors for component failures.\pause
+
+\textbf{FMECA ${\lambda}_{p}$ value.}
+This is the overall failure rate of a base component.
+This will typically be the failure rate per million ($10^6$) or
+billion ($10^9$) hours of operation.\pause reference MIL1991. \pause
+
+\textbf{FMECA $\alpha$ value.}
+The failure mode probability, usually denoted by $\alpha$ is the  probability of 
+a particular failure~mode occurring within a component. \pause reference FMD-91.  
+%, should it fail.
+%A component with N failure modes will thus have
+%have an $\alpha$ value associated with each of those modes.
+%As the $\alpha$ modes are probabilities, the sum of all $\alpha$ modes for a component must equal one.
+\end{frame}
+
+\begin{frame}
+\frametitle{ FMECA - Failure Modes Effects and Criticality Analysis}
+\textbf{FMECA $\beta$ value.}
+The second probability factor $\beta$, is the probability that the failure mode
+will cause a given system failure.\pause
+This corresponds to `Bayesian' probability, given a particular
+component failure mode, the probability of a given system level failure.
+\pause
+\textbf{FMECA `t' Value}\pause
+The time that a system will be operating for, or the working life time of the product is
+represented by the variable $t$. 
+%for probability of failure on demand studies,
+%this can be the number of  operating cycles or demands expected.
+\pause
+\textbf{Severity `s' value}
+A weighting factor to indicate the seriousness of the putative system level error.
+%Typical classifications are as follows:~\cite{fmd91}
+\pause
+\begin{equation}
+ C_m  =  {\beta} .  {\alpha} . {{\lambda}_p} . {t} . {s}
+\end{equation}
+\pause
+Highest $C_m$ values would be at the top of a `to~do' list
+for a project manager.
+\end{frame}
+
+
+
+\section{FMEDA - Failure Modes Effects and Diagnostic Analysis}
+
+
+
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+\begin{figure}
+ \centering
+ \includegraphics[width=200pt]{./SIL.png}
+ % SIL.jpg: 350x286 pixel, 72dpi, 12.35x10.09 cm, bb=0 0 350 286
+ \caption{SIL requirements}
+\end{figure}
+
+\end{frame}
+
+
+
+
+
+\begin{frame}
+
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+
+\begin{itemize}
+   \pause \item \textbf{Statistical Safety}  \pause Safety Integrity Level (SIL) standards (EN61508/IOC5108).
+   \pause \item \textbf{Diagnostics}         \pause Diagnostic or self checking elements modelled
+   \pause \item \textbf{Complete Failure Mode Coverage}   \pause All failure modes of all components must be in the model
+  \pause \item \textbf{Guidelines}   \pause To system architectures and development processes
+\end{itemize}
+
+% FMEDA is the methodology behind statistical (safety integrity level)
+% type standards (EN61508/IOC5108). \pause
+% It provides a statistical overall level of safety
+% and allows diagnostic mitigation for self checking etc. \pause
+% It provides guidelines for the design and architecture
+% of computer/software systems for the four levels of 
+% safety Integrity.
+% %For Hardware 
+% \pause
+% FMEDA does force the user to consider all components in a system
+% by requiring that a MTTF value is assigned for each failure~mode; \pause
+% the MTTF may be statistically mitigated (improved)
+% if it can be shown that self-checking will detect failure modes.
+
+\end{frame}
+
+
+
+
+
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+\textbf{Failure Mode Classifications in FMEDA.}
+ \begin{itemize}
+ \pause \item \textbf{Safe or Dangerous}  \pause Failure modes are classified SAFE or DANGEROUS
+   \pause \item \textbf{Detectable failure modes}  \pause Failure modes are given the attribute DETECTABLE or UNDETECTABLE
+   \pause \item \textbf{Four attributes to Failure Modes}   \pause All failure modes may thus be Safe Detected(SD), Safe Undetected(SU), Dangerous Detected(DD), Dangerous Undetected(DU)
+  \pause \item \textbf{Four statistical properties of a system}   \pause  \\
+$ \sum \lambda_{SD}$, $\sum \lambda_{SU}$, $\sum \lambda_{DD}$, $\sum \lambda_{DU}$
+\end{itemize}
+
+% Failure modes are classified as Safe or Dangerous according 
+% to the putative system level failure they will cause. \pause
+% The Failure modes are also classified as Detected or
+% Undetected. 
+% This gives us four level failure mode classifications:
+% Safe-Detected (SD), Safe-Undetected (SU), Dangerous-Detected (DD) or Dangerous-Undetected (DU),
+% and the probabilistic failure rate of each classification 
+% is represented by lambda variables
+% (i.e. $\lambda_{SD}$, $\lambda_{SU}$, $\lambda_{DD}$, $\lambda_{DU}$).
+\end{frame}
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+\textbf{Diagnostic Coverage.}
+The diagnostic coverage is simply the ratio
+of the dangerous detected probabilities
+against the probability of all dangerous failures,
+and is normally expressed as a percentage. $\Sigma\lambda_{DD}$ represents
+the percentage of dangerous detected base component failure modes, and 
+$\Sigma\lambda_D$ the total number of dangerous base component failure modes.
+
+$$ DiagnosticCoverage = \Sigma\lambda_{DD} / \Sigma\lambda_D $$
+\end{frame}
+
+
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+The \textbf{diagnostic coverage} for safe failures, where  $\Sigma\lambda_{SD}$ represents the percentage of
+safe detected base component failure modes,
+and $\Sigma\lambda_S$ the total number of safe base component failure modes,
+is given as
+
+$$ SF = \frac{\Sigma\lambda_{SD}}{\Sigma\lambda_S} $$
+\end{frame}
+
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+\textbf{Safe Failure Fraction.}
+A key concept in  FMEDA is Safe Failure Fraction (SFF).
+This is the ratio of safe  and dangerous detected failures
+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. 
+
+\end{frame}
+
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+To achieve SIL levels, diagnostic coverage and SFF levels are prescribed along with
+hardware architectures and software techniques. \pause
+The overall   the aim of SIL is classify the safety of a system,
+by statistically determining how frequently it can fail dangerously.
+
+
+\end{frame}
+
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+{
+\begin{table}[ht]
+\caption{FMEA Calculations} % title of Table
+%\centering % used for centering table
+\begin{tabular}{|| l | l | c | c | l ||} \hline
+ \textbf{SIL} &   \textbf{Low Demand}     & \textbf{Continuous Demand}          \\ 
+              & Prob of failing on demand & Prob of failure per hour  \\ \hline \hline
+      4       & $ 10^{-5}$ to $< 10^{-4}$  &   $ 10^{-9}$ to $< 10^{-8}$                \\ \hline
+      3       &  $ 10^{-4}$ to $< 10^{-3}$ &    $ 10^{-8}$ to $< 10^{-7}$             \\ \hline
+      2       &  $ 10^{-3}$ to $< 10^{-2}$ &    $ 10^{-7}$ to $< 10^{-6}$             \\ \hline
+      1       &  $ 10^{-2}$ to $< 10^{-1}$ &    $ 10^{-6}$ to $< 10^{-5}$                        \\ \hline
+
+\hline
+\end{tabular}
+\end{table}
+}
+Table adapted from EN61508-1:2001 [7.6.2.9 p33]
+\end{frame}
+
+\begin{frame}
+\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
+FMEDA is a modern extension of FMEA, in that it will allow for 
+self checking features, and provides detailed recommendations for computer/software architecture. \pause
+It   has a simple final result, a Safety Integrity Level (SIL) from 1 to 4 (where 4 is safest).
+
+%FMEA can be used as a term simple to mean Failure Mode Effects Analysis, and is
+%part of product approval for many regulated products in the EU and the USA...
+
+\end{frame}
+
+
+
+
+\section{FMEA used for Safety Critical Approvals}
+
+\begin{frame}
+\frametitle{DESIGN FMEA: Safety Critical Approvals FMEA}
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=100pt,keepaspectratio=true]{./tech_meeting.png}
+ % tech_meeting.png: 350x299 pixel, 300dpi, 2.97x2.53 cm, bb=0 0 84 72
+ \caption{FMEA  Meeting}
+ \label{fig:tech_meeting}
+\end{figure}
+Static FMEA, Design FMEA, Approvals FMEA \pause
+
+Experts from Approval House and Equipment Manufacturer
+discuss selected component failure modes
+judged to be in critical sections of the product.
+
+
+
+\end{frame}
+
+\begin{frame}
+\frametitle{DESIGN FMEA: Safety Critical Approvals FMEA}
+
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=70pt,keepaspectratio=true]{./tech_meeting.png}
+ % tech_meeting.png: 350x299 pixel, 300dpi, 2.97x2.53 cm, bb=0 0 84 72
+ \caption{FMEA  Meeting}
+ \label{fig:tech_meeting}
+\end{figure}
+
+\begin{itemize}
+  \pause \item Impossible to look at all component failures let alone apply FMEA rigorously.
+  \pause \item In practise, failure scenarios for critical sections are contested, and either justified or extra safety measures implemented.
+   \pause \item Often Meeting notes or minutes only. Unusual for detailed arguments to be documented.
+\end{itemize}
+
+\end{frame}
+
+\section{FMEA - General Criticism}
+\begin{frame}
+\frametitle{FMEA - General Criticism}
+
+\begin{itemize}
+  \pause \item FMEA type methodologies were designed for simple electro-mechanical systems of the 1940's to 1960's.
+  \pause \item Reasoning Distance - component failure to system level symptom
+  \pause \item State explosion - impossible to perform rigorously
+  \pause \item Difficult to re-use previous analysis work
+  \pause \item Very Difficult to model simultaneous failures.
+  
+\end{itemize}
+
+%
+
+\end{frame}
+
+
+\subsection{FMEA - Better Methodology - Wish List}
+ 
+\begin{frame}
+\frametitle{FMEA - Better Metodology - Wish List}
+
+\begin{itemize}
+  
+   \pause \item State explosion  
+  \pause \item  Rigorous (total coverage)
+   \pause \item Reasoning Traceable  
+   \pause \item Re-useable
+ \pause \item Simultaneous failures
+  %\pause \item  
+\end{itemize}
+
+%FMEDA is a modern extension of FMEA, in that it will allow for 
+%self checking features, and provides detailed recommendations for computer/software architecture,
+%but
+
+\end{frame}
+\section{Failure Mode Modular De-Composition}
+\begin{frame}
+ \frametitle{FMMD - Failure Mode Modular De-Composition}
+% 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 
+% $f$ is the number of failure modes per component.
+% 
+% \begin{equation}
+%   \label{eqn:fmea_state_exp}
+%   N.(N-1).f % \\
+%   %(N^2 - N).f 
+% \end{equation}
+
+\begin{itemize}
+  
+   \pause \item Analysis occurs in small stages, within {\fgs}  
+  \pause \item  Each {\fg} is analysed until we have a set of its symptoms of failure.
+   \pause \item A {\dc} is created with its failure modes being the symptoms from the {\fg}  
+   \pause \item We can now use {\dcs} as higher level components
+ \pause \item We can build a failure model hierarchy in this way
+  %\pause \item  
+\end{itemize}
+
+% The FMMD methodology breaks the analysis down into small stages,
+% by making the analyst choose {\fgs} of components, to which FMEA is applied.
+% When analysed, a set of symptoms of failure for the {\fg} is used to create a derived~component. \pause
+% The derived components failure modes, are the symptoms of the {\fg}
+% from which it was derived. \pause
+% We can use derived components to form `higher~level' {\fgs}.
+% This creates an analysis hierarchy.
+\end{frame}
+
+
+\subsection{FMMD Outline of Methodology}
+\begin{frame}
+\frametitle{FMMD - Outline of Methodology}
+\begin{itemize}
+  \pause \item Select `{\fgs}' of components ( groups that perform a well defined function).
+  \pause \item Using the failure modes of the components create failure scenarios.
+  \pause \item Analyse each failure scenario of the {\fg}. 
+  \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  $ \bowtie ( FunctionalGroup ) \rightarrow {DerivedComponent} $
+  %\item could use AMALG instead here $ \amalg $
+\end{itemize}
+\end{frame}
+
+
+
+\subsection{FMMD - Example - Milli Volt Amplifier}
+\begin{frame}
+\frametitle{FMMD - Example - Milli Volt Amplifier}
+\begin{figure}
+ \centering
+ \includegraphics[width=100pt]{./mvampcircuit.png}
+ % mvampcircuit.png: 243x143 pixel, 72dpi, 8.57x5.04 cm, bb=0 0 243 143
+\end{figure}
+
+We return to the milli-volt amplifier as an example to analyse.
+\pause
+We can begin by looking for functional groups.\pause
+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).
+
+\end{frame}
+
+
+\begin{frame}
+\frametitle{FMMD - Example - Resistor and failure modes}
+Resistor and its failure modes represented as a directed graph.
+
+\begin{figure}
+ \centering
+ \includegraphics[width=200pt]{./resistor_failure_graph.png}
+ % resistor_failure_graph.png: 391x279 pixel, 93dpi, 10.68x7.62 cm, bb=0 0 303 216
+ \label{fig:resasfm}
+\end{figure}
+
+\end{frame}
+
+
+\subsubsection{Potential Divider}
+\begin{frame}
+\frametitle{FMMD - Example - Failure mode analysis of Potential Divider}
+
+
+\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
+     FS3: R2 SHORT    &  &  $HIGH$ &  &  $PDHigh$             \\ \hline
+     FS4: R2 OPEN     &  &  $LOW$  &  &  $PDLow$                        \\ \hline
+\hline
+\end{tabular}
+\end{table}
+
+\begin{figure}
+ \centering
+ \includegraphics[width=100pt,keepaspectratio=true]{./pd.png}
+ % pd.png: 361x241 pixel, 72dpi, 12.74x8.50 cm, bb=0 0 361 241
+\end{figure}
+\end{frame}
+
+
+
+\begin{frame}
+\frametitle{FMMD - Example - Potential Divider as Derived Component}
+\begin{figure}
+ \centering
+ \includegraphics[width=175pt]{./pd_failures_as_graph.png}
+ % pd_dc_failures_as_graph.png: 389x284 pixel, 93dpi, 10.63x7.76 cm, bb=0 0 301 220
+ \label{fig:pd}
+\end{figure}
+\end{frame}
+
+
+\begin{frame}
+\frametitle{FMMD - Example - Potential Divider as Derived Component}
+\begin{figure}
+ \centering
+ \includegraphics[width=200pt]{./pd_dc_failures_as_graph.png}
+ % pd_dc_failures_as_graph.png: 389x284 pixel, 93dpi, 10.63x7.76 cm, bb=0 0 301 220
+ \label{fig:pd}
+\end{figure}
+\end{frame}
+
+\begin{frame}
+\frametitle{FMMD - Example - Potential Divider as Derived Component}
+
+We can now use this pre-analysed potential divider `derived~component'
+in a higher level design.
+
+\begin{figure}
+ \centering
+ \includegraphics[width=100pt]{./pd_dc_failures_as_graph.png}
+ % pd_dc_failures_as_graph.png: 389x284 pixel, 93dpi, 10.63x7.76 cm, bb=0 0 301 220
+ \label{fig:pd}
+\end{figure}
+\end{frame}
+
+\subsection{Non Inverting OP-AMP}
+
+\begin{frame}
+\frametitle{FMMD - Example - Non Inverting OP-AMP}
+\begin{figure}
+ \centering
+ \includegraphics{./mvampcircuit.png}
+ % mvampcircuit.png: 243x143 pixel, 72dpi, 8.57x5.04 cm, bb=0 0 243 143
+\end{figure}
+
+\end{frame}
+
+
+
+\begin{frame}
+\frametitle{FMMD - Example - Non Inverting OP-AMP}
+\begin{figure}
+ \centering
+ \includegraphics[width=300pt]{./non_inv_amp_fmea.png}
+ % non_inv_amp_fmea.png: 964x492 pixel, 96dpi, 25.50x13.02 cm, bb=0 0 723 369
+\end{figure}
+
+\end{frame}
+
+
+\begin{frame}
+\frametitle{FMMD - Example - Non Inverting OP-AMP}
+% \begin{figure}
+%  \centering
+%  \includegraphics[width=200pt]{./opamp_failures_as_graph.png} // op amp failure modes
+%  % opamp_failures_as_graph.png: 329x440 pixel, 93dpi, 8.99x12.02 cm, bb=0 0 255 341
+% \end{figure}
+\begin{figure}
+ \centering
+ \includegraphics[width=150pt]{./fg_opamp_pd_as_graph.png}
+ % fg_opamp_pd_as_graph.png: 750x826 pixel, 93dpi, 20.49x22.56 cm, bb=0 0 581 640
+\end{figure}
+\end{frame}
+
+
+
+\begin{frame}
+\frametitle{FMMD - Example - Non Inverting OP-AMP}
+\begin{figure}
+ \centering
+ \includegraphics[width=150pt]{./n_inv_dc.png}
+ % n_inv_dc.png: 296x326 pixel, 72dpi, 10.44x11.50 cm, bb=0 0 296 326
+\end{figure}
+
+\end{frame}
+
+
+
+\begin{frame}
+\frametitle{FMMD - Example - Non Inverting OP-AMP}
+\begin{figure}
+ \centering
+ \includegraphics[width=200pt]{./fmmd_exm_h.png}
+ % fmmd_exm_h.png: 376x241 pixel, 72dpi, 13.26x8.50 cm, bb=0 0 376 241
+\end{figure}
+
+
+\end{frame}
+
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+%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, the figure below 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}
+\pause
+For the sake of example we consider each functional group to
+be three components, the figure below shows
+how the levels work and converge to a top or system level.
+\end{frame}
+ 
+ \begin{frame}
+ \frametitle{FMMD - Failure Mode Modular De-Composition}
+The fact FMMD analyses small groups of components at a time, and organises them
+into a hierarchy
+addresses the state explosion problem. \pause
+
+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).f 
+\end{equation}
+% 
+% %\end{frame}
+ \end{frame}
+
+
+
+\begin{frame}
+\frametitle{FMMD - comparing number of checks RFMEA $\ldots$ FMMD}
+ 
+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.
+
+ 
+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} {c}^{n}.c.f.(c-1) 
+\end{equation}
+ 
+
+\end{frame}
+
+
+
+% 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 `$c-1$' 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 $f$ is the number of failures per component.
+
+
+% 
+% 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
+
+%\section{Example}/bowtie
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+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 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)
+will require 81 base level components.
+
+$$
+%\begin{equation}
+  \label{eqn:fmea_state_exp22}
+  81.(81-1).3 = 19440 % \\
+  %(N^2 - N).f 
+%\end{equation}
+$$
+
+$$
+%\begin{equation}
+ % \label{eqn:anscen}
+  \sum_{n=0}^{3} {3}^{n}.3.3.(2) = 720
+%\end{equation}
+$$
+\end{frame}
+
+
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+
+
+
+\begin{itemize}
+  \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 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
+% 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. 
+
+\end{frame}
+
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+
+To determine  all possible double simultaneous failures for rigorous FMEA 
+ the order $O(N^3)$.
+
+
+\begin{equation}
+  \label{eqn:fmea_state_exp2}
+  N.(N-1).(N-2).f % \\
+  %(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} {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 ($FailureMode \rightarrow Symptom$)
+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.
+
+
+\end{frame}
+
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+\textbf{Re-usability}
+Electronic Systems use commonly re-used functional groups (such as potential~dividers, amplifier configurations etc)
+Once a derived component is determined, it can generally be used in other projects.
+ 
+\end{frame}
+
+
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+\textbf{Total coverage}
+With FMMD we can ensure that all component failure modes
+have been represented as a symptom in the derived components created from them.
+We can thus apply automated checking to ensure that no
+failure modes, from base or derived components have been
+missed in an analysis.
+\end{frame}
+
+
+
+\subsection{conclusion}
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+\textbf{Conclusion: FMMD}
+
+\begin{itemize}
+  \pause \item Addresses State Explosion
+   \pause \item Addresses total coverage of all components and their failure modes
+   \pause \item Provides traceable reasoning
+  \pause \item derived components are re-use-able
+\end{itemize}
+\end{frame}
+
+\begin{frame}
+\frametitle{FMMD - Failure Mode Modular De-Composition}
+\textbf{Questions?}
+\end{frame}
+
+\end{document}
diff --git a/presentations/System_safety_2012/master_uml.dia b/presentations/System_safety_2012/master_uml.dia
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