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142
presentations/fmea/fmea_pres.tex
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@ -111,11 +111,11 @@ For the sake of example let us choose resistor R1 in the OP-AMP gain circuitry.
\begin{frame}
Note here that we have had to look at the failure~mode
in relation to the entire circuit.
in relation to the entire circuit. \pause
We have used intuition to determine the probable
effect of this failure mode.
effect of this failure mode. \pause
We have not examined this failure mode
against every other component in the system.
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.
@ -162,14 +162,14 @@ $100*99*3=29,700$.
\frametitle{Rigorous Double Failure FMEA}
For looking at potential double failure scenarios (two components
failing within a given time frame) and the order becomes
$N^3$.
$N^3$. \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
@ -198,14 +198,14 @@ double failure scenarios (for burner lock-out scenarios).
\begin{frame}
\frametitle{PFMEA}
Production FMEA (or PFMEA), is FMEA used to prioritise, in terms of
cost, problems to be addressed in product production.
cost, problems to be addressed in product production.\pause
It focuses on known problems, determines the
frequency they occur and their cost to fix.
frequency they occur and their cost to fix.\pause
This is multiplied together and called an RPN
number.
number.\pause
Fixing problems with the highest RPN number
will return most cost benefit.
will return most cost benefit.\pause
\end{frame}
@ -326,8 +326,8 @@ Applies some Bayesian statistics (probabilities of component failures and those
\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.
FMECA has three probability factors for component failures.
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.
@ -347,11 +347,11 @@ a particular failure~mode occurring within a component. \pause reference FMD-91.
\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.
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}
\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,
@ -360,7 +360,7 @@ represented by the variable $t$.
\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}
@ -386,34 +386,59 @@ for a project manager.
\end{frame}
\begin{frame}
\frametitle{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
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.
\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}
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. $\lambda_{SD}$, $\lambda_{SU}$, $\lambda_{DD}$, $\lambda_{DU}$).
\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 $\lambda_{SD}$, $\lambda_{SU}$, $\lambda_{DD}$, $\lambda_{DU}$
\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}
@ -557,7 +582,7 @@ judged to be in critical sections of the product.
\end{frame}
\subsection{FMEA - Better Metodology - Wish List}
\subsection{FMEA - Better Methodology - Wish List}
\begin{frame}
\frametitle{FMEA - Better Metodology - Wish List}
@ -596,14 +621,23 @@ judged to be in critical sections of the product.
% %(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.
% 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}
@ -617,8 +651,8 @@ 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 i.e. $ \bowtie ( FunctionalGroup ) \rightarrow {DerivedComponent} $
%\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}
@ -634,7 +668,7 @@ This creates an analysis hierarchy.
% mvampcircuit.png: 243x143 pixel, 72dpi, 8.57x5.04 cm, bb=0 0 243 143
\end{figure}
We can return to the milli-volt amplifier as an example to analyse.
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.
@ -786,10 +820,11 @@ in a higher level design.
\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.
%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}
@ -797,7 +832,10 @@ how the levels work and converge to a top or system level.
\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}