

EN61508:6\cite{en61508}[B.6.6]
describes FMEA as: 
\begin{quotation}
"To analyse a system design, by examining all possible sources of failure
of a system's components and determining the effects of these failures
on the behaviour and safety of the system."
\end{quotation}.


\section{F.M.E.A.}

\subsection{FMEA}
%\tableofcontents[currentsection]





\subsection{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}
   \item Failure
    \item Mode
    \item Effects
   \item Analysis
\end{itemize}



% % \begin{itemize}
%  \item Failure 
%  \item Mode 
%  \item Effects 
%  \item Analysis
% \end{itemize}


\subsection{FMEA basic concept}


\begin{itemize}
   \item \textbf{F - Failures of given component} Consider a component in a system
    \item \textbf{M - Failure Mode} Look at one of the ways in which it can fail (i.e. determine a component `failure~mode')
    \item \textbf{E - Effects} Determine the effects this failure mode will cause to the system we are examining
   \item \textbf{A - Analysis} Analyse how much impact this symptom will have on the environment/people/the system itsself
\end{itemize}




 \subsection{ 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]{./CH2_FMEA/mvamp.png}
 % mvamp.png: 561x403 pixel, 72dpi, 19.79x14.22 cm, bb=0 0 561 403
\end{figure}






 \subsection{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}







 \subsection{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}
   \item \textbf{F - Failures of given component} The resistor (R1) could fail by going OPEN or SHORT (EN298 definition).
    \item \textbf{M - Failure Mode} Consider the component failure mode SHORT
    \item \textbf{E - Effects} This will drive the minus input LOW causing a HIGH OUTPUT/READING
   \item \textbf{A - Analysis} The reading will be out of normal range, and we will have an erroneous milli-volt reading
\end{itemize}





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.



\subsection{Rigorous FMEA - State Explosion}

 \subsection{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.




\subsection{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}




\subsection{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.
$100*99*3=29,700$.






 \subsection{Rigorous Double Failure FMEA}
For looking at potential double failure scenarios (two components
failing within a given time frame) and the order becomes
$N^3$. 

\begin{equation}
  \label{eqn:fmea_double}
  N.(N-1).(N-2).f % \\
  %(N^2 - N).f 
\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).



 
\subsection{Four main Variants of FMEA}
 \begin{itemize}
  \item \textbf{PFMEA - Production}   Car Manufacture etc
    \item \textbf{FMECA - Criticallity}   Military/Space
    \item \textbf{FMEDA - Statistical safety}    EN61508/IOC1508  Safety Integrity Levels
   \item \textbf{DFMEA - Design or static/theoretical}    EN298/EN230/UL1998
\end{itemize}





\section{PFMEA - Production FMEA : 1940's to present}


 \subsection{PFMEA}
Production FMEA (or PFMEA), is FMEA used to prioritise, in terms of
cost, problems to be addressed in product production.

It focuses on known problems, determines the 
frequency they occur and their cost to fix.
This is multiplied together and called an RPN
number.
Fixing problems with the highest RPN number
will return most cost benefit.





% benign example of PFMEA in CARS - make something up.
\subsection{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.


 





%\subsection{Production FMEA : Example Ford Pinto : 1975}

 \subsection{PFMEA Example: Ford Pinto: 1975}

\begin{figure}[h]
 \centering
 \includegraphics[width=300pt]{./CH2_FMEA/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}





 \subsection{PFMEA Example: Ford Pinto: 1975}

\begin{figure}[h]
 \centering
 \includegraphics[width=300pt]{./CH2_FMEA/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}






 \subsection{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
 





\section{FMECA - Failure Modes Effects and Criticality Analysis}
 



\subsection{ FMECA - Failure Modes Effects and Criticallity Analysis}
\begin{figure}
 \centering
 %\includegraphics[width=100pt]{./military-aircraft-desktop-computer-wallpaper-missile-launch.jpg}
 \includegraphics[width=300pt]{./CH2_FMEA/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).




\subsection{ 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.

\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. reference MIL1991. 

\textbf{FMECA $\alpha$ value.}
The failure mode probability, usually denoted by $\alpha$ is the  probability of 
a particular failure~mode occurring within a component.  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.



\subsection{ 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.
This corresponds to `Bayesian' probability, given a particular
component failure mode, the probability of a given system level failure.

\textbf{FMECA `t' Value}
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.

\textbf{Severity `s' value}
A weighting factor to indicate the seriousness of the putative system level error.
%Typical classifications are as follows:~\cite{fmd91}

\begin{equation}
 C_m  =  {\beta} .  {\alpha} . {{\lambda}_p} . {t} . {s}
\end{equation}

Highest $C_m$ values would be at the top of a `to~do' list
for a project manager.




\section{FMEDA - Failure Modes Effects and Diagnostic Analysis}




\subsection{ 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}









\subsection{ FMEDA - Failure Modes Effects and Diagnostic Analysis}

\begin{itemize}
    \item \textbf{Statistical Safety}   Safety Integrity Level (SIL) standards (EN61508/IOC5108).
    \item \textbf{Diagnostics}          Diagnostic or self checking elements modelled
    \item \textbf{Complete Failure Mode Coverage}    All failure modes of all components must be in the model
   \item \textbf{Guidelines}    To system architectures and development processes
\end{itemize}

FMEDA is the methodology behind statistical (safety integrity level)
type standards (EN61508/IOC5108). 
It provides a statistical overall level of safety
and allows diagnostic mitigation for self checking etc. 
It provides guidelines for the design and architecture
of computer/software systems for the four levels of 
safety Integrity.
%For Hardware 
%
FMEDA does force the user to consider all hardware components in a system
by requiring that a MTTF value is assigned for each failure~mode; 
the MTTF may be statistically mitigated (improved)
if it can be shown that self-checking will detect failure modes.
For software it provides procedural quality guidelines and constraints (such as forbidding certain
programming languages and/or features.








\subsection{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
\textbf{Failure Mode Classifications in FMEDA.}
 \begin{itemize}
  \item \textbf{Safe or Dangerous}   Failure modes are classified SAFE or DANGEROUS
    \item \textbf{Detectable failure modes}   Failure modes are given the attribute DETECTABLE or UNDETECTABLE
    \item \textbf{Four attributes to Failure Modes}    All failure modes may thus be Safe Detected(SD), Safe Undetected(SU), Dangerous Detected(DD), Dangerous Undetected(DU)
   \item \textbf{Four statistical properties of a system}     \\
$ \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. 
% 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. $\lambda_{SD}$, $\lambda_{SU}$, $\lambda_{DD}$, $\lambda_{DU}$).


\subsection{ 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.

$$ DiagnosticCoverage = \Sigma\lambda_{DD} / \Sigma\lambda_D $$




\subsection{ 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

$$ SF = \frac{\Sigma\lambda_{SD}}{\Sigma\lambda_S} $$



\subsection{ 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.

$$ SFF = \big( \Sigma\lambda_S + \Sigma\lambda_{DD} \big) / \big( \Sigma\lambda_S + \Sigma\lambda_D \big) $$

SFF determines how proportionately fail-safe a system is, not how reliable it is ! 
Weakness in this philosophy;  adding extra safe failures (even unused ones) improves the SFF. 




\subsection{ 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. 
The overall   the aim of SIL is classify the safety of a system,
by statistically determining how frequently it can fail dangerously.





\subsection{ 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]



\subsection{ 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. 
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...






\section{FMEA used for Safety Critical Approvals}


\subsection{DESIGN FMEA: Safety Critical Approvals FMEA}
\begin{figure}[h]
 \centering
 \includegraphics[width=300pt,keepaspectratio=true]{./CH2_FMEA/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 

Experts from Approval House and Equipment Manufacturer
discuss selected component failure modes
judged to be in critical sections of the product.






\subsection{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}
   \item Impossible to look at all component failures let alone apply FMEA rigorously.
   \item In practise, failure scenarios for critical sections are contested, and either justified or extra safety measures implemented.
    \item Often Meeting notes or minutes only. Unusual for detailed arguments to be documented.
\end{itemize}

