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Oh doh looks like I forgot some typos in the ch5 I sent to Chris

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75
submission_thesis/CH2_FMEA/copy.tex
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@ -8,33 +8,24 @@ of a system's components and determining the effects of these failures
on the behaviour and safety of the system." on the behaviour and safety of the system."
\end{quotation}. \end{quotation}.
\section{Concepts}
\paragraph{Forward and backward searches}
A forward search starts with possible failure causes
and uses logic and reasoning to determine system level outcomes.
A backward search starts with system level events
works back down (and not necessarily to
base components in a system) using de-composition of
of the system and logic.
FMEA based methodologies are forward searches\cite{Lutz:1997:RAU:590564.590572} and top down
methodologies such as FTA~\cite{nucfta,nasafta}
\paragraph{Reasoning distance}
A reasoning distance is the number of stages of logic and reasoning
required to map a failure cause to its potential outcomes.
%.... general concept... simple ideas about how complex a
%failure analysis is the more modules and components are involved
% cite for forward and backward search related to safety critical software
%{sfmeaforwardbackward}
\section{FMEA} \section{FMEA}
%\subsection{FMEA} %\subsection{FMEA}
%\tableofcontents[currentsection] %\tableofcontents[currentsection]
\paragraph{FMEA basic concept.}
FMEA~\cite{safeware}[pp.341-344] is widely used, and proof of its use is a mandatory legal requirement
for a large proportion of safety critical products sold in the European Union.
The acronym FMEA can be expanded as follows:
\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 its-self.
\end{itemize}
%
FMEA is a broad term; it could mean anything from an informal check on how FMEA is a broad term; it could mean anything from an informal check on how
how failures could affect some equipment in an initial brain-storming session how failures could affect some equipment in an initial brain-storming session
in product design, to formal submission as part of safety critical certification. in product design, to formal submission as part of safety critical certification.
@ -67,21 +58,11 @@ the effectiveness of FMEA.
% % \item Analysis % % \item Analysis
% % \end{itemize} % % \end{itemize}
\clearpage %\clearpage
\paragraph{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}
FMEA is a procedure based on the low level components of a system, and an example FMEA is a procedure which starts with the failure modes of the low level components of a system, an example
analysis will serve to demonstrate it in practise. analysis will serve to demonstrate it in practise.
\paragraph{ FMEA Example: Milli-volt reader} \paragraph{ FMEA Example: Milli-volt reader}
@ -148,7 +129,7 @@ approach in looking for system failures.
\section{Theoretical Concepts in FMEA} \section{Theoretical Concepts in FMEA}
\subsection{The unacceptability of a single component failure causing a catastrophe} \paragraph{The unacceptability of a single component failure causing a catastrophe}
FMEA, due to its inductive bottom-up approach, is very good FMEA, due to its inductive bottom-up approach, is very good
at finding potential single component failures that could have catastrophic implications. at finding potential single component failures that could have catastrophic implications.
@ -157,7 +138,7 @@ for unearthing these failure scenarios.
It is less useful for determining catastrophic events for multiple It is less useful for determining catastrophic events for multiple
simultaneous\footnote{Multiple simultaneous failures are taken to mean failure that occur within the same detection period.} failures. simultaneous\footnote{Multiple simultaneous failures are taken to mean failure that occur within the same detection period.} failures.
\subsection{Impracticality of Field Data for modern systems} \paragraph{Impracticality of Field Data for modern systems}
Modern electronic components, are generally very reliable, and the systems built from them Modern electronic components, are generally very reliable, and the systems built from them
are thus very reliable too. Reliable field data on failures will, therefore be sparse. are thus very reliable too. Reliable field data on failures will, therefore be sparse.
@ -172,7 +153,25 @@ However, we can use FMEA (more specifically the FMEDA variant, see section~\ref{
working from known component failure rates, to obtain working from known component failure rates, to obtain
statistical estimates of the equipment reliability. statistical estimates of the equipment reliability.
\paragraph{Forward and backward searches}
A forward search starts with possible failure causes
and uses logic and reasoning to determine system level outcomes.
Forward search types of fault analysis is said to be `inductive'.
A backward search starts with (undesirable) system level events
works back down to potential causes using de-composition of
of the system and logic.
FMEA based methodologies are forward searches\cite{Lutz:1997:RAU:590564.590572} and top down
methodologies such as FTA~\cite{nucfta,nasafta}
Forward search types of fault analysis is said to be `deductive'.
\paragraph{Reasoning distance}
A reasoning distance is the number of stages of logic and reasoning
required to map a failure cause to its potential outcomes.
%.... general concept... simple ideas about how complex a
%failure analysis is the more modules and components are involved
% cite for forward and backward search related to safety critical software
%{sfmeaforwardbackward}
\subsection{FMEA and the State Explosion Problem} \subsection{FMEA and the State Explosion Problem}
\paragraph{Rigorous Single Failure FMEA} \paragraph{Rigorous Single Failure FMEA}
@ -369,7 +368,7 @@ for a project manager.
\item \textbf{Guidelines} To system architectures and development processes \item \textbf{Guidelines} To system architectures and development processes
\end{itemize} \end{itemize}
FMEDA is the methodology behind statistical (safety integrity level) FMEDA is the fundamental methodology of the statistical (safety integrity level)
type standards (EN61508/IOC5108). type standards (EN61508/IOC5108).
It provides a statistical overall level of safety It provides a statistical overall level of safety
and allows diagnostic mitigation for self checking etc. and allows diagnostic mitigation for self checking etc.
@ -386,12 +385,6 @@ For software it provides procedural quality guidelines and constraints (such as
programming languages and/or features. programming languages and/or features.
\subsection{ FMEDA - Failure Modes Effects and Diagnostic Analysis} \subsection{ FMEDA - Failure Modes Effects and Diagnostic Analysis}
\label{sec:FMEDA} \label{sec:FMEDA}
\textbf{Failure Mode Classifications in FMEDA.} \textbf{Failure Mode Classifications in FMEDA.}

1
submission_thesis/CH4_FMMD/copy.tex
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@ -725,6 +725,7 @@ as a building block for other {\fgs} in the same way as we used the base compone
% %
\paragraph{Failure Mode Analysis of a generic op-amp.} \paragraph{Failure Mode Analysis of a generic op-amp.}
% %
\label{sec:opamp_fms}
%\clearpage %\clearpage
Let us now consider the op-amp as a {\bc}. According to Let us now consider the op-amp as a {\bc}. According to
FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes %(with assigned probabilities): FMD-91~\cite{fmd91}[3-116] an op amp may have the following failure modes %(with assigned probabilities):

84
submission_thesis/CH5_Examples/copy.tex
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@ -606,15 +606,15 @@ Both approaches are followed in the next two sub-sections.
\subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}} \subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}}
We cannot simply re-use the $PD$ from section~\ref{subsec:potdiv}, not simply because We cannot simply re-use the {\dc} $PD$ from section~\ref{subsec:potdiv}, not just because
the potential divider is inverted, but, in addition the the potential divider is inverted, but in addition, it facilitates the
output feedback forms a current balance with the input signal. %---that potential divider would only be valid if the input signal were negative. output feedback forming a current balance with the input signal. %---that potential divider would only be valid if the input signal were negative.
%We want if possible to have detectable errors. %We want if possible to have detectable errors.
%HIGH and LOW failures are more observable than the more generic failure modes such as `OUTOFRANGE'. %HIGH and LOW failures are more observable than the more generic failure modes such as `OUTOFRANGE'.
%If we can refine the operational states of the functional group, we can obtain clearer %If we can refine the operational states of the functional group, we can obtain clearer
%symptoms. %symptoms.
Were the input to be guaranteed % the input will only be Were the input to be guaranteed % the input will only be
positive, we could the potential divider (see table~\ref{tbl:pdneg}). positive, we can view it as an inverted potential divider (see table~\ref{tbl:pdneg}).
\begin{table}[h+] \begin{table}[h+]
\caption{Inverted Potential divider: Single failure analysis} \caption{Inverted Potential divider: Single failure analysis}
@ -1010,7 +1010,7 @@ We begin by identifying functional groups from the components in the circuit.
Looking first at the components in the signal path, we notice that we have a non-inverting Looking first at the components in the signal path, we notice that we have a non-inverting
amplifier formed by R1,R2 and IC1. In fact apart from being amplifier formed by R1,R2 and IC1. In fact apart from being
inverted visually on the schematic it is identical to the example inverted visually on the schematic, it is identical to the example
used in section~\ref{sec:noninvamp} (the first practical example used to demonstrate FMMD). used in section~\ref{sec:noninvamp} (the first practical example used to demonstrate FMMD).
We thus re-use this and can express the failure modes for it thus: We thus re-use this and can express the failure modes for it thus:
@ -1129,9 +1129,9 @@ Here it is more intuitive to model the resistors not as a potential divider, but
\end{table} \end{table}
Collecting the symptoms we can see that this amplifier fails Collecting the symptoms we can see that this amplifier fails
in 4 ways %$\{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput\}$. in four ways. %$\{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput\}$.
%We can now %We can now
we create a derived component, $SEC\_AMP$, to represent it We create a derived component, $SEC\_AMP$, to represent it
with failure modes described by: with failure modes described by:
$$ fm(SEC\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} .$$ $$ fm(SEC\_AMP) = \{ AMPHigh, AMPLow, LowPass, AMPIncorrectOutput \} .$$
@ -1763,7 +1763,7 @@ Thus, $BUFF45$ is a {\dc} representing an actively buffered $45^{\circ}$ phase s
From the block circuit diagram (figure~\ref{fig:circuit3}), we see that there are three From the block circuit diagram (figure~\ref{fig:circuit3}), we see that there are three
$45^{\circ}$ phase shifter circuits in series. Together these apply a $135^{\circ}$ phase shift to the signal. $45^{\circ}$ phase shifter circuits in series. Together these apply a $135^{\circ}$ phase shift to the signal.
% %
We use this property to model a higher level {\dc}, that of a 135 degree phase shifter. We use this property to model a higher level {\dc}, that of a $135^{\circ}$ phase shifter.
% %
The three $BUFF45$ {\dcs} form a The three $BUFF45$ {\dcs} form a
functional group which is analysed in table~\ref{tbl:phs135buffered}. functional group which is analysed in table~\ref{tbl:phs135buffered}.
@ -1820,7 +1820,7 @@ Finally we form a final {\fg} with $PHS135BUFFERED$ and $PHS225AMP$,
\end{tabular} \end{tabular}
\end{table} \end{table}
% %
Collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes: collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes:
$$ $$
fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift, fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift,
$$ $$
@ -1968,7 +1968,7 @@ to analyse in the future.
%is higher, by an order of $O(N^2)$. %is higher, by an order of $O(N^2)$.
Smaller functional groups mean less by-hand checks are required. Smaller functional groups mean less by-hand checks are required.
It also means a more finely grained model. This means that It also means a more finely grained model. This means that
there are more {\dcs} and this increases the potential for re-use of pre-analysed {\dcs}. there are more {\dcs} and therefore increases the potential for re-use of pre-analysed {\dcs}.
% HTR The more we can modularise, the more we decimate the $O(N^2)$ effect % HTR The more we can modularise, the more we decimate the $O(N^2)$ effect
% HTR of complexity comparison. % HTR of complexity comparison.
% %
@ -2046,7 +2046,8 @@ of the input voltage (i.e. the value of the sum of 1's and 0's is proportional t
The parts for the \sd are a mixture of analogue (resistors, capacitors, OpAmps) and digital The parts for the \sd are a mixture of analogue (resistors, capacitors, OpAmps) and digital
(D type flip flop, and a digital clock). We examine the failure modes of all components in this circuit below. (D type flip flop, and a digital clock). We examine the failure modes of all components in this circuit below.
% %
IC1,2 and 3 are all OpAmps and we have failure modes from section~\ref{sec:opamp_fms}. IC1,IC2 and IC3 are all OpAmps and we have failure modes for this component type
from section~\ref{sec:opamp_fms}.
% %
$$ fm(OPAMP) = \{ HIGH, LOW, NOOP, LOW\_SLEW \} $$ $$ fm(OPAMP) = \{ HIGH, LOW, NOOP, LOW\_SLEW \} $$
% %
@ -2146,36 +2147,29 @@ It therefore has the failure modes of an Op-amp.
\begin{table}[h+] \begin{table}[h+]
\center \center
% \center % \center
\caption{ High Impedance Signal Buffer : Failure Mode Effects Analysis} % title of Table \caption{ High Impedance Signal Buffer : Failure Mode Effects Analysis} % title of Table
This is an OpAmp in a signal buffer configuration.
As it is performing one particular function
we my consider it as a derived component, that of a High Impedance Signal Buffer (HISB).
\begin{tabular}{|| l | l | c | c | l ||} \hline \begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{failure result} & & \textbf{Symptom} \\ %\textbf{Failure Scenario} & & \textbf{failure result} & & \textbf{Symptom} \\
% & & & & \\ % & & & & \\
\textbf{Failure} & & \textbf{$HISB$ } & & \textbf{Derived Component} \\ \textbf{Failure} & & \textbf{$HISB$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\ \textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline\hline \hline\hline
FS1: $IC2$ $HIGH$ & & output perm. high & & HIGH \\ FS1: $IC2$ $HIGH$ & & output perm. high & & HIGH \\
FS2: $IC2$ $LOW$ & & output perm. low & & LOW \\ FS2: $IC2$ $LOW$ & & output perm. low & & LOW \\
FS3: $IC2$ $NOOP$ & & no current to output & & $NOOP$ \\ FS3: $IC2$ $NOOP$ & & no current to output & & $NOOP$ \\
FS4: $IC2$ $LOW\_SLEW$ & & delay signal & & $LOW\_{SLEW}$ \\ \hline FS4: $IC2$ $LOW\_SLEW$ & & delay signal & & $LOW\_{SLEW}$ \\ \hline
\end{tabular} \end{tabular}
\end{table} \end{table}
% \hline % \hline
% %
% \end{tabular} % \end{tabular}
% \end{table} % \end{table}
We create the {\dc} $HISB$ and its failure mode may be stated as $$fm(HISB) = \{HIGH, LOW, NOOP, LOW_{SLEW} \}$$. This is an OpAmp in a signal buffer configuration.
As it is performing one particular function
we my consider it as a derived component, that of a High Impedance Signal Buffer (HISB).
%
We create the {\dc} $HISB$ and its failure mode may be stated as $$fm(HISB) = \{HIGH, LOW, NOOP, LOW_{SLEW} \}.$$
\subsubsection{Digital level to analogue level conversion ($DL2AL$).} \subsubsection{Digital level to analogue level conversion ($DL2AL$).}
The integrator is implemented in digital electronics, but the output from the D type flip flop is a digital signal. The integrator is implemented in digital electronics, but the output from the D type flip flop is a digital signal.
@ -2186,8 +2180,9 @@ to the inverting input of IC3.
\paragraph{Potential divider Formed by R3,R4.} \paragraph{Potential divider Formed by R3,R4.}
We re-use the analysis from table~\ref{tbl:pdfmea}, and use the derived component $PD$ We re-use the analysis from table~\ref{tbl:pdfmea}, and use the derived component $PD$
to represent the potential divider formed by R3 and R4. Because PD is a derived component, we can denote this to represent the potential divider formed by R3 and R4.
by super-scripting it with its abstraction level of 1, thus $PD$. %Because PD is a derived component, we can denote this
%by super-scripting it with its abstraction level of 1, thus $PD$.
$$ $$
fm(PD) = \{ HIGH, LOW \}. fm(PD) = \{ HIGH, LOW \}.
$$ $$
@ -2301,7 +2296,7 @@ have created our first {\dcs}. %and can now take stock of the situation
These are: These are:
\begin{itemize} \begin{itemize}
\item SUMJINT --- A summing junction and integrator, \item SUMJINT --- A summing junction and integrator,
\item HISB --- A High impedance buffer, \item HISB --- A high impedance buffer,
\item DIGITALBUFF --- A one bit digital buffer, \item DIGITALBUFF --- A one bit digital buffer,
\item DL2AL --- A digital to analog level converter, \item DL2AL --- A digital to analog level converter,
\item DIGBUF --- A digital one bit buffer/memory. \item DIGBUF --- A digital one bit buffer/memory.
@ -2313,7 +2308,7 @@ We now use these {\dcs} to create higher level {\fgs}.
We represent this We represent this
in the Euler diagram in figure~\ref{fig:eulersd}. in the Euler diagram in figure~\ref{fig:eulersd}.
The next stage is to create {\fgs} from these initial {\dcs} The next stage is to create {\fgs} from these initial {\dcs}
and make a complete failure mode mode for the {\sd}. and make a complete failure mode for the {\sd}.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
@ -2468,8 +2463,8 @@ We analyse the buffered {\sd} circuit in table~\ref{tbl:sdadc}.
\end{tabular} \end{tabular}
\end{table} \end{table}
%\clearpage %\clearpage
We now collect the symptoms for the \sd $ \; We now collect the symptoms for the \sd
\{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$. $$ \; \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}.$$
We can now create a {\dc} to represent the analogue to digital converter, $SADC^4$. We can now create a {\dc} to represent the analogue to digital converter, $SADC^4$.
$$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$$ $$fm(SSDADC) = \{OUTPUT\_OUT\_OF\_RANGE, OUTPUT\_INCORRECT\}$$
We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}. We now show the final {\dc} hierarchy in figure~\ref{fig:eulersdfinal}.
@ -2583,15 +2578,15 @@ of components, {\fgs} and symptoms of failure for a functional group.
A programmatic function has similarities with a {\fg} as defined by the FMMD process. A programmatic function has similarities with a {\fg} as defined by the FMMD process.
% %
An FMMD {\fg} is placed into a hierarchy. An FMMD {\fg} is placed into a hierarchy.
A Software function is placed into a hierarchy, that of its call-tree. A software function is placed into a hierarchy, that of its call-tree.
A software function typically calls other functions and uses data sources via hardware interaction, which could be viewed as its `components'. A software function typically calls other functions and uses data sources via hardware interaction, which could be viewed as its `components'.
It has outputs, i.e. it can perform actions It has outputs, i.e. it can perform actions
on data or hardware on data or hardware
which will be used by functions that may call it. which will be used by functions that may call it.
%
We can map a software function to a {\fg} in FMMD. Its failure modes We can map a software function to a {\fg} in FMMD. Its failure modes
are the failure modes of the software components (other functions it calls) are the failure modes of the software components (other functions it calls)
and the hardware its reads values from. and the hardware from which it reads values.
Its outputs are the data it changes, or the hardware actions it performs. Its outputs are the data it changes, or the hardware actions it performs.
%% %%
%% Talk about how software specification will often say how hardware %% Talk about how software specification will often say how hardware
@ -2631,7 +2626,7 @@ and the subsequent hierarchy. With software already written, that hierarchy is f
Software written for safety critical systems is usually constrained to Software written for safety critical systems is usually constrained to
be modular~\cite{en61508}[3] and non recursive~\cite{misra}[15.2]. %{iec61511}. be modular~\cite{en61508}[3] and non recursive~\cite{misra}[15.2]. %{iec61511}.
Because of this we can assume direct call trees~\footnote{A typical embedded system Because of this we can assume direct call trees~\footnote{A typical embedded system
will have a run time call tree, and interrupt driven call tress}. Functions call functions will have a run time call tree, and (possibly multiple) interrupt sourced call tress.}. Functions call functions
from the top down and eventually call the lowest level library or IO from the top down and eventually call the lowest level library or IO
functions that interact with hardware/electronics. functions that interact with hardware/electronics.
@ -2691,8 +2686,8 @@ that can alter the accuracy of the signal.
% %
%This circuit has many advantages for safety. %This circuit has many advantages for safety.
If the signal becomes disconnected If the signal becomes disconnected
it reads $0mA$ at the receiving end: as this is outside the {\ft} range it reads $0mA$ at the receiving end: as this is outside the {\ft} range,
it is easy to detect as an error condition rather than an incorrect value. it is easily detectable as an error condition rather than an incorrect value.
% %
Should the driving electronics go wrong at the source end, it will usually Should the driving electronics go wrong at the source end, it will usually
supply far too little or far too much current, also making error conditions easy to detect. supply far too little or far too much current, also making error conditions easy to detect.
@ -2717,7 +2712,7 @@ The diagram in figure~\ref{fig:ftcontext}, shows some equipment which is sending
signal to a micro-controller system. signal to a micro-controller system.
The signal is locally driven over a load resistor, and then read into the micro-controller via The signal is locally driven over a load resistor, and then read into the micro-controller via
an ADC and its multiplexer. an ADC and its multiplexer.
With the voltage detected at the ADC the multiplexer can read the intended quantitative With the voltage determined at the ADC we read the intended quantitative
value from the external equipment. value from the external equipment.
\subsection{Simple Software Example} \subsection{Simple Software Example}
@ -2730,7 +2725,7 @@ Let us assume the {\ft} detection is via a \ohms{220} resistor, and that we read
from an ADC into the software. from an ADC into the software.
Let us define any value outside the 4mA to 20mA range as an error condition. Let us define any value outside the 4mA to 20mA range as an error condition.
% %
As a voltage, we use ohms law~\cite{aoe} to determine the voltage ranges: $V=IR$, $0.004A * \ohms{220} = 0.88V$ As we read a voltage voltage, we use Ohms law~\cite{aoe} to determine the mA current detected: $V=IR$, $0.004A * \ohms{220} = 0.88V$
and $0.020A * \ohms{220} = 4.4V$. and $0.020A * \ohms{220} = 4.4V$.
% %
Our acceptable voltage range is therefore Our acceptable voltage range is therefore
@ -2795,9 +2790,9 @@ We now look at the function called by \textbf{read\_4\_20\_input}, \textbf{read\
voltage for a given ADC channel. voltage for a given ADC channel.
% %
This function This function
deals directly with the hardware in the micro-controller that we are running the software on. deals directly with the hardware in the micro-controller on which the software is running. %software on.
% %
Its job is to select the correct channel (ADC multiplexer) and then to initiate a The software's job is to select the correct channel (ADC multiplexer) and then to initiate a
conversion by setting an ADC 'go' bit (see code sample in figure~\ref{fig:code_read_ADC}). conversion by setting an ADC 'go' bit (see code sample in figure~\ref{fig:code_read_ADC}).
% %
It takes the raw ADC reading and converts it into a It takes the raw ADC reading and converts it into a
@ -2874,7 +2869,7 @@ We now have a very simple software structure, a call tree, shown in figure~\ref{
\end{figure} \end{figure}
This software is above the hardware in the conceptual call tree---from a programmatic perspective---%in software terms---the This software is above the hardware in the conceptual call tree---from a programmatic perspective---%in software terms---the
software is reading values from the `lower~level' electronics. the software is reading values from the `lower~level' electronics.
% %
FMEA is always a bottom-up process and so we must begin with this hardware. FMEA is always a bottom-up process and so we must begin with this hardware.
% %
@ -3127,7 +3122,7 @@ The postcondition for the function $read\_4\_20\_input$, {\em /* ensure: value i
% \paragraph{Final Functional Group} % \paragraph{Final Functional Group}
For single failures these are the two ways in which this function For single failures these are the two ways in which this function
can fail. An $OUT\_OF\_RANGE$ will be flagged by the error flag variable. can fail. An $OUT\_OF\_RANGE$ will be flagged by the error flag variable.
The $VAL\_ERR$ will simply mean that the value read is simply wrong. The $VAL\_ERR$ will simply mean that the value read is incorrect.
We can finally make a {\dc} to represent a failure mode model for our function $read\_4\_20\_input$ thus: We can finally make a {\dc} to represent a failure mode model for our function $read\_4\_20\_input$ thus:
@ -3165,8 +3160,9 @@ as a hierarchical diagram, see figure~\ref{fig:eulerswhw}. % see figure~\ref{fig
We can represent the hierarchy in figure~\ref{fig:hd} algebraically, using the `$\derivec$' function We can represent %the hierarchy in figure~\ref{fig:hd} algebraically,
using the groups as intermediate stages: the analysis hierarchy algebraically using the `$\derivec$' function:
%using the groups as intermediate stages:
\begin{eqnarray*} \begin{eqnarray*}
G_1 &=& \{R,ADC\} \\ G_1 &=& \{R,ADC\} \\
CMATV &=& \;\derivec (G_1) \\ CMATV &=& \;\derivec (G_1) \\
@ -3207,7 +3203,7 @@ it stretches from the component failure mode to the top---or---system level fail
For this reason applying traditional FMEA to software stretches For this reason applying traditional FMEA to software stretches
the reasoning distance even further. This is exacerbated by the fact that traditional SFMEA is the reasoning distance even further. This is exacerbated by the fact that traditional SFMEA is
performed separately from HFMEA~\cite{sfmea,sfmeaa}, additionally even the software/hardware performed separately from HFMEA~\cite{sfmea,sfmeaa}, additionally even the software/hardware
interfacing is treated as a seperate FMEA task~\cite{sfmeainterface,embedsfmea,procsfmea} interfacing is treated as a separate FMEA task~\cite{sfmeainterface,embedsfmea,procsfmea}
We now have a {\dc} for a {\ft} input in software. We now have a {\dc} for a {\ft} input in software.