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Working through Chris Garret comments on CH5

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4
related_papers_books/view_all_pdfs.sh Executable file
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@ -0,0 +1,4 @@
fred=`ls *.pdf`
for l in $fred; do evince $l || acroread $l; echo $l; done

13
submission_thesis/CH2_FMEA/copy.tex
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@ -30,6 +30,19 @@ 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
in product design, to formal submission as part of safety critical certification.
%
FMEA is always performed in context. That is, the equipment is always analysed for a particular purpose
and in a given environment. An `O' ring for instance can fail by leaking
but if fitted to a water seal on a garden hose, the system level failure is a
would be a slight leak at the tap outside the house.
Applied to the rocket engine on a space shuttle the failure mode
is a catastrophic fire and destruction of the spacecraft~\cite{challenger}.
%
At a lower level, consider a resistor and capacitor forming a potential divider to ground.
This could be considered a low pass filter in some electrical environments,
but for fixed frequencies the same circuit could be used as a phase changer.
The failure modes of the latter, could be `no~signal' and `all~pass',
but when used as a phase changer, would be `no~signal' and `no~phase' change.
This chapter describes basic concepts of FMEA, uses a simple example to
demonstrate a single FMEA analysis stage, describes the four main variants of FMEA in use today
and explores some concepts with which we can discuss and evaluate

362
submission_thesis/CH5_Examples/copy.tex
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@ -32,34 +32,47 @@ a variety of typical embedded system components including analogue/digital and e
% % we are using for our particular project).
%
%This is followed by several example FMMD analyses,
The first applies FMMD to a common configuration of
the inverting amplifier (see section~\ref{sec:invamp}) using
an op-amp and two resistors; this demonstrates how the re-use of the potential divider from section~\ref{subsec:potdiv}.
The inverting amplifier is analysed again, but this time with a different
\begin{itemize}
\item The first example applies FMMD to an operational amplifier inverting amplifier (see section~\ref{sec:invamp})
%using an op-amp and two resistors;
this demonstrates how the re-use of a potential divider {\dc} from section~\ref{subsec:potdiv}.
This inverting amplifier is analysed again, but this time with a different
composition of {\fgs}. The two approaches, i.e. choice of membership for {\fgs}, are then discussed.
%~\ref{sec:chap4}
%can be re-used. %, but with provisos.
%
%The first
%(see section~\ref{sec:diffamp})
Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used
\item Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used
to create a differencing amplifier.
Building on the two approaches from section~\ref{sec:invamp}, re-use of the non-inverting amplifier {\dc} from section~\ref{sec:invamp}
is discussed in the context of this circuit,
where its re-use is appropriate in the first stage and
not in the second.
%
Section~\ref{sec:fivepolelp} analyses a Sallen-Key based five pole low pass filter.
\item Section~\ref{sec:fivepolelp} analyses a Sallen-Key based five pole low pass filter.
This demonstrates re-use the first Sallen-Key analysis, %encountered as a {\dc}
increasing test effeciency. %saving time and effort for the analyst.
increasing test efficiency. This example also serves to show a deep hierarchy of {\dcs}.
\item Section~\ref{sec:bubba} shows FMMD applied to a
loop topology---using a `Bubba' oscillator---demonstrating how FMMD id different to fault diagnosis techniques.
%which uses
%four op-amp stages with supporting components.
Two analysis strategies are employed, one using
initially identified {\fgs} and the second using a more complex hierarchy of {\fgs} and {\dcs}, showing
that a finer grained/more de-composed approach offers more re-use possibilities in future analysis tasks.
\item Section~\ref{sec:sigmadelta} demonstrates FMMD can be applied to mixed anal;ogue and digital circuitry
using a sigma delta ADC.
%shows FMMD analysing the sigma delta
%analogue to digital converter---again with a circular signal path---which operates on both
%analogue and digital signals.
\end{itemize}
%~\ref{sec:chap4}
%can be re-used. %, but with provisos.
%
Section~\ref{sec:bubba} shows FMMD applied to a circular circuit topology---the `Bubba' oscillator---which uses
four op-amp stages with supporting components. Two analysis stategies are employed, one using
initially identified {\fgs} and the second using a more complex hierarchy of {\fgs} and {\dcs}.
%The first
%(see section~\ref{sec:diffamp})
%
Section~\ref{sec:sigmadelta} shows FMMD analysing the sigma delta
analogue to digital converter---again with a circular signal path---which operates on both
analogue and digital signals.
%
%
%
% Moving Pt100 to metrics
%
@ -67,7 +80,7 @@ analogue and digital signals.
%failure mode classification % analysis for top level events traced back to {\bc} failure modes
%and the analysis of double simultaneous failure modes.
%
Finally section~\ref{sec:elecsw} demonstrates FMMD analysis of a combined electronic and software system.
% Now in CHAPTER 6: Finally section~\ref{sec:elecsw} demonstrates FMMD analysis of a combined electronic and software system.
% \section{Basic Concepts Of FMMD}
%
@ -599,7 +612,7 @@ Finally section~\ref{sec:elecsw} demonstrates FMMD analysis of a combined electr
%This configuration is interesting from methodology pers.
There are two obvious ways in which we can model this circuit:
One is to do this in two stages, by considering the gain resistors to be an inverted potential divider
One is to do this in two stages, by considering the gain resistors to be a potential divider
and then combining it with the OPAMP failure mode model.
The second is to place all three components in one {\fg}.
Both approaches are followed in the next two sub-sections.
@ -607,14 +620,22 @@ Both approaches are followed in the next two sub-sections.
\subsection{First Approach: Inverting OPAMP using a Potential Divider {\dc}}
We cannot simply re-use the {\dc} $PD$ from section~\ref{subsec:potdiv}, not just because
the potential divider is inverted, but in addition, it facilitates the
output feedback forming a current balance with the input signal. %---that potential divider would only be valid if the input signal were negative.
the potential divider is floating. That is the polarity of
the R2 side of the potential divider is determined by the output from the op-amp.
The circuit schematic stipulates that the input is positive.
What we have then, in normal operation, is an inverted potential divider.
%, but in addition, it facilitates the
%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.
%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
%symptoms.
Were the input to be guaranteed % the input will only be
positive, we can view it as an inverted potential divider (see table~\ref{tbl:pdneg}).
%Were the input to be guaranteed % the input will only be
We can therefore view it as an inverted potential divider
and analyse it as such, see table~\ref{tbl:pdneg}.
We assume a valid range for the output value of this circuit.
Thus negative or low voltages can be considered as LOW
and voltages higher than this range considered as HIGH.
\begin{table}[h+]
\caption{Inverted Potential divider: Single failure analysis}
@ -807,9 +828,11 @@ We can now form a {\fg} from the OpAmp and the $INVPD$
\subsection{Second Approach: Inverting OpAmp analysing with three components in one larger {\fg}}
\label{subsec:invamp2}
Here we analyse the same problem without using an intermediate $PD$
derived component.
derived component. We would have to do this
if the input voltage was not constrained to being positive.
This concern is re-visited in the differencing amplifier example in the next section.
%We can use this for a more general case, because we can examine the
%effects on the circuit for each operational case (i.e. input +ve
@ -882,6 +905,13 @@ from the pre-analysed inverted potential divider against the OpAmp.
Both analysis strategies obtained the same failure modes for the
inverting amplifier (i.e. the same failure modes for the {\dc} INVAMP).
\subsection{Conclusion}
All FMEA is performed in the context of the environment and functionality of the enitity
under analysis.
This example shows that for the condition where the input voltage
is constrained to being positive, we can apply two levels of de-composition.
For the unconstrained case, we have to consider all three components as one larger {\fg}.
% METRICS The complexity comparison figures
% METRICS bear this out. For the two stage analysis, using equation~\ref{eqn:rd2}, we obtain a CC of $4.(2-1)+6.(2-1)=10$
% METRICS and for the second analysis a CC of $8.(3-2)=16$.
@ -914,8 +944,9 @@ The circuit in figure~\ref{fig:circuit1} amplifies the difference between
the input voltages $+V1$ and $+V2$.
The circuit is configured so that both inputs use the non-inverting,
and thus high impedance inputs, meaning that they will not
electrically over-load and/or unduly influence
the sensors or circuitry supplying the voltage signals used for measurement.
electrically load the previous stage.
%over-load and/or unduly influence
%the sensors or circuitry supplying the voltage signals used for measurement.
It would be desirable to represent this circuit as a {\dc} called say $DiffAMP$.
We begin by identifying functional groups from the components in the circuit.
@ -1090,7 +1121,7 @@ consisting of $R3,R4,IC2$.
This is in exactly the same configuration as the first amplifier, but it is being fed by the first amplifier.
The first amplifier was grounded and received as input `+V1' (presumably
a positive voltage).
This means the junction of R1 R3 is always +ve.
This means the junction of R2 R3 is always +ve.
This means the input voltage `+V2' could be lower than this.
This means R3 R4 is not a fixed potential divider, with R4 being on the positive side.
It could be on either polarity (i.e. the other way around R4 could be the negative side).
@ -1163,6 +1194,9 @@ two derived components of the type $NI\_AMP$ and $SEC\_AMP$.
\hline
TC1: $NI\_AMP$ AMPHigh & IC2 output driven high & DiffAMPLow \\
TC2: $NI\_AMP$ AMPLow & IC2 output driven low & DiffAMPHigh \\
% Two test cases above, yes the voltage from the second op-amp will influence
% this, BUT we are considering single failure at the moment... 17NOV2012
TC3: $NI\_AMP$ LowPass & IC2 output with lag & DiffAMP\_LP \\ \hline
TC4: $SEC\_AMP$ AMPHigh & Diff amplifier high & DiffAMPHigh\\
TC5: $SEC\_AMP$ AMPLow & Diff amplifier low & DiffAMPLow \\
@ -1211,9 +1245,14 @@ the un-observability and would likely prompt re-design of this
circuit\footnote{A typical way to solve an un-observability such as this is
to periodically switch in test signals in place of the input signal.}.
\subsection{Conclusion}
This example shows a three stages hierarchy, and a graph tracing the base~component failure modes to the
top level event. It also re-visits the the decisions about membership of {\fgs}, due to the context
of the circuit raised in section~\ref{subsec:invamp2}.
\clearpage
\section{Five Pole Low Pass Filer, using two Sallen~Key stages.}
\section{Five Pole Low Pass Filter, using two Sallen~Key stages.}
\label{sec:fivepolelp}
\begin{figure}[h]
@ -1230,11 +1269,11 @@ to periodically switch in test signals in place of the input signal.}.
The circuit in figure~\ref{fig:circuit2} shows a five pole low pass filter.
Starting at the input, we have a first order low pass filter buffered by an op-amp,
the output of this is passed to a Sallen~Key~\cite{aoe}[p.267]~\cite{electronicssysapproach}[p.288] second order low-pass filter.
The output of this is passed into another Sallen~Key filter -- which although it may have different values
for its resistors/capacitors and thus have a different frequency response -- is identical from a failure mode perspective.
The output of this is passed into another Sallen~Key filter. % -- which although it may have different values
%for its resistors/capacitors and thus have a different frequency response -- is identical from a failure mode perspective.
Thus we can analyse the first Sallen~Key low pass filter and re-use it
for the second stage
(avoiding the repeat work that would have had to be performed using traditional FMEA).
(avoiding repeat work that would have had to be performed using traditional FMEA).
\begin{figure}[h]
@ -1251,9 +1290,9 @@ for the second stage
We begin with the first order low pass filter formed by $R10$ and $C10$.
%
This configuration (or {\fg}) is very commonly
used in electronics to remove unwanted high frequencies/interference
from a signal; here it is being used as a first stage of
a more sophisticated low pass filter.
used %in electronics
to remove unwanted high frequencies/noise
from a signal. %; here it is being used as a first stage of a more sophisticated low pass filter.
%
R10 and C10 act as a potential divider, with the crucial difference between a purely resistive potential divider being
that the impedance of the capacitor is lower for higher frequencies.
@ -1280,10 +1319,10 @@ We analyse the first order low pass filter in table~\ref{tbl:firstorderlp}.\\
\textbf{cause} & \textbf{Low Pass Filter} & \textbf{Failure Mode} \\
\hline
FS1: R10 SHORT & $No Filtering$ & $LPnofilter$ \\ \hline
FS1: R10 SHORT & $No Filtering$ & $LPallpass$ \\ \hline
FS2: R10 OPEN & $No Signal$ & $LPnosignal$ \\ \hline
FS3: C10 SHORT & $No Signal$ & $LPnosignal$ \\ \hline
FS4: C10 OPEN & $No Filtering$ & $LPnofilter$ \\ \hline
FS4: C10 OPEN & $No Filtering$ & $LPallpass$ \\ \hline
\hline
@ -1320,7 +1359,7 @@ from the $FirstOrderLP$ and the OpAmp component.
TC2: $OPAMP$ LatchDown & Output Low & LP1Low \\
TC3: $OPAMP$ No Operation & Output Low & LP1Low \\
TC4: $OPAMP$ Low Slew & Unwanted Low pass filtering & LP1filterincorrect \\ \hline
TC5: $LPnofilter $ & No low pass filtering & LP1filterincorrect \\
TC5: $LPallpass $ & No low pass filtering & LP1filterincorrect \\
TC6: $LPnosignal $ & No input signal & LP1nosignal \\ \hline
\hline
@ -1436,7 +1475,8 @@ We represent the desired FMMD hierarchy in figure~\ref{fig:circuit2h}.
\centering
\includegraphics[width=400pt]{./CH5_Examples/eulerfivepole.png}
% eulerfivepole.png: 883x343 pixel, 72dpi, 31.15x12.10 cm, bb=0 0 883 343
\caption{Euler diagram showing {\fg}/{\dc} relationships for the analysis of the Five Pole Sallen Key filter.}
\caption{Euler diagram showing {\fg}/{\dc} relationships for the analysis of the Five Pole Sallen Key filter. This
is an abstract version of figure~\ref{fig:circuit2002_FIVEPOLE}}.
\label{fig:circuit2h}
\end{figure}
@ -1500,7 +1540,9 @@ three op-amp driven non-inverting low pass filter elements. It is not surprising
From a safety point of view, the failure modes $LOW$, $HIGH$ and $NO\_SIGNAL$
could be easily detected; the failure symptom $FilterIncorrect$ may be less observable.
\subsection{Conclusion}
This example shows the analysis of a linear signal path circuit with three easily identifiable
{\fgs} and re-use of the Sallen-Key {\dc}.
\clearpage
\section{Quad Op-Amp Oscillator}
@ -1522,9 +1564,13 @@ The circuit implements an oscillator using four 45 degree phase shifts, and an i
gain and the final 180 degrees of phase shift (making a total of 360). % degrees of phase shift).
The circuit provides two outputs with a quadrature phase relationship.
%
From a fault finding perspective this circuit cannot be de-composed because the whole circuit is enclosed within a feedback loop.
From a fault finding perspective this circuit cannot be de-composed
because the whole circuit is enclosed within a feedback loop,
hence a fault anywhere in the loop is likely to affect all stages.
%
However, this is not a problem for FMMD, as {\fgs} are readily identifiable.
The signal path is circular (its a positive feedback circuit) and most failures would simply cause the output to stop oscillating.
%
%The signal path is circular (its a positive feedback circuit) and most failures would simply cause the output to stop oscillating.
%The top level failure modes for the FMMD hierarchy bear this out.
%However, FMMD is a bottom -up analysis methodology and we can therefore still identify
%{\fgs} and apply analysis from a failure mode perspective.
@ -1533,7 +1579,7 @@ The signal path is circular (its a positive feedback circuit) and most failures
% METRICS ($4.4 +10 \times 2 = 36$) failure modes. Applying equation~\ref{eqn:rd2} gives a complexity comparison figure of $13.36=468$.
% METRICS We now create FMMD models and compare the complexity of FMMD and FMEA.
%
We start the FMMD process by determining {\fgs}.
%We start the FMMD process by determining {\fgs}.
We initially identify three types of functional groups, an inverting amplifier (analysed in section~\ref{fig:invamp}),
a 45 degree phase shifter (a {$10k\Omega$} resistor and a $10nF$ capacitor) and a non-inverting buffer
amplifier. We can name these $INVAMP$, $PHS45$ and $NIBUFF$ respectively.
@ -1565,30 +1611,9 @@ This consists of a resistor and a capacitor. We already have failure mode models
we now need to see how these failure modes would affect the phase shifter. Note that the circuit here
is identical to the low pass filter in circuit topology (see \ref{sec:lp}), but its intended use is different.
We have to analyse this circuit from the perspective of it being a {\em phase~shifter} not a {\em low~pass~filter}.
Our functional group for the phase shifter consists of a resistor and a capacitor, $G_0 = \{ R, C \}$.
Our functional group for the phase shifter consists of a resistor and a capacitor, $G_0 = \{ R, C \}$
(FMMD analysis details at section~\ref{detail:PHS45})
\begin{table}[h+]
\caption{PhaseShift: Failure Mode Effects Analysis: Single Faults} % title of Table
\label{tbl:firstorderlp}
\begin{tabular}{|| l | c | l ||} \hline
% \textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\
% & & \textbf{Low Pass Filter} & & \\
\textbf{Failure} & \textbf{$PHS45$ } & \textbf{Derived Component} \\
\textbf{cause} & \textbf{Effect} & \textbf{Failure Mode} \\
\hline
FS1: R SHORT & 0 degree's of phase shift & $0\_phaseshift$ \\
% 90 degree's of phase shift & & $90\_phaseshift$
FS2: R OPEN & No Signal & $nosignal$ \\ \hline
FS3: C SHORT & Grounded,No Signal & $nosignal$ \\
FS4: C OPEN & 0 degree's of phase shift & $0\_phaseshift$ \\ \hline
\hline
\end{tabular}
\end{table}
% PHS45
$$ fm (G_0) = \{ nosignal, 0\_phaseshift \} $$
@ -1641,67 +1666,9 @@ or in Euler diagram format as in figure~\ref{fig:bubbaeuler1}.
\label{fig:bubbaeuler1}
\end{figure}
%
\begin{table}[h+]
\caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table
\label{tbl:bubbalargefg}
\begin{tabular}{|| l | l | c | c | l ||} \hline
% \textbf{Failure Scenario} & & \textbf{Bubba} & & \textbf{Symptom} \\
% & & \textbf{Oscillator} & & \\
\textbf{Failure} & & \textbf{$BubbaOscillator$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS3: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS4: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS5: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS7: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS8: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
%FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS9: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS10: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS11: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS12: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS13: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS14: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS15: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS16: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS17: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS18: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS19: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS20: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS21: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\
FS22: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\
FS23: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\
FS24: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS1: $CAP_{10nF}$ $OPEN$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
% FS1: $CAP_{10nF}$ $SHORT$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
\hline
\end{tabular}
\end{table}
Collecting symptoms from table~\ref{tbl:bubbalargefg} we can show that for single failure modes, applying $fm$ to the bubba oscillator
The detail of the FMMD analysis can be found in section~\ref{detail:BUBOSC1}.
Applying $fm$ to the bubba oscillator
returns three failure modes,
%
$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$
@ -1794,33 +1761,9 @@ Finally we form a final {\fg} with $PHS135BUFFERED$ and $PHS225AMP$,
% model of the bubba oscillator.
% The proposed hierarchy is shown in figure~\ref{fig:poss2finalbubba}.
%
\begin{table}[h+]
\caption{BUFF45: Failure Mode Effects Analysis} % title of Table
\label{tbl:buff45}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{BUFF45} & & \textbf{Symptom} \\
% & & & & \\
\textbf{Failure} & & \textbf{$BUFF45$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $0\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
%FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $90\_phaseshift$ \\ \hline
FS3: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS4: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS5: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
\hline
\end{tabular}
\end{table}
%
collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes:
%
We analyse the {\fg} (see section~\ref{detail:BUFF45}) and create a derived component, $BUFF45$ which has the following failure modes:
$$
fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift,
$$
@ -1829,43 +1772,7 @@ $$
%
We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
%
\begin{table}[h+]
\caption{PHS135BUFFERED: Failure Mode Effects Analysis} % title of Table
\label{tbl:phs135buffered}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{PHS135 Buffered} & & \textbf{Symptom} \\
% & & & & \\
\textbf{Failure} & & \textbf{$PHS135BUFFERED$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
%FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
FS3: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS4: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
% FS6: $PHS45_2$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
FS5: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS6: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
% FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
\hline
\end{tabular}
\end{table}
%
%
Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes:
$$
fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal .\} % 180\_phaseshift,
$$
%
%
%$$ CC (PHS135BUFFERED) = 3 \times 2 = 6 $$
%
@ -1873,36 +1780,9 @@ $$
%
The $PHS225AMP$ consists of a $PHS45$, providing $45^{\circ}$ of phase shift, and an
$INVAMP$, providing $180^{\circ}$ giving a total of $225^{\circ}$.
Detailed FMMD analysis may be found in section~\ref{detail:PHS225AMP}.
%
\begin{table}[h+]
\caption{PHS225AMP: Failure Mode Effects Analysis} % title of Table
\label{tbl:phs225amp}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\
% & & \textbf{Oscillator} & & \\
\textbf{Failure} & & \textbf{$PHS225AMP$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $180\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
% FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $270\_phaseshift$ \\ \hline
FS3: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS4: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS5: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS6: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
\hline
\end{tabular}
\end{table}
%
Collecting symptoms from table~\ref{tbl:phs225amp}, we can create a derived component $PHS225AMP$ which has the following failure modes:
$$
fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift,
$$
%
%$$ CC(PHS225AMP) = 7 \times 1 $$
%
@ -1911,38 +1791,15 @@ The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\cir
%
%
To complete the analysis we now bring the derived components $PHS135BUFFERED$ and $PHS225AMP$ together
and perform FMEA with these, to obtain a model for the Bubba Oscillator.
%
\begin{table}[h+]
\caption{BUBBAOSC: Failure Mode Effects Analysis} % title of Table
\label{tbl:bubba2}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{BUBBAOSC} & & \textbf{Symptom} \\
% & & & & \\
\textbf{Failure} & & \textbf{$BUBBAOSC$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
%FS1: $PHS135BUFFERED$ $180\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
FS1: $PHS135BUFFERED$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
FS2: $PHS135BUFFERED$ $90\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ \hline
% FS4: $PHS225AMP$ $270\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
FS4: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\
FS5: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \hline
\hline
\end{tabular}
\end{table}
%
Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes:
and perform FMEA with these (see section~\ref{detail:BUBBAOSC}), to obtain a model for the Bubba Oscillator.
%Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes:
$$
fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc},
$$
%
%We could trace the DAGs here and ensure that both analysis strategies worked ok.....
%
@ -1972,6 +1829,17 @@ there are more {\dcs} and therefore increases the potential for re-use of pre-an
% HTR The more we can modularise, the more we decimate the $O(N^2)$ effect
% HTR of complexity comparison.
%
\subsection{conclusion}
With FMMD there is always a choice for the membership of {\fgs}.
This example has shown that the simple approach, identifying
initial {\fgs} and using them to build a large {\fg} to model the circuit
gives a valid result.
However, it involves a large reasoning distance, the final stage
having 24 failure modes to consider against each of the other seven {\dcs}.
A finer grained approach produces more potentially re-usable {\dcs} and
involves a several stages with lower reasoning distances.
\clearpage

262
submission_thesis/appendixes/detailed_analysis.tex Normal file
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@ -0,0 +1,262 @@
%%% Appendix for detailed workings out from CH5
\chapter{Detailed FMMD analyses}
\section{Bubba Oscillator FMMD analyses}
For clarity the detailed workings of the FMMD analysis stages in many of the examples
in chapter 5 have been moved here for reference.
\subsection{PHS45 Detailed Analysis}
\label{detail:PHS45}
\begin{table}[h+]
\caption{PhaseShift: Failure Mode Effects Analysis: Single Faults} % title of Table
\label{tbl:firstorderlp}
\begin{tabular}{|| l | c | l ||} \hline
% \textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\
% & & \textbf{Low Pass Filter} & & \\
\textbf{Failure} & \textbf{$PHS45$ } & \textbf{Derived Component} \\
\textbf{cause} & \textbf{Effect} & \textbf{Failure Mode} \\
\hline
FS1: R SHORT & 0 degree's of phase shift & $0\_phaseshift$ \\
% 90 degree's of phase shift & & $90\_phaseshift$
FS2: R OPEN & No Signal & $nosignal$ \\ \hline
FS3: C SHORT & Grounded,No Signal & $nosignal$ \\
FS4: C OPEN & 0 degree's of phase shift & $0\_phaseshift$ \\ \hline
\hline
\end{tabular}
\end{table}
% PHS45
\subsection{Bubba Oscillator: One Large Functional Group: Detailed Analysis}
\label{detail:BUBOSC1}
\begin{table}[h+]
\caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table
\label{tbl:bubbalargefg}
\begin{tabular}{|| l | l | c | c | l ||} \hline
% \textbf{Failure Scenario} & & \textbf{Bubba} & & \textbf{Symptom} \\
% & & \textbf{Oscillator} & & \\
\textbf{Failure} & & \textbf{$BubbaOscillator$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS3: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS4: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS5: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS7: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS8: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
%FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS9: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS10: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS11: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS12: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS13: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS14: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS15: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS16: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS17: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS18: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS19: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS20: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS21: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\
FS22: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\
FS23: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\
FS24: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS1: $CAP_{10nF}$ $OPEN$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
% FS1: $CAP_{10nF}$ $SHORT$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
\hline
\end{tabular}
\end{table}
Collecting symptoms from table~\ref{tbl:bubbalargefg} we can show that for single failure modes, applying $fm$ to the bubba oscillator
returns three failure modes,
%
$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$
\subsection{BUFF45: Detailed Analysis}
\label{detail:BUFF45}
\begin{table}[h+]
\caption{BUFF45: Failure Mode Effects Analysis} % title of Table
\label{tbl:buff45}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{BUFF45} & & \textbf{Symptom} \\
% & & & & \\
\textbf{Failure} & & \textbf{$BUFF45$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $0\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
%FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $90\_phaseshift$ \\ \hline
FS3: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS4: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS5: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
\hline
\end{tabular}
\end{table}
collecting symptoms from table~\ref{tbl:buff45}, we can create a derived component $BUFF45$ which has the following failure modes:
$$
fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift,
$$
%
\subsection{PHS135BUFFERED: Failure Mode Effects Analysis} % title of Table
\label{detail:PHS135BUFFERED}
\begin{table}[h+]
\caption{PHS135BUFFERED: Failure Mode Effects Analysis} % title of Table
\label{tbl:phs135buffered}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{PHS135 Buffered} & & \textbf{Symptom} \\
% & & & & \\
\textbf{Failure} & & \textbf{$PHS135BUFFERED$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
%FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
FS3: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS4: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
% FS6: $PHS45_2$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
FS5: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS6: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
% FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
\hline
\end{tabular}
\end{table}
%
%
Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes:
$$
fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal .\} % 180\_phaseshift,
$$
%
\subsection{PHS225AMP: Failure Mode Effects Analysis} % title of Table
\label{detail:PHS225AMP}
\begin{table}[h+]
\caption{PHS225AMP: Failure Mode Effects Analysis} % title of Table
\label{tbl:phs225amp}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\
% & & \textbf{Oscillator} & & \\
\textbf{Failure} & & \textbf{$PHS225AMP$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $180\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ \hline
% FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $270\_phaseshift$ \\ \hline
FS3: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS4: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS5: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS6: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
\hline
\end{tabular}
\end{table}
%
Applying FMMD we create a derived component $PHS225AMP$ which has the following failure modes:
$$
fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift,
$$
\subsection{BUBBAOSC: Failure Mode Effects Analysis} % title of Table
\label{detail:BUBBAOSC}
\begin{table}[h+]
\caption{BUBBAOSC: Failure Mode Effects Analysis} % title of Table
\label{tbl:bubba2}
\begin{tabular}{|| l | l | c | c | l ||} \hline
%\textbf{Failure Scenario} & & \textbf{BUBBAOSC} & & \textbf{Symptom} \\
% & & & & \\
\textbf{Failure} & & \textbf{$BUBBAOSC$ } & & \textbf{Derived Component} \\
\textbf{cause} & & \textbf{Effect} & & \textbf{Failure Mode} \\
\hline
%FS1: $PHS135BUFFERED$ $180\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
FS1: $PHS135BUFFERED$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
FS2: $PHS135BUFFERED$ $90\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ \hline
% FS4: $PHS225AMP$ $270\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
FS4: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\
FS5: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \hline
\hline
\end{tabular}
\end{table}
%
Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes:
$$
fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc},
$$
\clearpage
\section{Sigma Delta Detailed FMMD Analyses}

2
submission_thesis/thesis.tex
View File

@ -92,7 +92,7 @@
\input{CH7_Conclusion/copy}
\appendix
\input{appendixes/detailed_analysis}
\input{appendixes/formal}
\input{appendixes/algorithmic}