Need to check the Bubba OSC. Chris said the 90_degree

symptom of the PHS45 was actually 0_degrees.
So that ripples through.
And then do the SUMJ, mix it with the opamp
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Robin Clark 2012-09-23 18:41:07 +01:00
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PNG_DIA = cfg2.png cfg.png compco2.png compco3.png compco.png component.png componentpl.png fmmd_uml2.png fmmd_uml.png partitioncfm.png master_uml.png top_down_de_comp.png dc1.png dc2.png eulerfmmd.png PNG_DIA = cfg2.png cfg.png compco2.png compco3.png compco.png component.png componentpl.png fmmd_uml2.png fmmd_uml.png partitioncfm.png master_uml.png top_down_de_comp.png dc1.png dc2.png eulerfmmd.png
%.png:%.dia %.png:%.dia

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@ -830,6 +830,7 @@ as {\fcs} in table~\ref{tbl:ampfmea1}.
% %
% %
% %
\label{sec:invamp}
% %
\begin{figure}[h+] \begin{figure}[h+]
\centering \centering
@ -1476,11 +1477,11 @@ that it inherits a set of failure modes.
%We thus have a `new' component, %or system building block, but %We thus have a `new' component, %or system building block, but
%with a known and traceable %with a known and traceable
%fault behaviour. %fault behaviour.
A {\fg} must comprise of two or more components, and the UML diagram shows this A {\fg} must comprise of at least one component, and the UML diagram shows this
with the two to many relationship. with the one to many relationship.
Under exceptional circumstances a component may need to be a member of more than Under exceptional circumstances a component may need to be a member of more than
one {\fg} (this is looked at in section~\ref{sec:sideeffects}). The relationship between one {\fg} (this is looked at in section~\ref{sec:sideeffects}). The relationship between
the {\fg} and component is therefore $ \star \leftrightarrow 2..\star$. the {\fg} and component is therefore $ \star \leftrightarrow 1..\star$.
% %
A {\fg} will only be associated with one {\dc} and is given a one to one relationship in the UML diagram. A {\fg} will only be associated with one {\dc} and is given a one to one relationship in the UML diagram.
% %

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@ -5,7 +5,7 @@ PNG_DIA = blockdiagramcircuit2.png bubba_oscillator_block_diagram.png circuit1
poss1finalbubba.png poss2finalbubba.png pt100.png pt100_doublef.png pt100_singlef.png \ poss1finalbubba.png poss2finalbubba.png pt100.png pt100_doublef.png pt100_singlef.png \
pt100_tc.png pt100_tc_sp.png shared_component.png stat_single.png three_tree.png \ pt100_tc.png pt100_tc_sp.png shared_component.png stat_single.png three_tree.png \
tree_abstraction_levels.png vrange.png sigma_delta_block.png ftcontext.png ct1.png hd.png \ tree_abstraction_levels.png vrange.png sigma_delta_block.png ftcontext.png ct1.png hd.png \
sigdel1.png sdadc.png sigdel1.png sdadc.png bubba_euler_1.png bubba_euler_2.png

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@ -7,7 +7,16 @@
% %
% * OPERATIONAL STATE (perhaps a self test on an ADC where it is set to output and driven high and low and read) % * OPERATIONAL STATE (perhaps a self test on an ADC where it is set to output and driven high and low and read)
% to do: 23SEP2012
%
% 90_degrees is an incorrect failure mode in bubba and must be purged
%
% summing junction in sigma delta is not a valid fg, prob have to include
% the op-amp....
%
% very annoying to have to pull out the comparison complexity.
% makes the comparisons between approaches have less meaning.
% have to discuss this.
\label{sec:chap5} \label{sec:chap5}
@ -25,15 +34,18 @@ we are conforming to for our particular project).
This is followed by several example FMMD analyses, This is followed by several example FMMD analyses,
the first analysing a common configuration of the first analysing a common configuration of
the inverting amplifier (see section~\ref{sec:invamp}) using the inverting amplifier (see section~\ref{sec:invamp}) using
an op-amp and two resistors, which demonstrates how the potential divider from section~\ref{subsec:potdiv} an op-amp and two resistors, which demonstrates how the re-use of the potential divider from section~\ref{subsec:potdiv}.
~\ref{sec:chap4} The inverting amplifier is analysed again, but this time with different
can be re-used. %, but with provisos. {\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 %The first
%(see section~\ref{sec:diffamp}) %(see section~\ref{sec:diffamp})
Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used Section~\ref{sec:diffamp} analyses a circuit where two op-amps are used
to create a differencing amplifier. to create a differencing amplifier.
Re-use of the potential divider model is discussed in the context of this circuit, Building on the two approaches section~\ref{sec:invamp}, re-use of the potential divider {\dc}
is discussed in the context of this circuit,
where its re-use is appropriate in the first stage and where its re-use is appropriate in the first stage and
not in the second. not in the second.
% %
@ -48,6 +60,7 @@ Section~\ref{sec:sigmadelta} shows FMMD analysing the sigma delta analogue to di
analogue and digital signals. analogue and digital signals.
% %
% Moving Pt100 to metrics % Moving Pt100 to metrics
%
%Sections~\ref{sec:Pt100}~and~\ref{sec:Pt100d} demonstrate both statistical %Sections~\ref{sec:Pt100}~and~\ref{sec:Pt100d} demonstrate both statistical
%failure mode classification % analysis for top level events traced back to {\bc} failure modes %failure mode classification % analysis for top level events traced back to {\bc} failure modes
%and the analysis of double simultaneous failure modes. %and the analysis of double simultaneous failure modes.
@ -222,13 +235,14 @@ as shown below.
\item Shorted 3.9\% $\mapsto$ SHORT \item Shorted 3.9\% $\mapsto$ SHORT
\item Lead damage 1.9\% $\mapsto$ OPEN. \item Lead damage 1.9\% $\mapsto$ OPEN.
\end{itemize} \end{itemize}
%
The main causes of drift are overloading of components. The main causes of drift are overloading of components.
This is borne out in in the FMD-91~\cite{fmd91}[232] entry for a resistor network where the failure This is borne out in in the FMD-91~\cite{fmd91}[232] entry for a resistor network where the failure
modes do not include drift. modes do not include drift.
% %
If we can ensure that our resistors will not be exposed to overload conditions, the If we can ensure that our resistors will not be exposed to overload conditions, the
probability of drift (sometimes called parameter change) occurring probability of drift (sometimes called parameter change) occurring
is significantly reduced, enough for some standards to exclude it~\cite{en298}. is significantly reduced, enough for some standards to exclude it~\cite{en298}~\cite{en230}.
\paragraph{Resistor failure modes according to EN298.} \paragraph{Resistor failure modes according to EN298.}
@ -554,121 +568,7 @@ component {\fms} in FMEA or FMMD and require interpretation.
% is shown as a `$\derivec$' symbol. % is shown as a `$\derivec$' symbol.
% %
% %
% %
% \section{Example Analysis: Non-Inverting OPAMP}
% \label{sec:noninvamp}
% Consider a non inverting op-amp designed to amplify
% a small positive voltage (typical use would be a thermocouple amplifier
% taking a range from 0 to 25mV and amplifying it to the useful range of an ADC, approx 0 to 4 volts).
%
%
% \begin{figure}[h+]
% \centering
% \includegraphics[width=100pt]{CH5_Examples/mvampcircuit.png}
% % mvampcircuit.png: 243x143 pixel, 72dpi, 8.57x5.04 cm, bb=0 0 243 143
% \label{fig:mvampcircuit}
% \caption{positive mV amplifier circuit}
% \end{figure}
%
% We can begin by looking for functional groups.
% The resistors $ R1, R2 $ perform a fairly common function in electronics, that of the potential divider.
% So we can examine $\{ R1, R2 \}$ as a {\fg}.
%
%
% \subsection{The Resistor in terms of failure modes}
%
% We can now determine how the resistors can fail.
% We consider the {\fms} for resistors to be OPEN and SHORT (see section~\ref{ros}).
% %, i.e.
% %$ fm(R) = \{ OPEN, SHORT \} . $
%
% We can express the failure modes of a component using the function $fm$, thus for the resistor, $ fm(R) = \{ OPEN, SHORT \}$.
%
%
% We have two resistors in this circuit and therefore four component failure modes to consider for the potential divider.
% We can now examine what effect each of these failures will have on the {\fg} (see table~\ref{tbl:pd}).
%
%
% \subsection{Analysing a potential divider in terms of failure modes}
%
%
% \label{potdivfmmd}
%
%
%
% \begin{figure}[h+]
% \centering
% \includegraphics[width=100pt,keepaspectratio=true]{CH5_Examples/pd.png}
% % pd.png: 361x241 pixel, 72dpi, 12.74x8.50 cm, bb=0 0 361 241
% \label{fig:pdcircuit}
% \caption{Potential Divider Circuit}
% \end{figure}
%
%
% \begin{table}[h+]
% \caption{Potential Divider: Single failure analysis}
% \begin{tabular}{|| l | l | c | c | l ||} \hline
% \textbf{Failure Scenario} & & \textbf{Pot Div Effect} & & \textbf{Symptom} \\
% \hline
% FS1: R1 SHORT & & $LOW$ & & $PDLow$ \\
% FS2: R1 OPEN & & $HIGH$ & & $PDHigh$ \\ \hline
% FS3: R2 SHORT & & $HIGH$ & & $PDHigh$ \\
% FS4: R2 OPEN & & $LOW$ & & $PDLow$ \\ \hline
% \hline
% \end{tabular}
% \label{tbl:pd}
% \end{table}
%
% We can now create a {\dc} for the potential divider, $PD$.
%
% $$ fm(PD) = \{ PDLow, PDHigh \}$$
%
% %Let us now consider the op-amp. According to
% %FMD-91~\cite{fmd91}[3-116] an op-amp may have the following failure modes:
% %latchup(12.5\%), latchdown(6\%), nooperation(31.3\%), lowslewrate(50\%).
%
%
% \subsection{Analysing the non-inverting amplifier in terms of failure modes}
%
% From section~\ref{sec:opamp_fms}
% $$ fm(OPAMP) = \{L\_{up}, L\_{dn}, Noop, L\_slew \} $$
%
%
% We can now form a {\fg} with $PD$ and $OPAMP$.
%
% \begin{figure}
% \centering
% \includegraphics[width=300pt]{CH5_Examples/non_inv_amp_fmea.png}
% % non_inv_amp_fmea.png: 964x492 pixel, 96dpi, 25.50x13.02 cm, bb=0 0 723 369
% \label{fig:invampanalysis}
% \end{figure}
%
%
%
%
% \begin{table}[h+]
% \caption{NIAMP: Single failure analysis}
% \begin{tabular}{|| l | l | c | c | l ||} \hline
% \textbf{Failure Scenario} & & \textbf{Non In Amp Effect} & & \textbf{Symptom} \\
% \hline
% FS1: PD HIGH & & $LOW$ & & $Low$ \\
% FS2: PD LOW & & $HIGH$ & & $High$ \\ \hline
% FS3: OPAMP $L_{UP}$ & & $HIGH$ & & $High$ \\
% FS4: OPAMP $L_{DOWN}$ & & $LOW$ & & $Low$ \\
% FS5: OPAMP $Noop$ & & $LOW$ & & $Low$ \\
% FS5: OPAMP $Low slew$ & & $LOW$ & & $Lowpass$ \\ \hline
%
% \hline
% \end{tabular}
% \label{tbl:pd}
% \end{table}
%
% We can collect symptoms from the analysis and create a derived component
% to represent the non-inverting amplifier $NI\_AMP$.
% We can now express the failure mode behaviour of this type of amplifier thus:
%
% $$ fm(NIAMP) = \{ {lowpass}, {high}, {low} \}.$$
%
% %
\clearpage \clearpage
@ -1591,7 +1491,7 @@ determine {\dcs}.
This has been analysed in section~\ref{sec:invamp}. This has been analysed in section~\ref{sec:invamp}.
The inverting amplifier, as a {\dc}, has the following failure modes: The inverting amplifier, as a {\dc}, has the following failure modes:
$$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \}. $$ $$ fm(INVAMP) = \{ AMP\_High, AMP\_Low, LowPass \}. $$ % \{ HIGH, LOW, LOW PASS \}. $$
% METRICS and has a CC of 10. % METRICS and has a CC of 10.
@ -1612,7 +1512,8 @@ Our functional group for the phase shifter consists of a resistor and a capacito
\textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\ \textbf{Failure Scenario} & & \textbf{First Order} & & \textbf{Symptom} \\
& & \textbf{Low Pass Filter} & & \\ & & \textbf{Low Pass Filter} & & \\
\hline \hline
FS1: R SHORT & & 90 degree's of phase shift & & $90\_phaseshift$ \\ \hline FS1: R SHORT & & 0 degree's of phase shift & & $0\_phaseshift$ \\ \hline
% 90 degree's of phase shift & & $90\_phaseshift$ \\ \hline
FS2: R OPEN & & No Signal & & $nosignal$ \\ \hline FS2: R OPEN & & No Signal & & $nosignal$ \\ \hline
FS3: C SHORT & & Grounded,No Signal & & $nosignal$ \\ \hline FS3: C SHORT & & Grounded,No Signal & & $nosignal$ \\ \hline
FS4: C OPEN & & 0 degree's of phase shift & & $0\_phaseshift$ \\ \hline FS4: C OPEN & & 0 degree's of phase shift & & $0\_phaseshift$ \\ \hline
@ -1624,10 +1525,10 @@ Our functional group for the phase shifter consists of a resistor and a capacito
% PHS45 % PHS45
$$ fm (G_0) = \{ 90\_phaseshift, nosignal, 0\_phaseshift \} $$ $$ fm (G_0) = \{ nosignal, 0\_phaseshift \} $$
$$ CC(G_0) = 4.1 = 4 $$
%$$ CC(G_0) = 4 \times 1 = 4 $$
%23SEP2012
\subsection{Non Inverting Buffer: NIBUFF.} \subsection{Non Inverting Buffer: NIBUFF.}
The non-inverting buffer functional group, is comprised of one component, an op-amp. The non-inverting buffer functional group, is comprised of one component, an op-amp.
@ -1654,17 +1555,25 @@ Initially we use the first identified {\fgs} to create our model without further
\subsection{FMMD Analysis using initially identified functional groups} \subsection{FMMD Analysis using initially identified functional groups}
Our functional group for this analysis can be expressed thus: Our functional group for this analysis can be expressed thus:
$$ G^1_0 = PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} .$$ or in Euler diagram format as in figure~\ref{fig:bubbaeuler1}.
$$ G^1_0 = \{ PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 PHS45^1_4, INVAMP^1_0 \} ,$$
\begin{figure}[h+] % HTR 23SEP2012 \begin{figure}[h+]
% HTR 23SEP2012 \centering
% HTR 23SEP2012 \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/poss1finalbubba.png}
% HTR 23SEP2012 % largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
% HTR 23SEP2012 \caption{Bubba Oscillator: One large functional group using the initial functional groups to model oscillator.}
% HTR 23SEP2012 \label{fig:poss1finalbubba}
% HTR 23SEP2012 \end{figure}
\begin{figure}[h]
\centering \centering
\includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/poss1finalbubba.png} \includegraphics[width=400pt]{./CH5_Examples/bubba_euler_1.png}
% largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390 % bubba_euler_1.png: 946x404 pixel, 72dpi, 33.37x14.25 cm, bb=0 0 946 404
\caption{Bubba Oscillator: One large functional group using the initial functional groups to model oscillator.} \caption{Euler diagram showing the hierarchy of the initial FMMD analysis performed on the Bubba Oscillator circuit.}
\label{fig:poss1finalbubba} \label{fig:bubbaeuler1}
\end{figure} \end{figure}
\begin{table}[h+] \begin{table}[h+]
\caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table \caption{Bubba Oscillator: Failure Mode Effects Analysis: One Large Functional Group} % title of Table
\label{tbl:bubbalargefg} \label{tbl:bubbalargefg}
@ -1677,40 +1586,40 @@ $$ G^1_0 = PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 P
FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS1: $PHS45_1$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline % FS3: $PHS45_1$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS4: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ FS3: $NIBUFF_1$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS5: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS4: $NIBUFF_1$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS6: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS5: $NIBUFF_1$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS8: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS7: $PHS45_2$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS9: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ FS8: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline %FS10: $PHS45_2$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS11: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ FS9: $NIBUFF_2$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS12: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS10: $NIBUFF_2$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS13: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS11: $NIBUFF_2$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS14: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline FS12: $NIBUFF_2$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS15: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS13: $PHS45_3$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS16: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ FS14: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline % FS17: $PHS45_3$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS18: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\ FS15: $NIBUFF_3$ $L_{up}$ & & output high No Oscillation & & $NO_{osc}$ \\
FS19: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS16: $NIBUFF_3$ $L_{dn}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS20: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\ FS17: $NIBUFF_3$ $N_{oop}$ & & output low No Oscillation & & $NO_{osc}$ \\
FS21: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline FS18: $NIBUFF_3$ $L_{slew}$ & & signal lost & & $NO_{osc}$ \\ \hline
FS22: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\ FS19: $PHS45_4$ $0\_phaseshift$ & & osc frequency high & & $HI_{fosc}$ \\
FS23: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ FS20: $PHS45_4$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline % FS24: $PHS45_4$ $90\_phaseshift$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
FS25: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\ FS21: $INVAMP$ $OUTOFRANGE$ & & signal lost & & $NO_{osc}$ \\
FS26: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\ FS22: $INVAMP$ $ZEROOUTPUT$ & & signal lost & & $NO_{osc}$ \\
FS27: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\ FS23: $INVAMP$ $NOGAIN$ & & signal lost & & $NO_{osc}$ \\
FS28: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline FS24: $INVAMP$ $LOWPASS$ & & signal lost & & $NO_{osc}$ \\ \hline
% FS1: $CAP_{10nF}$ $OPEN$ & & osc frequency low & & $LO_{fosc}$ \\ \hline % FS1: $CAP_{10nF}$ $OPEN$ & & osc frequency low & & $LO_{fosc}$ \\ \hline
@ -1724,23 +1633,25 @@ $$ G^1_0 = PHS45^1_1, NIBUFF^0_1, PHS45^1_2, NIBUFF^0_2, PHS45^1_3, NIBUFF^0_3 P
Collecting symptoms from table~\ref{tbl:bubbalargefg} we can show that for single failure modes, applying $fm$ to the bubba oscillator Collecting symptoms from table~\ref{tbl:bubbalargefg} we can show that for single failure modes, applying $fm$ to the bubba oscillator
returns three failure modes, returns three failure modes,
$$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}, LO_{fosc} \} . $$ $$ fm(BubbaOscillator) = \{ NO_{osc}, HI_{fosc}\} . $$ %, LO_{fosc} \} . $$
For the final stage of this FMMD model, we can calculate the complexity using equation~\ref{eqn:rd2}. %For the final stage of this FMMD model, we can calculate the complexity using equation~\ref{eqn:rd2}.
$$ CC = 28.8 = 224$$ %$$ CC = 28 \times 8 = 224$$
To obtain the total comparison complexity ($TCC$), we need to add the complexity from the %To obtain the total comparison complexity ($TCC$), we need to add the complexity from the
{\dcs} that $BubbaOscillator$ was built from. %{\dcs} that $BubbaOscillator$ was built from.
$$ TCC = 28.8 + 4.4 + 4.0 + 10 = 250$$ %$$ TCC = 28 \times 8 + 4 \times 4 + 4 \times 0 + 10 = 250$$
%As we have re-used the analysis for BUFF45 we could even reasonably remove %As we have re-used the analysis for BUFF45 we could even reasonably remove
%$3.4=12$ from this result, because the results from $BUFF45$ have been used four times. %$3 \times 4=12$ from this result, because the results from $BUFF45$ have been used four times.
Traditional FMEA would have lead us to a much higher comparison complexity %Traditional FMEA would have lead us to a much higher comparison complexity
of $468$ failure modes to check against components. %of $468$ failure modes to check against components.
However, the analysis here appears top-heavy; we should be able to refine the model more %However,
and break this down into smaller functional groups, by allowing more stages of hierarchy and hopefully The analysis here appears top-heavy; we should be able to refine the model more
this should lead a further reduction in the complexity comparison figure. and break this down into smaller functional groups, by allowing more stages of hierarchy.
%and hopefully
%this should lead a further reduction in the complexity comparison figure.
By decreasing the size of the modules with further refinement, By decreasing the size of the modules with further refinement,
we may also discover new derived components that may be of use for other analyses in the future. we may also discover new derived components that may be of use for other analyses in the future.
@ -1748,20 +1659,27 @@ we may also discover new derived components that may be of use for other analyse
\clearpage \clearpage
\subsection{FMMD Analysis using more hierarchical stages} \subsection{FMMD Analysis of Bubba Oscillator using more hierarchical stages}
The example above---from the initial {\fgs}---used one very large functional group to model the circuit. The example above---from the initial {\fgs}---used one very large functional group to model the circuit.
This mean a quite large comparison complexity for this final stage. %This mean a quite large comparison complexity for this final stage.
We should be able to determine smaller {\fgs} and refine the model further. We should be able to determine smaller {\fgs} and refine the model further.
\begin{figure}[h+] % HTR 23SEP2012 \begin{figure}[h+]
\centering % HTR 23SEP2012 \centering
\includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/poss2finalbubba.png} % HTR 23SEP2012 \includegraphics[width=300pt,keepaspectratio=true]{CH5_Examples/poss2finalbubba.png}
% largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390 % HTR 23SEP2012 % largeosc.png: 916x390 pixel, 72dpi, 32.31x13.76 cm, bb=0 0 916 390
\caption{Bubba Oscillator: Smaller Functional Groups, One more FMMD hierarchy stage.} % HTR 23SEP2012 \caption{Bubba Oscillator: Smaller Functional Groups, One more FMMD hierarchy stage.}
\label{fig:poss2finalbubba} % HTR 23SEP2012 \label{fig:poss2finalbubba}
\end{figure} % HTR 23SEP2012 \end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=400pt]{./CH5_Examples/bubba_euler_2.png}
% bubba_euler_2.png: 1241x617 pixel, 72dpi, 43.78x21.77 cm, bb=0 0 1241 617
\caption{Euler diagram showing functional groupings for the Bubba oscillator using a more de-composed approach.}
\label{fig:bubbaeuler2}
\end{figure}
% %
We take the $NIBUFF$ and $PHS45$ We take the $NIBUFF$ and $PHS45$
@ -1771,7 +1689,8 @@ and with those three, form a $PHS135BUFFERED$
functional group. functional group.
$PHS135BUFFERED$ is a {\dc} representing an actively buffered $135^{\circ}$ phase shifter. $PHS135BUFFERED$ is a {\dc} representing an actively buffered $135^{\circ}$ phase shifter.
A PHS45 {\dc} and an inverting amplifier\footnote{Inverting amplifiers always apply a $180^{\circ}$ phase shift.}, form a {\fg} A PHS45 {\dc} and an inverting amplifier\footnote{Inverting amplifiers always apply a $180^{\circ}$ phase shift.},
form a {\fg}
providing an amplified $225^{\circ}$ phase shift, which we can call $PHS225AMP$. providing an amplified $225^{\circ}$ phase shift, which we can call $PHS225AMP$.
%---with the remaining $PHS45$ and the $INVAMP$ (re-used from section~\ref{sec:invamp})in a second group $PHS225AMP$--- %---with the remaining $PHS45$ and the $INVAMP$ (re-used from section~\ref{sec:invamp})in a second group $PHS225AMP$---
@ -1801,12 +1720,12 @@ Finally we can merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see fig
\hline \hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $0\_phaseshift$ \\ FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $0\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $90\_phaseshift$ \\ \hline %FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $90\_phaseshift$ \\ \hline
FS4: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\ FS3: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS5: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ FS4: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS6: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ FS5: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline FS6: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
\hline \hline
@ -1817,10 +1736,10 @@ Finally we can merge $PHS135BUFFERED$ and $PHS225AMP$ in a final stage (see fig
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) = \{ 90\_phaseshift, 0\_phaseshift, NO\_signal .\} fm (BUFF45) = \{ 0\_phaseshift, NO\_signal .\} % 90\_phaseshift,
$$ $$
$$ CC(BUFF45) = 7.1 = 7 $$ %$$ CC(BUFF45) = 7 \times 1 = 7 $$
We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}. We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
@ -1835,15 +1754,15 @@ We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
\hline \hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline %FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
FS4: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ FS3: $PHS45_2$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS5: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ FS4: $PHS45_2$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
FS6: $PHS45_2$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline % FS6: $PHS45_2$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
FS7: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\ FS5: $PHS45_3$ $0\_phaseshift$ & & phase shift low & & $90\_phaseshift$ \\
FS8: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ FS6: $PHS45_3$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline % FS9: $PHS45_3$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
@ -1855,11 +1774,11 @@ We can now combine three $BUFF45$ {\dcs} and create a $PHS135BUFFERED$ {\dc}.
Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes: Collecting symptoms from table~\ref{tbl:phs135buffered}, we can create a derived component $PHS135BUFFERED$ which has the following failure modes:
$$ $$
fm (PHS135BUFFERED) = \{ 90\_phaseshift, 180\_phaseshift, NO\_signal .\} fm (PHS135BUFFERED) = \{ 90\_phaseshift, NO\_signal .\} % 180\_phaseshift,
$$ $$
$$ CC (PHS135BUFFERED) = 3.2 = 6 $$ %$$ CC (PHS135BUFFERED) = 3 \times 2 = 6 $$
@ -1873,14 +1792,14 @@ The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\cir
\textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\ \textbf{Failure Scenario} & & \textbf{PHS225AMP} & & \textbf{Symptom} \\
& & \textbf{Oscillator} & & \\ & & \textbf{Oscillator} & & \\
\hline \hline
FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $270\_phaseshift$ \\ FS1: $PHS45_1$ $0\_phaseshift$ & & phase shift low & & $180\_phaseshift$ \\
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\ FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline % FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $270\_phaseshift$ \\ \hline
FS4: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\ FS3: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS5: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\ FS4: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS6: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\ FS5: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS7: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline FS6: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
\hline \hline
@ -1889,10 +1808,10 @@ The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\cir
Collecting symptoms from table~\ref{tbl:phs225amp}, we can create a derived component $PHS225AMP$ which has the following failure modes: Collecting symptoms from table~\ref{tbl:phs225amp}, we can create a derived component $PHS225AMP$ which has the following failure modes:
$$ $$
fm (PHS225AMP) = \{ 270\_phaseshift, 180\_phaseshift, NO\_signal .\} fm (PHS225AMP) = \{ 180\_phaseshift, NO\_signal .\} % 270\_phaseshift,
$$ $$
$$ CC(PHS225AMP) = 7.1 $$ %$$ CC(PHS225AMP) = 7 \times 1 $$
The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\circ}$ of phase shift). The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\circ}$ of phase shift).
@ -1909,13 +1828,13 @@ and perform FMEA with these.
\textbf{Failure Scenario} & & \textbf{BUBBAOSC} & & \textbf{Symptom} \\ \textbf{Failure Scenario} & & \textbf{BUBBAOSC} & & \textbf{Symptom} \\
& & & & \\ & & & & \\
\hline \hline
FS1: $PHS135BUFFERED$ $180\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\ %FS1: $PHS135BUFFERED$ $180\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
FS2: $PHS135BUFFERED$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\ FS1: $PHS135BUFFERED$ $no\_signal$ & & signal lost & & $NO_{osc}$ \\
FS3: $PHS135BUFFERED$ $90\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ \hline FS2: $PHS135BUFFERED$ $90\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ \hline
FS4: $PHS225AMP$ $270\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\ % FS4: $PHS225AMP$ $270\_phaseshift$ & & phase shift high & & $LO_{fosc}$ \\
FS5: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\ FS4: $PHS225AMP$ $180\_phaseshift$ & & phase shift low & & $HI_{osc}$ \\
FS6: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \hline FS5: $PHS225AMP$ $NO\_signal$ & & lost signal & & $NO_{signal}$ \\ \hline
\hline \hline
@ -1926,33 +1845,36 @@ and perform FMEA with these.
Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes: Collecting symptoms from table~\ref{tbl:bubba2}, we can create a derived component $BUBBAOSC$ which has the following failure modes:
$$ $$
fm (BUBBAOSC) = \{ LO_{fosc}, HI_{osc}, NO\_signal .\} fm (BUBBAOSC) = \{ HI_{osc}, NO\_signal .\} % LO_{fosc},
$$ $$
%We could trace the DAGs here and ensure that both analysis strategies worked ok..... %We could trace the DAGs here and ensure that both analysis strategies worked ok.....
$$ CC(BUBBAOSC) = 6.(2-1) = 6 $$ %$$ CC(BUBBAOSC) = 6 \times (2-1) = 6 $$
We can now add the comparison complexities for all levels of the analysis represented in figure~\ref{fig:poss2finalbubba}. % We can now add the comparison complexities for all levels of the analysis represented in figure~\ref{fig:poss2finalbubba}.
We have at the lowest level two $PHS45$ {\dcs} giving a CC of 8 and $INVAMP$ with a CC of 10, at the next level four $BUFF45$ {\dcs} giving $(4-1).7=21$, % We have at the lowest level two $PHS45$ {\dcs} giving a CC of 8 and $INVAMP$ with a CC of 10,
and penultimately $PHS135BUFFERED$ with 6 and $PHS225AMP$ with 7. The final top stage of the hierarchy, $BUBBAOSC$ has a CC of 6. % at the next level four $BUFF45$ {\dcs} giving $(4-1).7=21$,
Our total comparison complexity is $58$, this contrasts with $468$ for traditional `flat' FMEA, % and penultimately $PHS135BUFFERED$ with 6 and $PHS225AMP$ with 7.
and $250$ for our first stage functional groups analysis. % The final top stage of the hierarchy, $BUBBAOSC$ has a CC of 6.
This has meant a drastic reduction in the number of failure-modes to check against components. % Our total comparison complexity is $58$, this contrasts with $468$ for traditional `flat' FMEA,
It has also given us five {\dcs}, building blocks, which may be re-used for similar circuitry % and $250$ for our first stage functional groups analysis.
% This has meant a drastic reduction in the number of failure-modes to check against components.
It has %also
given us five {\dcs}, building blocks, which could potentially be re-used for similar circuitry
to analyse in the future. to analyse in the future.
\subsection{Comparing both approaches} \subsection{Comparing both approaches}
In general with large functional groups the comparison complexity %In general with large functional groups the comparison complexity
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 possibility of re-use. there are more {\dcs} and this increases the possibility of re-use.
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
of complexity comparison. % HTR of complexity comparison.
\section{Sigma Delta Analogue to Digital Converter.} %($\Sigma \Delta ADC$)} \section{Sigma Delta Analogue to Digital Converter.} %($\Sigma \Delta ADC$)}