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added start of discussion on approvals specifying specific failure modes

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for given components
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Robin Clark 2012-02-09 13:53:58 +00:00
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old_thesis/opamp_circuits_C_GARRETT/opamps.tex
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@ -75,15 +75,17 @@ for instance, commonly used configurations of parts are used to create
amplifiers, filters, potential dividers etc.
%It is therefore natural to collect parts to form functional groups.
It is common design practise in electronics, to use collections of parts in specific configurations
to form well defined and known building blocks.
to form well-defined and well-known building blocks.
These commonly used configurations of parts, or {\fgs}, will
also have a specific failure mode behaviour.
We can take a {\fg} and determine its symptoms of failure.
When we have done this we can treat this as a component in its own right.
If we terms `parts' as base~components and components we have determined
from functional groups as derived components, we can modularise the FMEA task.
from functional groups as derived components, we can modularise FMEA.
If we start building {\fgs} from derived components we can start to build a modular
hierarchical failure mode model.
hierarchical failure mode model. Modularising FMEA should give benefits of reducing reasoning distance,
allowing re-use of modules and reducing the number of by-hand analysis checks to consider.
\paragraph {Definitions}
@ -289,14 +291,28 @@ the number of failure modes in its sub-systems/components..
\section{Examples of Derived Component like concepts in safety literature}
Idea stage on this section
Idea stage on this section, integrated circuits and some compond parts (like digital resistors)
are treated like base components. i.e. this sets a precedent for {\dcs}.
\begin{itemize}
\item Look at OPAMP circuits, pick one (say $\mu$741)
\item examine number of components and failure modes
\item Digital transistor perhaps, inside two resistors and a transistor.
\item outline a proposed FMMD analysis
\item Show FMD-91 OPAMP failure modes -- compare with FMMD
\end{itemize}
The gas burner standard (EN298~\cite{en298}), only considers OPEN and SHORT for resistors
(and for some types of resistors OPEN only).
FMD-91~\cite{fmd91}(the US military failure modes guide) also includes `parameter change' in its description of resistor failure modes.
Now a resistor will generally only suffer parameter change when over stressed.
EN298 stipulates down rating by 60\% to maximum stress
possible in a circuit. So even if you have a resistor that preliminary tells you would
never be subjected to say more than 5V, but there is say, a 24V rail
on the circuit, you have to choose resistors able to cope with the 24V
stress/load and then down rate by 60\%. That is to say the resitor should be rated for a maximum
voltage of $ > 38.4V$ and should be rated 60\% higher for its power consumption at $38.4V$.
Because of down-rating, it is reasonable to not have to consider parameter change under EN298 approvals.
\clearpage
Two areas that cannot be automated. Choosing {\fgs} and the analysis/symptom collection process itself.
@ -847,9 +863,7 @@ We now have can express the failure mode behaviour of this type of amplifier thu
$$ fm(NIAMP) = \{ {lowpass}, {high}, {low} \}.$$
With this two stage analysis we have a comparison complexity (see equation~\ref{eqn:rd2}) of
$4.(2-1)=4$ for the potential divider and $6.(2-1)=6$, giving a total of $10$ for the $NIAMP$.
For this simple example, traditional flat/non-modular FMEA would have a CC of $(3-1).(4+2+2)=16$.
\clearpage
\section{Inverting OPAMP}
@ -925,40 +939,42 @@ This gives the same results as the analysis from figure~\ref{fig:invampanalysis}
%The differences are the root causes or component failure modes that
%lead to the symptoms (i.e. the symptoms are the same but causation tree will be different).
$$ fm(NIAMP) = \{ {lowpass}, {high}, {low} \}.$$
$$ fm(INVAMP) = \{ {lowpass}, {high}, {low} \}.$$
\subsection{Inverting OPAMP using three components}
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
or input -ve), see table~\ref{tbl:invamp}. Because symptom collection is defined as surjective (from component failure modes
to symptoms) we cannot have a component failure mode that maps to two different symptoms (within a functional group).
Note that here we have a more general symptom $ OUT OF RANGE $ which could mean either
$HIGH$ or $LOW$ output.
\subsection{Inverting OPAMP analysing with three components in one {\fg}}
%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
%or input -ve), see table~\ref{tbl:invamp}.
%Because symptom collection is defined as surjective (from component failure modes
%to symptoms) we cannot have a component failure mode that maps to two different symptoms (within a functional group).
%Note that here we have a more general symptom $ OUT OF RANGE $ which could mean either
%$HIGH$ or $LOW$ output.
% 08feb2012 bugger considering -ve input. It complicates things.
% maybe do an ac amplifier later at some stage.
\begin{table}[h+]
\caption{Inverting Amplifier: Single failure analysis: 3 components}
\begin{tabular}{|| l | l | c | c | l ||} \hline
\textbf{Failure Scenario} & & \textbf{Inverted Amp Effect} & & \textbf{Symptom} \\ \hline
\hline
FS1: R1 SHORT +ve in & & NEGATIVE out of range & & $ OUT OF RANGE $ \\
FS1: R1 SHORT -ve in & & POSITIVE out of range & & $ OUT OF RANGE $ \\ \hline
FS1: R1 SHORT & & NEGATIVE out of range & & $ HIGH $ \\
% FS1: R1 SHORT -ve in & & POSITIVE out of range & & $ OUT OF RANGE $ \\ \hline
FS2: R1 OPEN +ve in & & zero output & & $ ZERO OUTPUT $ \\
FS2: R1 OPEN -ve in & & zero output & & $ ZERO OUTPUT $ \\ \hline
FS2: R1 OPEN & & zero output & & $ LOW $ \\
% FS2: R1 OPEN -ve in & & zero output & & $ ZERO OUTPUT $ \\ \hline
FS3: R2 SHORT +ve in & & $INVAMP_{nogain} $ & & $ NO GAIN $ \\
FS3: R2 SHORT -ve in & & $INVAMP_{nogain} $ & & $ NO GAIN $ \\ \hline
FS3: R2 SHORT & & $INVAMP_{nogain} $ & & $ LOW $ \\
% FS3: R2 SHORT -ve in & & $INVAMP_{nogain} $ & & $ NO GAIN $ \\ \hline
FS4: R2 OPEN +ve in & & NEGATIVE out of range $ $ & & $ OUT OF RANGE$ \\
FS4: R2 OPEN -ve in & & POSITIVE out of range $ $ & & $OUT OF RANGE $ \\ \hline
FS4: R2 OPEN & & NEGATIVE out of range $ $ & & $ LOW$ \\
% FS4: R2 OPEN -ve in & & POSITIVE out of range $ $ & & $OUT OF RANGE $ \\ \hline
FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ OUT OF RANGE $ \\ \hline
FS5: AMP L\_DN & & $ INVAMP_{low} $ & & $ LOW $ \\ \hline
FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ OUT OF RANGE $ \\ \hline
FS6: AMP L\_UP & & $INVAMP_{high} $ & & $ HIGH $ \\ \hline
FS7: AMP NOOP & & $INVAMP_{nogain} $ & & $ NO GAIN $ \\ \hline
@ -969,7 +985,7 @@ $HIGH$ or $LOW$ output.
\end{table}
$$ fm(INVAMP) = \{ OUT OF RANGE, ZERO OUTPUT, NO GAIN, LOW PASS \} $$
$$ fm(INVAMP) = \{ HIGH, LOW, NO GAIN, LOW PASS \} $$
%Much more general. OUT OF RANGE symptom maps to many component failure modes.
@ -979,14 +995,31 @@ $$ fm(INVAMP) = \{ OUT OF RANGE, ZERO OUTPUT, NO GAIN, LOW PASS \} $$
\clearpage
\subsection{Comparison between the two approaches}
%\clearpage
If the input voltage can be negative the potential divider
becomes reversed in polarity.
This means that detecting which failure mode has occurred from knowing the symptom, has become a more difficult task; or in other words
the observability of the causes of failure are reduced. Instead of the more specific symptoms $HIGH$ or $LOW$ we
obtain $OUT OF RANGE$ instead.
\subsection{Comparison between the two approaches}
\label{sec:invampcc}
The first analysis looks at an inverted potential divider, analyses its failure modes,
and from this we obtain a {\dc} (INVPD).
We applied a second analysis stage with the known failure modes of the op-amp and the failure modes of INVPD.
The second analysis (3 components) has to look at the effects of each failure mode of each resistor
on the op-amp circuit. This is more to think about---or in other words an increase in the complexity of the analysis---than comparing the two known failure modes
from the pre-analysed inverted potential divider. The complexity comparison figures
bear this out. For the two stage analysis, using equation~\ref{eqn:rd2}, we obtain a CC of $4.(2-1)+6.(2-1)=10$
and for the second analysis a CC of $8.(3-2)=16$.
% CAN WE MODULARISE TOO FAR???? CAN W MAKE IT TOO FINELY GRAINED. 08FEB2012
%Again, for the two stage analysis, using equation~\ref{eqn:rd}, we obtain a CC of $4.(2-1)+6.(2-1)=10$
%and for the second analysis a CC of $8.(3-2)=16$.
%If the input voltage can be negative the potential divider
%becomes reversed in polarity.
%This means that detecting which failure mode has occurred from knowing the symptom, has become a more difficult task; or in other words
%the observability of the causes of failure are reduced. Instead of the more specific symptoms $HIGH$ or $LOW$ we
%obtain $OUT OF RANGE$ instead.
\clearpage
\section{Op-Amp circuit 1}
@ -1531,8 +1564,9 @@ determine {\dcs}.
This has been analysed in section~\ref{sec:invamp}.
The inverting amplifier, as a {\dc}, has the following failure modes:
$$ fm(INVAMP) = \{ OUT OF RANGE, ZERO OUTPUT, NO GAIN, LOW PASS \} $$
$$ fm(INVAMP) = \{ HIGH, LOW, LOW PASS \} $$
and has a CC of 10.
\subsection{Phase shifter: PHS45}
@ -1668,7 +1702,7 @@ $$ CC = 28.8 = 224$$
To obtain the total comparison complexity $TCC$, we need to add the complexity from the
{\dcs} that $BubbaOscillator$ was built from.
$$ TCC = 28.8 + 4.4 + 4.0 = 240$$
$$ TCC = 28.8 + 4.4 + 4.0 + 10 = 250$$
%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.
@ -1811,10 +1845,10 @@ The $PHS225AMP$ consists of a $PHS45$ and an $INVAMP$ (which provides $180^{\cir
FS2: $PHS45_1$ $no\_signal$ & & signal lost & & $NO_{signal}$ \\
FS3: $PHS45_1$ $90\_phaseshift$ & & phase shift high & & $180\_phaseshift$ \\ \hline
FS4: $NIBUFF_1$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS5: $NIBUFF_1$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS6: $NIBUFF_1$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS7: $NIBUFF_1$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
FS4: $INVAMP$ $L_{up}$ & & output high & & $NO_{signal}$ \\
FS5: $INVAMP$ $L_{dn}$ & & output low & & $NO_{signal}$ \\
FS6: $INVAMP$ $N_{oop}$ & & output low & & $NO_{signal}$ \\
FS7: $INVAMP$ $L_{slew}$ & & signal lost & & $NO_{signal}$ \\ \hline
\hline
@ -1869,10 +1903,10 @@ $$ CC(BUBBAOSC) = 6.(2-1) = 6 $$
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, 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, at the next level four $BUFF45$ {\dcs} giving $(4-1).7=21$,
and penultimately $PHS135BUFFERED$ with 6 and $PHS225AMP$ with 7. The final top stage of the hierarchy, $BUBBAOSC$ has a CC of 6.
Our total comparison complexity is $48$, this contrasts with 468 for traditional `flat' FMEA,
and 240 for our first stage functional groups analysis.
Our total comparison complexity is $58$, this contrasts with $468$ for traditional `flat' FMEA,
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 may be re-used for similar circuitry
to analyse in the future.