From c4222e1b504dfae30401ca6ba49855cdd56e91de Mon Sep 17 00:00:00 2001 From: Robin Clark Date: Thu, 9 Feb 2012 13:53:58 +0000 Subject: [PATCH] added start of discussion on approvals specifying specific failure modes for given components --- .../opamp_circuits_C_GARRETT/opamps.tex | 122 +++++++++++------- 1 file changed, 78 insertions(+), 44 deletions(-) diff --git a/old_thesis/opamp_circuits_C_GARRETT/opamps.tex b/old_thesis/opamp_circuits_C_GARRETT/opamps.tex index bd00668..753dc55 100644 --- a/old_thesis/opamp_circuits_C_GARRETT/opamps.tex +++ b/old_thesis/opamp_circuits_C_GARRETT/opamps.tex @@ -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.