Monte Carlo question

[Charles Schuler]

Is there any situation where a Monte Carlo analysis would produce values
that exceed worst-case values? If it's a dumb question, I apologize but it
happened.

 

[Kevin Aylward]

Is there any situation where a Monte Carlo analysis would produce
values that exceed worst-case values?

Yes.

If by Monte Carlo you mean simply noting tolerances of each component
parameter, and varying them all randomly, then this might well give an
overestimate in actual voltages and currents. Some variations are
negatively correlated, for example, suppose for the sake of argument,
whenever you increased a resistace, a capacitace was always reduced,
this would attempt to keep the time constant more constant!

Secondly, *practical* Monte Carlo simulations may not be good enougth.
It is often simply not realistic to do 100's of runs if a transient
simulation is going to take, say 2 hours for each run. For these cases,
you are pretty much stuck with doing some sort of "Worst Case"
analysis(e.g http://www.anasoft.co.uk/worstcase.html). That is,
selecting the max and min parameter conditions for all types of
components and doing the runs for these conditions only. Typically 16
corner types might be done (http://www.anasoft.co.uk/WCSETUP.GIF. I will
note that the 4 corner version is usually not good enough.

Note that parameter variations are based on the concept of sigma, the
standard deviation. Typically the "worst case" value is a 3 (or maybe 6)
sigma away from the mean. A worst case value does not mean that that
value will not be exceeded. For gaussian distributed parameters, *any*
value is theoretically possible. A 3 sigma value will catch 97%.

Of course, a "Worst Case" *parameter* varying design does not guarantee
that the worst case *waveforms* will be produced, however, it might well
be good enougth.

The reality of design is that it is impossible to have a design that is
absolutely fail safe. It is simply impossible to do all the simulations
that should be required. Secondly, the models themselves are never 100%
accurate. You just have to use engineering judgment to do the best you
can.

Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Malcolm Reeves]

Is there any situation where a Monte Carlo analysis would produce values
that exceed worst-case values? If it's a dumb question, I apologize but it
happened.

I suspect this is because worst-case analysis does not actually do
worst case for all most?) real circuits. What WC analysis does is
vary each component slightly, one at time and see which way the node
you have specifies goes. Then finally it sets all the components to
their extremes to give the "worst case". But this is only worst case
if all component effects are linear and they don't interact.

For example, consider a simple LC tuned circuit where you say the
worst case is maximum signal and nominal values are below the on-tune
point. WC analysis will work out that it needs to increase L and C
(climbing up the curve). Then it will set L and C to maximum
tolerance and completely overshoot the peak.

On the other hand MC analysis will do a random selection of all
possible values and with enough runs will probably find a set near to
the true WC of exactly on-tune. So it is entirely possible, even
likely, for MC to a value worst than WC.


--

Malcolm Reeves BSc CEng MIEE MIRSE, Full Circuit Ltd, Chippenham, UK
([email protected], [email protected] or [email protected]).
Design Service for Analogue/Digital H/W & S/W Railway Signalling and Power
electronics. More details plus freeware, Win95/98 DUN and Pspice tips, see:

http://www.fullcircuit.com or http://www.fullcircuit.co.uk

NEW - Desktop ToDo/Reminder program (free)

 

[Charles Schuler]

Thanks MUCH Kevin and Malcom:

I am still trying to get my head wrapped around this. Since you two have
been so kind, one more question. If a simulator uses a Normal Distribution
(for Monte Carlo), then 99.7% of the values plugged (randomly) in will lie
between the mean - 3 sigma and the mean + 3 sigma. If this is so, then my
results are showing too many "outliers." Another thing: one of the basic
ideas taught to me was that tolerances ala statistical error tend to cancel
and produce less error than worse case. You know, if you build enough
circuits, the high guys will tend to cancel the low guys.

 

[Kevin Aylward]

Thanks MUCH Kevin and Malcom:

I am still trying to get my head wrapped around this. Since you two
have been so kind, one more question. If a simulator uses a Normal
Distribution (for Monte Carlo), then 99.7% of the values plugged
(randomly) in will lie between the mean - 3 sigma and the mean + 3
sigma. If this is so, then my results are showing too many
"outliers."

I would need to see more details on this.

Another thing: one of the basic ideas taught to me was
that tolerances ala statistical error tend to cancel and produce less
error than worse case. You know, if you build enough circuits, the
high guys will tend to cancel the low guys.

Yes, but the theoretical maximum case will still be the total sum. Its
only the standard deviation that is rms summed. If the distribution is
truly gaussian, then there is finite probability of *any* value.

Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Malcolm Reeves]

Thanks MUCH Kevin and Malcom:

I am still trying to get my head wrapped around this. Since you two have
been so kind, one more question. If a simulator uses a Normal Distribution
(for Monte Carlo), then 99.7% of the values plugged (randomly) in will lie
between the mean - 3 sigma and the mean + 3 sigma. If this is so, then my
results are showing too many "outliers." Another thing: one of the basic
ideas taught to me was that tolerances ala statistical error tend to cancel
and produce less error than worse case. You know, if you build enough
circuits, the high guys will tend to cancel the low guys.

With problem like this I find the best way is to go back a bit. So
test your theory. Make a noddy circuit with 1 or more resistors and a
voltage source then do MC. Plot V/I. Is the distribution what you
expect?


--

Malcolm Reeves BSc CEng MIEE MIRSE, Full Circuit Ltd, Chippenham, UK
([email protected], [email protected] or [email protected]).
Design Service for Analogue/Digital H/W & S/W Railway Signalling and Power
electronics. More details plus freeware, Win95/98 DUN and Pspice tips, see:

http://www.fullcircuit.com or http://www.fullcircuit.co.uk

NEW - Desktop ToDo/Reminder program (free)