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Standard Deviation Summary in Monte Carlo Simulations Across Multiple Corners

alho1

The tool versions are below:

Virtuoso IC 6.1.8-64b.500.33
Spectre 23.1.0.063 64bit

Hello,

When performing a Monte Carlo simulation, the Yield tab shows a standard deviation in the results.

If the simulation is performed with several corners (not parameters), the question is which standard deviation value is used for the summary output. Each corner has its own standard deviation.

Is the worst-case standard deviation used for the summary? If so, why is it sometimes the larger and sometimes the smaller value?

At 100% yield it seems to always be the larger value (worst case), but at 0% yield it is sometimes the larger and sometimes the smaller value.

Does anyone know how this value is determined?

Thanks very much for your reply!

Alexander

Parents
  • Andrew Beckett

    Alexander,

    According to this: Inconsistency in value of Standard Deviation across Yield View tab and Summary View in Assembler, Explorer and ADE XL it should be the "worst case" standard deviation, but what that might mean is the standard deviation of the corner with the worst mean (and the spec might affect which direction that is). Not sure - I'll see if my colleague in product engineering who covers this knows.

    Regards,

    Andrew

  • Andrew Beckett
    in reply to Andrew Beckett

    Alexander,

    In newer versions, there's now a tooltip explaining that it's the standard deviation of the worst corner. However, what is not clear is how it determines which is the worst corner (especially if there are no specs). I'm trying to find that out.

    Andrew

  • alho1
    in reply to Andrew Beckett

    Hi Andrew,

    thanks for looking into this.

    Regards,

    Alexander

  • alho1
    in reply to Andrew Beckett

    Hi,

    did you find anything out?

    Regards,

    Alexander

  • Andrew Beckett
    in reply to alho1

    Yes.

    For >, the summary will take the row with the minimum (mean -target)/std;
    For <, the summary will take the row with the minimum -(mean - target)/std.

    It depends on spec type and the distance between mean and target

    I did then ask what happens if either a) it's a double-sided spec (i.e. range) or b) there's no spec. I haven't heard back yet on that; I was originally waiting for a complete answer, but in the meantime the above might be a useful start!

    Andrew

  • alho1
    in reply to alho1

    Something else I noticed: Andrew, your formulas for handling values greater than and less than the target are almost always correct. However, I found one specific case where the result appears to be wrong (see screenshot 2).

    In this example, the formula does not select the row containing the minimum value. When comparing this case to screenshot 1, there are no obvious differences in the setup, except that the resulting value deviates further from the target.

    In both cases, the mean is below the target value, which means the result lies outside the expected range.

    Is this intended behavior, or could this be a bug?

  • Andrew Beckett
    in reply to alho1

    In the second screenshot, the (mean-target)/std is quite close (around -60.55/-60.65) for the two rows, and given that the results are only being shown to 4 significant digits, a small offset to the mean (say) could move those either way around. I suspect that's all what you're seeing. For example, if the mean was 1.2262 then 1.189m would be the standard deviation under the minimum (mean-target)/std criteria.

    To be honest, I'm not that sure how statistically useful the summary std dev is anyway...

    Andrew

Reply
  • Andrew Beckett
    in reply to alho1

    In the second screenshot, the (mean-target)/std is quite close (around -60.55/-60.65) for the two rows, and given that the results are only being shown to 4 significant digits, a small offset to the mean (say) could move those either way around. I suspect that's all what you're seeing. For example, if the mean was 1.2262 then 1.189m would be the standard deviation under the minimum (mean-target)/std criteria.

    To be honest, I'm not that sure how statistically useful the summary std dev is anyway...

    Andrew

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