Why can a moment-based POCV analysis report a mean that differs from the nominal delay value?

Short Answer

Ordinary, symmetric POCV models variation as a normal distribution, where the nominal delay and the statistical mean are the same number. Moment-based POCV instead allows an asymmetric distribution - a longer tail in one direction than the other - and once a distribution is skewed, its average value is no longer the same as the no-variation nominal value, so the library separately reports a mean shift describing exactly how far the mean has moved away from nominal.

Technical Explanation

• Normal (Gaussian) variation is symmetric, so mean equals nominal. In the default, single-parameter model, the distribution's mean value and its zero-variation nominal value are the same number, because a symmetric distribution has no reason to pull the average away from center.
• Moment-based modeling allows a skewed, asymmetric distribution instead. Advanced process nodes and very low supply voltages can make timing behavior genuinely asymmetric - a longer tail in the slow direction, for instance - which a purely symmetric model cannot represent accurately.
• Skewness is the parameter that captures this asymmetry. A skewness of zero means a symmetric, normal distribution; a negative value means a longer tail toward earlier/faster times, and a positive value means a longer tail toward later/slower times.
• Once skewness is nonzero, mean and nominal split into two different numbers. "Nominal" still means the timing behavior with no variation modeled at all, but "mean" now means the actual average of the skewed distribution, which has shifted away from that nominal value.
• Variation reports show the mean-shifted value, not the nominal value. Anywhere a moment-based POCV report shows a "mean" delay, slew, or constraint value, it is already reporting the value after the mean shift is applied - reading it as if it were still the simple nominal number will be wrong by exactly the mean-shift amount.
• Moment-based analysis needs libraries with moment-based LVF data and a specific license. If a normal (non-moment-based) POCV cell model is used inside a moment-based analysis, PrimeTime converts it using its minimum (early) and maximum (late) variation behavior; the full feature also requires a PrimeTime-ADV-PLUS license.

Follow-up Question & Model Response

If a cell's moment-based delay distribution has positive skewness - a longer tail toward slower delays - would you expect the mean shift to increase or decrease the effective late-direction margin compared to a symmetric model with the same nominal delay and standard deviation, and why?

Candidate Model Response: Positive skewness pulls the mean toward the slower, longer-tail side of the distribution, so the effective late-direction margin should increase compared to a symmetric model with the same nominal value and the same standard deviation, because the asymmetric model is explicitly saying the slow tail is heavier than a normal distribution would predict. A symmetric model with that same sigma would understate how far into the slow direction the real cell behavior can extend, which is exactly the accuracy problem moment-based modeling exists to fix at advanced nodes and low supply voltages. The mean shift is the mechanism that captures this - it moves the reported average delay closer to where the real, skewed distribution's mass actually sits, rather than leaving it at the symmetric-model nominal value.