Worst-case distance

In fabrication, the yield (Y = number of good samples/total number of samples) is one of the most important metrics. During the design phase, engineers aim to maximize yield by using simulation techniques and statistical models. Often, data follows a normal distribution, and for such distributions, there is a direct relationship between the design margin (relative to a given specification limit) and the yield. By expressing the specification margin in terms of standard deviation (sigma), yield (Y) can be calculated according to this specification. The concept of worst-case distance (WCD) extends this idea to more complex problems, such as non-normal distributions and multiple specifications.

View of the performance space with the performance acceptance region A and the distribution of performance (red) under statistical and operational variations, from which WCD can be calculated. Note: The statistical variables themselves are often uncorrelated, but the performances are correlated (as indicated by the stretch and rotation of the ellipsoids). Specifications are often defined by upper or lower limits, represented as straight lines. In the statistical variable space, specification limits typically take nonlinear shapes. WCD incorporates both perspectives in addressing the yield problem.

WCD is a metric originally applied in electronic design for yield optimization and design centering, and it is now used as a metric for quantifying the robustness of electronic systems and devices.

In yield optimization for electronic circuit design, WCD relates the following yield-influencing factors:

• Statistical distribution of design parameters, typically based on the technology process $s$
• Operating range of conditions under which the design will function $\Theta$
• Performance specification for performance parameters $f$

Although the strict mathematical formalism is complex, in a simplified interpretation, WCD is the maximum of all possible performance variances (i.e., within specification limits) divided by the distance to the performance specification, with the performance variances evaluated within the space defined by the operating range.

External links

• Survey on several statistical analysis approaches