In fabrication the yield Y=(number of good samples)/(total number of samples) is one of the most important measures. Also in the design phase engineers already try to maximize the yield by using simulation techniques and statistical models. Often the data follows the well-known bell-shaped normal distribution, and for such distributions there is a simple direct relationship between the design margin (to a given specification limit) and the yield. If we express the specification margin in terms of standard deviation sigma, we can immediately calculate yield Y according to this specification. The concept of worst-case distance (WCD) extends this simple idea for applying it to more complex problems (like having non-normal distributions, multiple specs, etc.).
The WCD[1] is a metric originally applied in electronic design for yield optimization and design centering, nowadays also applied as a metric for quantifying electronic system and device robustness.
[2]
View in performance space with performance acceptance region A and distribution of performance (red) under statistical and operation variations from which WCD can be calculated. Note: Often the statistical variables itself are not correlated but the performances do so (acc. to the stretch and rotation of the ellipsoids). Also often the specifications are set by just upper or lower limits – so being straight lines. If we would plot the statistical variable space, the spec-limits would typically become nonlinear shapes. WCD makes use of both ways of looking to the yield problem.
For yield optimization in electronic circuit design the WCD relates the following yield influencing factors to each other:
Statistical distribution of design parameters usually based on the used technology process
Operating range of operating conditions the design will work in
Performance specification for performance parameters
Although the strict mathematical formalism may be complex, in a simple interpretation the WCD is the maximum of all possible (i.e. being within the specification limits)
performance variances divided by the distance to the performance specification, given that the performance variances are evaluated under the space spanned by the operating range.
^Antreich, K.; Graeb, H. E. & Wieser, C. U. (1994), 'Circuit analysis and optimization driven by worst-case distances.', IEEE Trans. on CAD of Integrated Circuits and Systems 13 (1), 57-71 .
