Worst-case distance

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 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.

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 $$s$$
 * Operating range of operating conditions the design will work in $$\Theta$$
 * Performance specification for performance parameters $$f$$

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.