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In fabrication the yield 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 relation between the design margin and the yield. If we express the specification margin in terms of standard deviation sigma, we can immediately calculate yield Y according 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〔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 .〕 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 * ''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 ''range. Note: This interpretation is valid for normal (Gaussian) distributed variables and performances, luckily the "specification-margin" of a design is almost intuitively related to the yield, e.g. if we have a larger "safety margin" in our design to the limit(s) we are more on the safe side and the production will contain less fail samples. Actually the advantage of WCD is that it offers an elegant method to treat also non-normal and multi-variate distributions and still offerering a picturial, intuitive understanding! == Most simple non-trivial example == In the most simple non-trivial case there is only one normally distributed performance parameter with mean and standard deviation and one single upper limit for the performance specification . The WCD then calculates to: : In this example it is assumed that only statistical variances contribute to the observed performance variations, and that the performance parameter does not depend operating conditions. Once we found the WCD, we can (approximately) calculate from it the yield by using the error function (which is related to the cummulative distribution function of the normal Gaussian distribution) or by using look-up tables (e.g. WCD=3 is equivalent to Y=99.87%). For the discussion of any case, more complex than the above-mentioned example, see Antreich et al., 1993. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Worst-case distance」の詳細全文を読む スポンサード リンク
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