The Need for and Application of Statistical Design

A Systematic Statistical Circuit Analysis procedure is described which uses a simple algorithm to derive the distribution of a performance parameter from the distributions and tolerances of the individual components. The procedure requires the assumption or approximation that the individual components have a normal (Gaussian) distribution, although components with other distributions can also be treated. Applications of other than normal distributions is beyond the scope of this paper. Comparisons between statistical and worst-case design methods indicate that a severe economic penalty may be encountered by designing for the unlikely worst-case, rather than allowing for a fraction of failures to occur that are negligibly small compared to the uncontrolled catastrophic failures. Two examples are shown. One derives the performance parameter from the individual component tolerances, the other determines the required component tolerances from the desired performance. Comparisons with a corresponding worst-case analysis illustrates the economic and feasibility advantages gained through the use of statistical design methods.