Finding the Better of Two Similar Designs by Monte Carlo Techniques

During the iterative design of a system (or circuit) the designer is often faced with the problem of ranking two designs according to some criterion. If the system elements have uncertain values, each system manifestation can be evaluated as to whether or not it meets some performance criterion. The fraction which meets or exceeds the criterion is called the yield. Monte Carlo techniques can be used to simulate the population of systems and thus to estimate the ranking of two designs. The first result presented in the paper is a derivation of the probability that one design is better than another, along with confidence limits for that probability. If the two designs are topologically the same, i.e., they differ only in the nominal values and actual distributions of true parameter values, then the same set of random numbers can be used for one simulation of each design. Due to the similarity there may be a positive correlation between the 2 results which can then be used to narrow the confidence limits from the crude method mentioned above. The second result is a derivation of these narrow confidence limits.