ASSESSING MULTIVARIATE PROCESS PRODUCT YIELD VIA DISCRETE POINT APPROXIMATION/

The assessment of multivariate yield is central to the robust design o f products/processes. Currently, yield is evaluated via Monte Carlo si mulation. However, it requires thousands of replications per simulatio n to achieve an acceptably precise estimate of yield, this is often te dious and time consuming, thereby rendering it unattractive as an eval uation tool. We propose a discrete point approximation on each design variable, using general Beta distributions, for assessing reasonably p recise multivariate yield estimates, which require only a minute fract ion of the Monte Carlo replications/simulations required to estimate y ield (e.g., 3 and 5 design variables would require only 3(3) = 27 and 3(5) = 243 replications, respectively). The Beta distribution has the desirable property of being able to characterize a wide variety of pro cesses that may or may not be symmetric and which may or may not have a finite operating range. Using an approach that computes the roots of a polynomial, whose degree is determined by the number of discrete po ints, discrete three point approximations are obtained and tabulated f or twenty-five different Beta distributions. Based on several test exa mples, where design parameters are modeled as independent Beta random variates, our approach appears to be highly accurate, achieving virtua lly the same multivariate yield estimate as that obtained via Monte Ca rlo simulation. The substantial reduction in the number of replication s and associated computational time required to assess yield makes the iterative adjustment of design parameters a more practical design str ategy.