Procedure of the convolution method for estimating production yield with sample size information

The yield index S_pk proposed by Boyles (1994. Process capability with asymmetric tolerances. Communications in Statistics-Simulation and Computation, 23 (1), 615-643) provides an exact measure on the production yield of normal processes. Lee et al. (Lee, J.C., Hung, H.N., Pearn, W.L. and Kueng, T.L., 2002. On the distribution of the estimated process yield index S _pk. Quality and Reliability Engineering International, 18 (2), 111-116) considered a normal approximation for estimating S_pk. In this paper, we consider a convolution approximation for estimating S _pk, and compare with the normal approximation. The comparison results show that the convolution method does provide a more accurate estimation to Spk as well as the production yield than the normal approximation. An efficient step-by-step procedure based on the convolution method is developed to illustrate how to estimate the production yield. Also investigated is the accuracy of the convolution method which provides useful information about sample size required for designated power levels, and for convergence.