An Effective Procedure for Calculating Weibull Production Yield with Mean Shift

Abstract

Motorola, Inc. introduced its six sigma production quality initiative to the world in the 1980s. Six sigma production quality is estimated by assuming a 1.5 sigma shift to the process mean. Bothe provided a statistical reason for considering such a shift in the normal process mean, and he also provided a much more accurate capability calculation to measure the production yield (Bothe, D. R., "Statistical Reason for the 1.5 sigma Shift," Qual. Eng., Vol. 14(3), 2002, pp. 479-487). In this paper, we consider Weibull processes, which cover a wide class of non-normal processes. We calculate the mean shift adjustments under various sample sizes n and Weibull parameters, with the power fixed at 0.5. Then, we implement the derived results to develop an effective procedure to accurately calculate the production yield. Finally, to demonstrate the applicability of the proposed approach, the proposed procedure is applied to a real manufacturing process with mean shift.