A note on production yield measure for multiple lines

In today’s globally competitive environment, processes involving multiple manufacturing lines are quite common due to economies of scale considerations. Production yield measure indices C_pk and C_pu are the most popular yield-based indices and have been widely used in manufacturing industries for two-sided and one-sided specification limits, respectively. In this paper, two production yield indices for multiple lines (Formula presented.) and (Formula presented.) are considered and the approximate distributions of two natural estimators (Formula presented.) and (Formula presented.) are derived. For the convenience of industry applications, the lower confidence bounds and critical values are provided.