Sample size determination for lower confidence limits for estimating process capability indices

Abstract

Until recently, estimates of process indices have been point estimates. However, a more appropriate estimate would be provided by a confidence interval. In this case, a one sided interval is necessary, since the real interest is in how small the process index can be, and is called a lower confidence limit. Recent work by Chou et al. (Lower confidence limits on process capability indices. Journal of Quality Technology 1990;22(3):223–29), Kushler and Hurley (Confidence bounds for capability indices. Journal of Quality Technology 1992;24(4):188–95), and Franklin and Wasserman (A note on the conservative nature of the tables of lower confidence limits for C pk with a suggested correction. Communications in Statistics: Simulation and Computation 1992;21(4):1165–69) have provided exact and approximate formulas to determine these lower confidence limits for C p and C pk . In addition, recent work by Boyles (The Taguchi capability index. Journal of Quality Technology 1991;23(1):17–26) has provided approximate formulas to determine the lower confidence limits for C pm . This paper provides equations to estimate the approximate sample size necessary to achieve a desired confidence limit with specified confidence level. These equations are based on these formulas and are presented for C p , C pk , and C pm . In addition, some observations and recommendations are made.