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 Cpk 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 Cp and Cpk. 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 Cpm. 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 Cp, Cpk, and Cpm. In addition, some observations and recommendations are made.
