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

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., Kushler and Hurley, and Franklin and Wasserman has provided exact and approximate formulas to determine these lower confidence limits for Cp and Cpk. In addition, recent work by Boyles 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.