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

Until recently, estimates of process indices have been point estimates. How ever, a more appropriate estimate would be provided by a confidence interva l. 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 capa bility indices. Journal of Quality Technology 1990,22(3):223-29), Kushler a nd Hurley (Confidence bounds for capability indices. Journal of Quality Tec hnology 1992,24(4):188-95), and Franklin and Wasserman (A note on the conse rvative nature of the tables of lower confidence limits for C-pk With a sug gested correction. Communications in Statistics: Simulation and Computation 1992;21(4):1165-69) have provided exact and approximate formulas to determ ine these lower confidence limits for C-p and C-pk In addition, recent work by Boyles (The Taguchi capability index. Journal of Quality Technology 199 1;23(1):17-26) has provided approximate formulas to determine the lower con fidence limits for C-pm. This paper provides equations to estimate the appr oximate sample size necessary to achieve a desired confidence limit with sp ecified confidence level. These equations are based on these formulas and a re presented for C-p, C-pk, and C-pm. In addition, some observations and re commendations are made. (C) 1999 Elsevier Science Ltd. All rights reserved.