Bootstrap confidence limits for Wright's C_s

The process engineer wants to estimate an accurate process capability index(PCI) since he wants to decide whether the process is capable or not. If it is greater than or equal to the value 1, the process is considered capable. Confidence limit plays a major role for the correct interpretation of PCIs. Pearn and Chang(1997) have studied the performance of Wright's C_s under some skewed distributions, and showed that the percentage bias of the estimator increases as the skewness coefficient θ increases. What would be helpful would be a confidence limit estimation technique for PCIs that is nonparametric or free from assumptions of the distribution of the characteristic X. Bootstrapping is precisely such a technique. Thus, the purpose of this paper based on the consistency of bootstrap in Han et al.(1998) is to construct six bootstrap confidence limits used in reducing bias of estimations based on Hall(1988), and to compare their performances for C_s. Simulation study is under normal and lognormal distributions for some parameter values.