Nonparametric Confidence Limits of Quantile-Based Process Capability Indices

We propose an asymptotic nonparametric confidence interval for quantile-based process capability indices (PCIs) based on the superstructure (,) modified from (,) which contains the four basic PCIs, , , , and , as special cases. Since the asymptotic variance of the estimator for quantile-based PCIs involves the density function of the underlying process, the existing asymptotic results cannot be used directly to construct confidence limits for PCIs. To obtain a consistent estimator for the asymptotic variance of the estimated quantile-based PCIs, in this paper, we propose to use the kernel density estimator for the underlying process. Consequently, the confidence limits for PCIs are established based on the consistent estimates. A real-life example from manufacturing engineering is used to illustrate the implementation of the proposed methods. Simulation studies are also presented in this paper to compare the two quantile estimators that are used in the definition of PCIs.