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