Parametric Lower Confidence Limits of Quantile-Based Process Capability Indices

We consider a construction the parametric asymptotic and bootstrap lower confidence limits for the basic quantile-based process capability indices (PCIs) based on the unified superstructure C(Np) (u, v). The process quantiles are estimated using maximum likelihood estimation and the maximum likelihood estimator of C(Np) (u, v) is proposed. We also proved that the MLE of C(Np) (u, v) is asymptotically normally distributed. A general guideline of selecting the appropriate type of confidence limits is provided. Numerical examples based on real-life data are presented to illustrate the steps of implementing the proposed procedures.