Parametric Lower Confidence Limits of Quantile-Based Process Capability Indices

Abstract

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.

Key Words:

• Asymptotic and bootstrap confidence intervals
• Kolmogorov-Smirnov goodness-of-fit test
• maximum likelihood estimation
• process capability index
• quantile

Additional information

Notes on contributors

Cheng Peng

Cheng Peng is an Associate Professor of statistics at the University of Southern Maine, Portland, Maine, USA. His research interests include regression modeling, semiparametric inference, statistical process control, computer intensive statistics and biostatistics.