Estimation and confidence intervals of CNp(u, v) for logistic-exponential distribution with application

Article Type

Research Article

Publication Title

International Journal of System Assurance Engineering and Management

Abstract

The process capability index (PCI) has been one of the most useful indicators for evaluating the capability of a manufacturing process. Since PCI is based on sample observations, it is essentially an estimated value. Hence, it is natural to think of a confidence interval (CI) of the PCI. In this paper, bootstrap confidence intervals and highest posterior density (HPD) credible intervals of non-normal PCIs, CNpmk, CNpm, CNpk and CNp are studied through simulation when the underlying distribution is two parameter logistic-exponential (LE). First, maximum likelihood method is used to estimate the model parameters and then three bootstrap confidence intervals (BCIs) are considered for obtaining CIs of non-normal PCIs, CNpmk, CNpm, CNpk and CNp. Next, the Bayesian estimation is studied with respect to symmetric (squared error) loss function using gamma priors for the model parameters. In order to assess the performance of BCIs and HPD credible intervals of CNpmk, CNpm, CNpk and CNp with respect to average width, coverage probabilities and relative coverage, Monte Carlo simulations are conducted. Finally, a real data set, related to weight of the rubber edge of the speaker driver has been analyzed for illustrative purpose.

First Page

431

Last Page

446

DOI

https://10.1007/s13198-023-01870-y

Publication Date

3-1-2023

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