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

摘要

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, C_(Npmk),C_(Npm), C_(Npk) and C_(Np) 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, C_(Npmk), C_(Npm), C_(Npk) and C_(Np). 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 C_(Npmk), C_(Npm), C_(Npk) and C_(Np) 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.