Bias-Corrected Maximum Likelihood Estimation and Bayesian Inference for the Process Performance Index Using Inverse Gaussian Distribution

Tzong-Ru Tsai, Hua Xin, Ya-Yen Fan and Yuhlong Lio ()
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Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan
Hua Xin: School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
Ya-Yen Fan: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan
Yuhlong Lio: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA

Stats, 2022, vol. 5, issue 4, 1-18

Abstract: In this study, the estimation methods of bias-corrected maximum likelihood (BCML), bootstrap BCML (B-BCML) and Bayesian using Jeffrey’s prior distribution were proposed for the inverse Gaussian distribution with small sample cases to obtain the ML and Bayes estimators of the model parameters and the process performance index based on the lower specification process performance index. Moreover, an approximate confidence interval and the highest posterior density interval of the process performance index were established via the delta and Bayesian inference methods, respectively. To overcome the computational difficulty of sampling from the posterior distribution in Bayesian inference, the Markov chain Monte Carlo approach was used to implement the proposed Bayesian inference procedures. Monte Carlo simulations were conducted to evaluate the performance of the proposed BCML, B-BCML and Bayesian estimation methods. An example of the active repair times for an airborne communication transceiver is used for illustration.

Keywords: Bayesian estimation; bootstrap method; maximum likelihood estimation; process capability analysis; process performance index (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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