Work

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

Year: 2022

Type: article

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.

Source: Stats

DOI: 10.3390/stats5040064

Authors: Tzong-Ru Tsai, Hua Xin, Ya-Yen Fan, Yuhlong Lio

Institutions: Tamkang University, Northeast Petroleum University, University of South Dakota

Language: English

Topic: Advanced Statistical Process Monitoring

Subfield: Statistics, Probability and Uncertainty

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,256

Funders: National Natural Science Foundation of China, Ministry of Science and Technology, Taiwan