Statistical inference for the lifetime performance index of products with Pareto distribution on basis of general progressive type II censored sample

Abstract

In this paper, we study the statistical inference for the lifetime performance index of the Pareto distribution based on the general progressive type II censored data. Through data transformation, we derive the maximum likelihood estimator (MLE) of lifetime performance index and confidence interval. Further, the Bayesian estimator and the associated credible interval based on informative and non informative prior functions are also considered under the squared error loss function. Based on the non Bayesian and Bayesian estimators of lifetime performance indicators, the hypothesis testing process is constructed to evaluate the life performance of products. After the Monte Carlo simulation, we find that the Bayesian estimator is far better than MLE, and the Bayesian estimator based on informative prior has the best performance. The estimated mean squared errors for both MLE and Bayesian estimator are small, indicating that our considered method is effective to assess the lifetime performance of the products. Finally, a numerical example is analyzed for illustrative purposes.

Keywords:

• Pareto distribution
• lifetime performance index
• general progressive type II censoring
• Bayesian estimation
• MCMC

Acknowledgments

The authors would like to thank the editor and anonymous referees for their constructive comments and suggestions that have substantially improved the original manuscript.

Additional information

Funding

The authors' work was partially supported by the National Statistical Science Research Project of China (No. 2019LZ32).