Reliability inference of stress-strength model for the truncated proportional hazard rate distribution under progressively Type-II censored samples

This paper considers the reliability inference for the truncated proportional hazard rate stress-strength model based on progressively Type-II censoring scheme. When the stress and strength variables follow the truncated proportional hazard rate distributions, the maximum likelihood estimation and the pivotal quantity estimation of stress-strength reliability are derived. Based on the percentile bootstrap sampling technique, the 95% confidence interval of stress-strength reliability is obtained, as well as the related coverage percentage. Moreover, based on the Fisher Z transformation and the modified generalized pivotal quantity, the 95% modified generalized confidence interval for the stress-strength reliability is obtained. The performance of the proposed method is evaluated by the Monte Carlo simulation. The numerical results show that the pivotal quantity estimators performs better than the maximum likelihood estimators. At last, two real datasets are analyzed by the proposed methodology for illustrative purpose. The results of real example analysis show that our model can be applied to the practical problem, the truncated proportional hazard rate distribution can fit the failure data better than other distributions, and the algorithms in this paper are suitable to handle the small sample data.