On prediction of future failure times based on bathtub-shaped type-II censoring samples

In this paper, we focus on predicting future failure times under Type-II right censoring samples with bathtubshaped failure times. We first discuss the point and interval estimation of the unknown parameters using the maximum likelihood estimation and spacing-based methods. Various point predictors for future failure times are derived, using the best unbiased, maximum likelihood, conditional median, and median unbiased methods. Moreover, we establish the corresponding prediction intervals by applying different techniques including pivotal, Wald, highest conditional density, and shortest length methods. A simulation study is performed to assess the performance of the proposed prediction methods. Additionally, two real datasets are analyzed: one representing the survival times of patients treated for stomach cancer (Hand et al., 1994) and another from Lawless (2011), showing the duration in thousands of cycles until electrical appliances failed in a life test. These analyses illustrate the practical application of the proposed methods. Based on these numerical experiments, it is shown that the maximum likelihood predictor based on two-stage procedure and the conditional median predictor are the best point predictors for future failure times. Moreover, the highest conditional density method is identified as a strong candidate for establishing prediction intervals.