Reliability Inference and Remaining Useful Life Prediction Based on the Two-Parameter Bathtub-Shaped Lifetime Distribution Under Progressive Type-II Censoring

The two-parameter bathtub-shaped distribution is an important lifetime distribution. In this paper, we are interested in developing reliability inference and remaining useful life prediction methods for the two-parameter bathtub-shaped lifetime distribution under progressive type-II censoring. By constructing generalized pivotal quantities, the generalized confidence intervals for both model parameters and key reliability metrics, including quantiles, reliability functions, and remaining useful life are exploited. The proposed methods are further extended to accelerated life testing scenarios. The corresponding accelerated life testing model is constructed based on the two-parameter bathtub-shaped distribution. Furthermore, the generalized confidence intervals for model parameters, quantiles, reliability functions, and remaining useful life are also exploited under the designed stress level. Through comprehensive Monte Carlo simulations, and comparing our approach with Wald confidence intervals and bootstrap-p confidence intervals across moderate and large sample sizes, we confirm the superior coverage probability performance of the generalized confidence interval procedures. The practical applicability of our methodology is validated through two illustrative examples.