Assessing the lifetime performance index of weighted Lomax distribution based on progressive type-II censoring scheme for bladder cancer

In this paper, Health-related quality of life has not been adequately measured in bladder cancer. A recently developed reliable and disease-specific quality of life instrument (Bladder Cancer Index, BCD was used to measure. Progressive type II censoring schemes have potential usefulness in practice where budget constraints in place or there is a necessity for the speedy test. To test the process capability, the lifetime performance index C-L is widely recommended for evaluating the performance of the product's lifetime and evaluating the lifetime performance index C-L for the three-parameter Weighted-Lomax distribution (WLx) under progressive type-II censoring sample for a lower specification limit (L). The statistical inference concerning C-L is conducted via obtaining the maximum likelihood of C-L on the base of progressive type-II censoring. The asymptotic normal distribution of the MLE of C-L and the confidence interval is proposed. Moreover, the hypothesis testing of C-L for evaluating the lifetime performance of WLx data is conducted. Also, assuming the conjugate prior distribution and squared error loss function, this study constructs a Bayes estimator of C-L. The Bayes estimator of C-L is then utilized to develop a credible interval in the condition of known L. Moreover, we propose a Bayesian test to assess the lifetime performance of products. We also propose a Bayesian test to assess the lifetime performance of products. Finally, two examples are given, one of them is considering a real life data of the remission times of bladder cancer patients in endurance lifetime test and the other is a simulated example to illustrate the usage of the proposed procedure.