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

Abstract

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, BCI) 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 [Formula: see text] is widely recommended for evaluating the performance of the product’s lifetime and evaluating the lifetime performance index [Formula: see text] for the three-parameter Weighted-Lomax distribution (WLx) under progressive type-II censoring sample for a lower specification limit ([Formula: see text]). The statistical inference concerning [Formula: see text] is conducted via obtaining the maximum likelihood of [Formula: see text] on the base of progressive type-II censoring. The asymptotic normal distribution of the MLE of [Formula: see text] and the confidence interval is proposed. Moreover, the hypothesis testing of [Formula: see text] 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 [Formula: see text]. The Bayes estimator of [Formula: see text] is then utilized to develop a credible interval in the condition of known [Formula: see text]. 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.