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.

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

“…Assuming a life test is conducted on n products, each time a failed product is observed, a certain number of products are randomly removed from the remaining non-failed products [23]. That is to say, when the failure time of the first product is observed to be X 1:m:n , P 1 products are removed from the remaining n − 1 non-failed products, and n − 1 − P 1 products remain to be observed.…”

Statistical inference for multi stress–strength reliability based on progressive first failure with lifetime inverse Lomax distribution and analysis of transformer insulation data

“…Despite the fact that Bhattacharyya and Johnson 16 developed the multicomponent stress-strength model, it has garnered a lot of attention in recent years and has been explored by numerous researchers for both complete and censored data. Some of the recently appeared articles include Tolba et al, 17 Ramadan et al, 18 Kotb and Raqab, 19 Maurya and Tripathi, 20 Mahto et al, 21 Wang et al, 22 Jha et al, 23 El-Sagheer et al, 24 Rasekhi et al, 25 Alotaibi et al, 26 Maurya et al, 27 Sarhan et al, 28 Sarhan et al, 29 Kohansal and Shoaee, 30 Muse et al, 31 Jana and Bera, 32 Ahmad et al, 33 Ahmad et al 34 , Ramadan 35 and Wu and Kuş. 36 Well-known censoring techniques include the type-II censoring scheme, progressive type-II censoring scheme, and progressive first failure censoring system.…”

“…Some of the recently appeared articles include Tolba et al., 17 Ramadan et al., 18 Kotb and Raqab, 19 Maurya and Tripathi, 20 Mahto et al., 21 Wang et al., 22 Jha et al., 23 El‐Sagheer et al., 24 Rasekhi et al., 25 Alotaibi et al., 26 Maurya et al., 27 Sarhan et al., 28 Sarhan et al., 29 Kohansal and Shoaee, 30 Muse et al., 31 Jana and Bera, 32 Ahmad et al., 33 Ahmad et al 34 ,. Ramadan 35 and Wu and Kuş 36 …”

Assessing the Lifetime Performance Index with Digital Inferences of Power Hazard Function Distribution Using Progressive Type-II Censoring Scheme

“…Nevertheless, the assumption of normality for many processes in industry and business cannot be valid. A lot of papers were studied on the statistical inference for C L X based on various types of censored and progressive censored data for different models of which [ 3 – 17 ] dealt with progressive censoring from various points of view considering several lifetime distributions and its applications. Soliman et al [ 18 , 19 ] discussed assessing the life time performance index for exponentiated Frechet distribution using Prog-Type-II-C and progressive first failure censoring scheme.…”

“…The Prog-Type-II-C scheme is of use in this paper [ 11 – 17 ], which can be characterized as follows: we presume that n units are placed on a life testing experiment. Let X i , i =1,2,…, n be continuous identically distributed failure times of these units.…”