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In lifetime tests, the waiting time for items to fail may be long under usual use conditions, particularly when the products have high reliability. To reduce the cost of testing without sacrificing the quality of the data obtained, the products are exposed to higher stress levels than normal, which quickly causes early failures. Therefore, accelerated life testing is essential since it saves costs and time. This paper considers constant stress-partially accelerated life tests under progressive Type II censored samples. This is realized under the claim that the lifetime of products under usual use conditions follows Vtub-shaped lifetime distribution, which is also known as log-log distribution. The log–log distribution is highly significant and has several real-world applications since it has distinct shapes of its probability density function and hazard rate function. A graphical description of the log–log distribution is exhibited, including plots of the probability density function and hazard rate. The log–log density has different shapes, such as decreasing, unimodal, and approximately symmetric. Several mathematical properties, such as quantiles, probability weighted moments, incomplete moments, moments of residual life, and reversed residual life functions, and entropy of the log–log distribution, are discussed. In addition, the maximum likelihood and maximum product spacing methods are used to obtain the interval and point estimators of the acceleration factor, as well as the model parameters. A simulation study is employed to assess the implementation of the estimation approaches under censoring schemes and different sample sizes. Finally, to demonstrate the viability of the various approaches, two real data sets are investigated. [ABSTRACT FROM AUTHOR]

In this paper Chen-Burr XII distribution is constructed and graphical description of the probability density function, hazard rate and reversed hazard rate functions of the proposed model is obtained. Also, some statistical characteristics of the Chen-Burr XII distribution are discussed and some new models as sub-models from the Chen-Burr XII distribution are introduced. Moreover, maximum likelihood estimation of the parameters, reliability, hazard rate and reversed hazard rate functions of the Chen-Burr XII distribution are considered. Also, the asymptotic confidence intervals of the distribution parameters, reliability, hazard rate and reversed hazard rate functions are presented. Finally, three real life data sets are applied to prove how the Chen-Burr XII distribution can be applied in real life and to confirm its superiority over some existing distributions. [ABSTRACT FROM AUTHOR]

This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model. [ABSTRACT FROM AUTHOR]