In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.
In this paper, we introduce an extension of the exponentiated exponential(EE) distribution which offers a more flexible model for lifetime data. This model is generated by compound distribution with mixing exponential model. Several statistical and reliability properties of the proposed distribution are explored as the geometric extreme stability, sufficient conditions for the shape behavior of the density and hazard rate functions, the moments and mean residual life time. Estimation of unknown parameters using the maximum likelihood are obtained. Moreover, an application to a real data set is presented for illustrative purposes.
In this article, a test statistic for testing exponentiality versus a used better than aged in Laplace transform ordering class of life distribution based on a U-statistic is proposed. Pitman’s asymptotic efficiencies of the test are calculated and compared to other tests. The percentiles of this test statistic are tabulated for censored and non-censored data, and the powers of this test are estimated for some famously alternative distributions in reliability, such as the Weibull, Makeham, linear failure rate, and Gamma distributions. Finally, examples in different areas are used as practical applications of the proposed test.
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