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In this paper, the geometric process is introduced as a constant-stress accelerated model to analyze a series of life data that obtained from several increasing stress levels. The geometric process (GP) model is assumed when the lifetime of test units follows an extension of the exponential distribution. Based on progressive censoring, the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained. Moreover, a real dataset is analyzed to illustrate the proposed procedures. In addition, the approximate, bootstrap and credible confidence intervals (CIs) of the estimators are constructed. Finally, simulation studies are carried out to investigate the precision of the MLEs and BEs for the parameters involved.

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Clustered data with censored failure times frequently arise in clinical trials and tumorigenicity studies. For such data, the common and extensively used class of two-sample tests is the weighted log-rank tests. In this article, a double saddlepoint approximation is used to calculate the p-values of the null permutation distribution of these tests. This technique is demonstrated using three real clustered data sets. Comprehensive simulation studies are conducted to appraise the efficiency of the saddlepoint approximation. This approximation is far superior to the asymptotic normal approximation. This precision allows us to determine almost exact confidence intervals for the treatment impact.

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