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Lifetime distributions under progressive Type-II censored scheme have been attracting great interest due to their wide application in the fields of science, engineering, social sciences and medicine. Also, prediction of future events on the basis of the past and present knowledge without any doubt is one of the most important problems in statistics. In this paper, the Bayes estimators for the parameters of the Marshall-Olkin Weibull-exponential distribution are derived based on progressive Type-II censored scheme. The estimators are considered under two different 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. Also, the two-sample prediction method is applied to obtain the Bayesian prediction (point and interval) for future order statistics. A numerical example is provided to illustrate the theoretical results and an application using real data set is used to demonstrate how the results can be used in practice.

Accelerated life testing or partially accelerated life tests is very important in life testing experiments because it saves time and cost. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual conditions. This paper proposes, constant–stress partially accelerated life test using Type II censored samples, assuming that the lifetime of items under usual condition have the Topp Leone-inverted Kumaraswamy distribution. The Bayes estimators for the parameters, acceleration factor, reliability and hazard rate function are obtained. Bayes estimators based on informative priors is derived under the balanced square error loss function as a symmetric loss function and balanced linear exponential loss function as an asymmetric loss function. Also, Bayesian prediction (point and bounds) is considered for a future observation based on Type-II censored under two samples prediction. Numerical studies are given and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied to real data sets.