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In many experiments about lifetime examination, we will faced on restrictions of time and sample size, which this factors cause that the researcher can’t access to all of data. Therefore, it is valuable to study prediction of unobserved values based on information of available data. in this paper we have studied the prediction of unobserved values in two status of one-sample and two-sample, when the parent distribution is the exponential distribution and imposed restriction is double censoring. in each case the interval prediction by given cover will be obtain. Finally, a numerical example is given to illustrate the procedures.

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In this article introduce the sequential order statistics. Therefore based on multiply Type-II censored sample of sequential order statistics, Bayesian estimators are derived for the parameters of one- and two- parameter exponential distributions under the assumption that the prior distribution is given by an inverse gamma distribution and the Bayes estimator with respect to squared error loss is calculated. Moreover, prediction of future failure time is considered. Finally in example Bayesian estimator and non-bayesian estimatores, namely the Best Linear Unbiased Estimator (BLUE) and Approximate Maximum Likelihood Estimator (AMLE) are derived.