predicting future lifetime based on random number of three parameters weibull distribution

in this paper, two pivotal quantities are modified to construct prediction intervals for future lifetime based on random number of three parameters weibull distribution, which can be widely applied in reliability theory and lifetime problems. the case of fixed sample size is presented as a special case. the random number has one of three important distributions as special cases. an algorithm is constructed to explain the importance of the theoretical results in applications. simulation studies are conducted to investigate the efficiency of the purposed results. finally, two numerical examples for real lifetime data are presented to illustrate the paper.