Predicting observables from Weibull model based on general progressive censored data with asymmetric loss

The objective of this paper is to develop a methodology to construct and compute in a Bayesian setting, point and interval predictions based on general progressive Type-II censored data from Weibull model. Prediction bounds for the future observations (2-sample prediction) based on this type of censored will be derived. Bayesian predictions are obtained based on a continuous–discrete joint prior for the unknown two parameters. We have examined point predictions under symmetric and asymmetric loss functions. As application, the total duration time in a life test and the failure time of a kk-out-of-mm system may be predicted. An illustrative example consisting of various types of real data from an accelerated test on insulating fluid reported by Nelson (1982) [17] is presented. Finally, some numerical results using simulation study concerning different sample sizes, and different progressive censoring schemes were reported. A study of 10 000 randomly generated future samples from the same distribution shows that the actual prediction levels are satisfactory.