Bayesian Inference Based on the Interval Grouped Data from the Weibull Model with Application

In this paper, based on the interval grouped data, Bayesian approach is used to obtain estimator for the Weibull scale parameter and some lifetime such as the reliability and hazard functions. The estimation procedures have been developed and modified under squared error loss function (SELF) and general entropy loss function (GELF). The estimators are derived using the inverted gamma conjugate prior. Credible intervals and high posterior density (HPD) credible intervals are also obtained. Prediction for the future number of failures in the corresponding intervals is presented. Finally, real life example is applied to illustrate the performance of the estimation procedures.