A New Lifetime Mixture Model to Estimate Repair times using Bayesian Approach

Abstract

In this study 3-component mixture model using Ailamujia distribution  is analyzed under Bayesian paradigm. Joint posteriors are obtained for Jeffreys’ and gamma priors. Bayes estimators of  mixture parameters and  associated Bayes risks are derived using three loss functions i.e  squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF). The prior predictive method is used for hyper parameter elicitation . To numerically check the performance of Bayes estimators, simulated results are obtained for  different test termination times, parametric values and sample sizes.  Two  data sets,  on  repair times of refrigerator components and recovery times of cancer patients are analyzed to numerically exhibit the applicability of proposed mixture model.  Results  suggest that DLF is a better option for estimating the component parameters.