Reliability Prediction Updating Through Computational Bayesian for Mixed and Non-mixed Lifetime Data Using More Flexible New Extra Modified Weibull Model

Jamal A. Al-saleh, Satish K. Agarwal


A new lifetime reliability model with four parameters is proposed. We call it the extra modified Weibull model (EMWM), which is an extension of the modified Weibull model (MWM), capable of modeling a different shapes of hazard function. The new model is developed by introducing fourth parameter in MWM called indicator parameter. The main advantage of an indicator (fourth) parameter is that it gives the new model mixture and non-mixture options, besides different shapes of hazard function including bathtub. The model parameters can be estimated based on a Bayesian generalized posterior method that serves as a tool for model identification, and it gives an efficient computational updating approach with new ways of predicting and measuring behavior. To have insight of the new indicator parameter and to see its importance, we have considered three data sets [Murthy et al [1], Badar and Priest [2], and  Aarset [3]) which have been studied in the past. A prediction updating of the earlier studies of the data sets through the generalized posterior summaries using Markov Chain Monte Carlo (MCMC) Gibbs sampling approach are presented for the proposed model for the different parameters. The behavior of the parameters would help the users to have more clarity about the role of the indicator parameter, and hence may be useful for certain sets of data. The proposed model is fully adaptive to the available failure data and gives reliability engineers and scientists another option for modeling the life time data. We provide description of the mathematical properties of the new model along with failure rate function.


bayesian analysis; extra modified weibull model; gibbs sampling; indicator parameter; markov chain monte carlo; mixture model; modified weibull model.

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