A Bayesian Study on the estimate of Hazard function of coherent systems for weighted Lindley Distribution

In the study of technical system in reliability engineering, coherent systems play an important role. In this paper, we considered the weighted Lindley distribution as a lifetime distribution of components in a coherent system, with independent and identically distributed, which belongs to the class of the weighted distributions and provide a comprehensive understanding by adding flexibility in the existing standard distributions. So, different types of loss functions and different priors for the interested parameters are considered. The Bayes estimators for hazard function and mean residual life time of a coherent system and their respective posterior risks are computed by use of some computational methods, such as Monte Carlo and then compared for different loss function. Some simulation studies have been done in order to investigate the effect of sample size on the estimated parameters. A real-life application is also presented for the illustration purpose.