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In this article, a new generalization of linear failure rate called nonlinear failure rate is developed, analyzed, and applied to a real dataset. A comparison of Bayesian and frequentist approaches to the estimation of parameters and reliability characteristics of non-linear failure rate is investigated. The maximum likelihood estimators are obtained using the cross-entropy method to optimize the log-likelihood function. The Bayes estimators of parameters and reliability characteristics are obtained via Markov chain Monte Carlo method. A simulation study is performed in order to compare the proposed Bayes estimators with maximum likelihood estimators on the basis of their biases and mean squared errors. We demonstrate that the proposed model fits a well-known dataset better than other mixture models.

Non-linear failure rate: A comparison of the Bayesian and frequentist approaches to estimation