A New Flexible Four Parameter Bathtub Curve Failure Rate Model, and Its Application to Right-Censored Data

This article introduces a new flexible four parameter distribution by convolution of the exponential and Weibull distribution using the odd function transformation, which offers greater flexibility in terms of fit, its called the modified exponential-Weibull (MEW). The MEW model is designed to provide a more accurate description of failure time data resulting from a system with one or more failure modes and is characterized by a hazard rate (HR) that takes the shape of a bathtub due to its complexity. The moments properties, quantile function, and residual life are derived and discussed. We discussed the HR function and several distributional properties of the MEW model, and applied maximum likelihood and Bayesian techniques to estimate its unknown parameters. The Hamiltonian Monte Carlo (HMC) algorithm is employed to simulate the posterior distributions and verify the MEW Bayes estimators. We examined the behavior of the MEW model on two data sets with bathtub-shaped HR and compare it with five other popular bathtub-shaped methodologies. The results indicate that the MEW model provided the best description of the two failure time data sets, suggesting that the proposed model could be a viable candidate for solving various real-life problems.