Reliability Properties and Applications of Autorelevated Weibull Distribution

In this paper, we study the importance of a parsimonious transformation called autorelevation transform in constructing new lifetime models having flexible hazard rate function. By considering the Weibull baseline, we introduce the autorelevated Weibull distribution. The autorelevated Weibull distribution (ARW) model has increasing, decreasing, and upside-down bathtub shapes for the hazard rate function. Various properties of the ARW are studied, including quantiles, moment generating function, moments, and conditional moments. The aging and ordering properties of the ARW model are studied, and we establish its connection with the baseline model. Stress strength reliability analysis has been carried out. To estimate the unknown parameters of the proposed model, we consider the maximum likelihood method, method of least squares, weighted least squares, and the Cramer–von Mises method. Further, we provide asymptotic and bootstrap confidence intervals for the ARW parameters. A detailed simulation study has been employed to assess the performance of the estimators and confidence intervals. The proposed model is applied to two real-life datasets.