Weibull Distribution with Linear Shape Function

The main goal of the paper is to present a new, two-version flexible distribution that is a modification of the Weibull lifetime model. An innovative idea is to replace the Weibull shape parameter with a shape function. An additional goal is to propose an estimation method that measures the absolute values of the differences between the empirical and theoretical reliability functions. An extensive literature review is performed on 165 generalizations of the Weibull distribution, considering modalities and shapes of the hazard rate function (HRF). Properties of the proposed distribution and real data examples of the application of our proposal are presented. Cumulative failure functions of the bimodal models with a bathtub HRF are given.