Classical And Bayesian Inferences of a New Additive Weibull Extension Distribution with Application

Abstract

For the past few decades, many generalizations of Weibull distributions have been defined. The generalizations (modifications or extensions) are necessary to allow the resulting distributions provide a better fit for both monotones (increasing and decreasing) and non-monotone (formed like a bathtub-shaped and up-side-down bathtub) failure rate (FR) lifetime data sets available in the literature, which the classical Weibull distribution cannot model appropriately. In this article, another approach is adopted to extend the well-known additive Weibull (AddW) distribution to introduce a new five-parameter model named as generalized extended additive Weibull (GExAddW) distribution. The new model is constructed by re-defining the AddW model to a three-parameter model based on two alternate parametric forms of the Weibull reliability functions and then added two extra positive shape parameters to the resulting model to form the GExAddW distribution. Both classical and Bayesian inferences were carried out for the derived model. The GExAddW could be a viable candidate for modeling complex failure times. Moreover, with intricate nature of the model, we suggest using numerical approaches for its property’s computation. A detailed account of the distribution properties was presented. When modeling lifetime data with a non-monotonic failure rate shape, the GExAddW distribution fit the data better than alternative lifetime distributions.