The bivariate exponentiated additive Weibull distribution and its multivariate extension with applications

Abstract

Recently, Abd EL-Baset and Ghazal (2020) introduced the exponentiated additive Weibull distribution, which is very useful in modeling the reliability analysis of a product, such as reliability of decision-making and cost–benefit analysis. The products inherently decay with usage and age, resulting in more extreme failures. Fixing a failed product may take longer warranty servicing time, indicating that failure and warranty servicing times correlate to bivariate distributions. This paper introduces a bivariate exponentiated additive Weibull distribution such that the marginals have exponentiated additive Weibull distributions. Statistical properties, parameter estimation using the maximum likelihood, and the bootstrap confidence interval are presented. We also generalize the results for the multivariate case. A simulation study has been executed to evaluate the performance of the parameter estimation via mean square error and absolute bias. Finally, we use three datasets failure and warranty servicing times, American football league, and the air quality to compare the proposed bivariate model to other models. The results revealed that the proposed bivariate model delivers a better fit than other models.