The additive Perks distribution and its applications in reliability analysis

In this paper, the Additive Perks Distribution (ADP) is presented; this distribution describes the behavior of the bathtub curve, which is one of the most deeply rooted concepts in reliability analysis. The proposed distribution is based on the sum of the positive and negative hazard rate functions of the Perks distribution. ADP's statistical properties include Measures of Central Tendency, moments, moment generating function, statistical order, residual lifetime, reversed residual lifetime, Renyi entropy, time-varying, and life-stress relationship modeling presented. For estimating the ADP parameters, the Maximum Likelihood Method is used. On the other hand, the APD is tested in three case studies and compared with other distributions that can describe the failure rates in a bathtub curve. The results from the case studies showed that the APD is a good choice for describing the failure times in the shape of a bathtub curve.