Weibull Lindley distribution

Abstract

In reliability systems, there are known two types of systems namely series systems and parallel systems. In the series system, failure will occur if any of the possible events happen. Applications of the series system analysis also varies from inspecting the durability of manufactured products to examining diseases in human. Therefore, several distributions have been introduced to model failure data in series system. However, these distributions cannot model data with bathtub shaped hazard function even though it is the one mostly found in real life situation. As a result, distribution which can model lifetime data in series system with bathtub-shaped hazard function has to be developed. In real life application, there is condition where failure could occur caused by several independent events and has a bathtub shaped hazard function, for example engineering cases and competing risk. Weibull Lindley distribution, which was introduced by Asgharzadeh et al. (2018), is developed to solve the problem. As Weibull Lindley distribution describes lifetime data of an object that can experience failure caused by 2 possible events. It can model data with increasing, decreasing and bathtub shaped hazard function. Asgharzadeh et al. (2018) only show the modeling of Weibull Lindley distribution in medical field which is competing risk data. This paper discusses the process of forming the Weibull Lindley distribution, its properties and parameter estimation using the maximum likelihood method. In addition, the application of Weibull Lindley distribution in engineering field which is the lifetime data of machine consists of two independent components paired in series also be discussed.