Two methods to estimate the change points of a bathtub curve

The failure rate function of non-repairable components can be bathtub shaped. Two change points can be defined for a bathtub failure rate curve, which can be viewed as the partition points between the early use, normal use and wear-out phases. There is practical significance to determine the change points, and several non-parametric methods have been developed for this purpose. This paper presents two parametric methods to determine the change points of the bathtub curve. The proposed methods are based on a bathtub curve model with a finite support. A maximum likelihood method with a constraint is developed to estimate the parameters of this model. The methods are illustrated by three real-world examples. © RAMS Consultants.