Int J Performability Eng ›› 2013, Vol. 9 ›› Issue (5): 569-579.doi: 10.23940/ijpe.13.5.p569.mag

• Original articles • Previous Articles    

Two Methods to Estimate the Change Points of a Bathtub Curve


  1. Faculty of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114, CHINA


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.

Received on February 10, 2013, revised on June 20, 2013
References: 16