Change points estimations of bathtub-shaped hazard functions

Abstract

The life data analysis has been finding increasing importance for every industry, resulting in higher quality and cost reduction in current fierce competitive market. The hazard function for life models have three distinct phases of burn-in, useful life and wear-out shown in the bath-tub curves. Change points estimation is important for bathtub-shaped hazard function models in reliability and life data analysis for the product developer and designers to have a relatively accurate estimation of the burn-in, useful life and onset of the wear-out life phases. The applications are for determination and assisting to plan appropriate burn-in, guarantee, maintenance, repair and replacement strategies. In this research, life time interval is studied for bathtub shaped hazard function. Two change points are calculated for burn-in and useful life phases, as well as useful life and wear out phases. Two criteria are used in this study for determination of the change point including (1) minimum of hazard function and (2) maximum change in slope of hazard function. This research is structured as a parametric approach with Bayesian inference utilized as the parameter estimation. The modified Weibull distribution are determined as the suitable models for simulation of all three life phases. In this paper, failure data of an electronic system case is used for the method demonstration.