Bayesian calculation of degradation-based burn-in policy for heterogeneous item under two-dimensional warranty

Abstract

Two-dimensional (2D) warranty service has been greatly used in many heavy equipment and consumer durables. The items with 2D warranty are usually highly reliable and their heterogeneity is unavoidable. Degradation-based failure model is often used to characterize failure modes for highly reliable items. This paper proposes a degradation-based burn-in model for heterogeneous items with renewing 2D warranty. We consider that the degradation of item is modeled through the inverse Gaussian process and that the item is replaced by a new one as soon as it fails within warranty period. We screen the items based on the degradation information of the items during burn-in to enhance the reliability of items passed burn-in. The models based on performance and cost are proposed to analyze the burn-in procedures from different perspectives. Firstly, we investigate the properties of the optimal policies for the three burn-in models. Secondly, we further present a Bayesian method to solve the uncertainty of parameters in the model. The Bayesian method allows us to incorporate prior knowledge and update our beliefs based on observed data, providing more accurate and reliable estimates. Finally, we give an example of the gallium arsenide laser devices to illustrate the benefits of proposed model and method.