Dynamic linear degradation model: Dealing with heterogeneity in degradation paths

Abstract

General path models are usually considered to model degradation data. Their popularity is mainly due to the simplicity with which these models allow to represent different degradation mechanisms. Such models assumes that the functional form of the degradation path is common to all population and, in linear degradation models, it also assumes a time-invariant degradation rates for the units under test. This latter assumption is only reasonable if the devices constantly degrade over time. We introduce a dynamic linear degradation model to approach situations where the degradation paths do not regularly evolve through time. The proposed model assumes that degradation baselines and rates vary along time. This dynamic structure provides a local linear approximation for the true degradation path, which may assume different shapes. Inference for the failure times considers this sequential behavior and is discussed for future and under test units. We run a simulation study to evaluate the proposed model and to compare it to the Weibull linear degradation model. The laser emitters and Infrared Light-Emitting Diodes datasets are analyzed considering this new methodology. Results show that the proposed model is competitive and an useful approach to model degradation data that assume different shapes for the degradation paths.