Estimating degradation by a Wiener diffusion process subject to measurement error

Most materials and components degrade physically before they fail. Engineering degradation tests are designed to measure these degradation processes. Measurements in the tests reflect the inherent randomness of degradation itself as well as measurement errors created by imperfect instruments, procedures and environments. This paper describes a statistical model for measured degradation data that takes both sources of variation into account. The degradation process in the model is taken to be a Wiener diffusion process. The measurement errors are assumed to be independent normal random outcomes that are independent of the degradation process. The paper describes inference procedures for the model and discusses some practical issues that must be considered in dealing with the statistical problem. A case study is presented.