Degradation Data Analysis Using a Wiener Degradation Model With Three-Source Uncertainties

The degradation data have been widely applied in reliability analysis for deteriorating systems. However, the degradation data are usually contaminated by measurement errors that can severely affect the life estimation performance. This paper presents a degradation modeling and life estimation method using a Wiener degradation model by taking temporal uncertainty, measurement uncertainty, and unit-to-unit heterogeneity into account. The truncated normal distribution is employed to characterize the unit-to-unit heterogeneity in a population due to the fact that the degradation rates of many systems often manifest as positive values. The exact and explicit expressions of the life distribution are derived in the sense of the first hitting time by considering three kinds of uncertainties. The expectation maximization algorithm is used to estimate the model parameters because the resulting likelihood function includes hidden variables, which improves the estimation efficiency compared with the existing maximum likelihood estimation procedure. The effectiveness of the proposed approach is validated through a simulation example and a case study involving the degradation dataset of the LED.