Remaining useful life (RUL) prediction under time-varying operating conditions is critical to the prognostics and health management of rotating machinery. In the literature, both the degradation rate and variation of a machinery component are often assumed to be solely dependent on operating conditions. However, this strong assumption is usually violated in many industrial applications. In this article, a systematic method for RUL prediction for a rotating machinery component is developed by considering the joint dependency of degradation rate and variation on time-varying operating conditions. In particular, a system state function and an observation function are utilized to characterize the component's degradation process. A quantitative relationship between the drift and diffusion parameters is established to reflect their joint dependency on the operating conditions. A two-stage hybrid approach that jointly implements maximum likelihood estimation and least squares estimation methods is proposed to facilitate parameter estimation in model development based on offline degradation data, and a Bayesian algorithm based on online condition monitoring data is utilized for RUL prediction in online implementation. A simulation study and a real application to rolling element bearings are provided to illustrate the effectiveness of the proposed method in practice.

To obtain enough reliability information of highly reliable products, step-stress accelerated degradation test becomes more and more popular as it helps to shorten test duration and reduce sample size. A reasonable step-stress accelerated degradation test plan provides a possibility to predict product's lifetime precisely when it is designed by using an appropriate optimization criterion based on the valid degradation information. In this paper, we investigate the mechanism equivalence in designing an optimum step-stress accelerated degradation test plan under Wiener process. In particular, an algorithm for extracting valid test information is formulated based on degradation mechanism equivalence analysis. Then, we propose the M-optimality criterion to improve the mechanism equivalence of a step-stress accelerated degradation test when designing an optimum plan. Subject to the total cost constraint, a comparison is carried out between the optimum plan designed by using M-optimality criterion and other plans designed by using traditional criteria through the case of light intensity degradation of LEDs.

It is quite common to see that a unit of a product with a higher degradation rate also presents a more prominent dispersion. This phenomenon has motivated studies on developing new degradation models. In particular, a variety of Wiener process models have been developed by correlating the drift parameter and the diffusion parameter based on the statistical features of data. However, no insightful explanations are provided for such interesting correlations. In this article, degradation mechanism equivalence is first introduced based on the acceleration factor invariant principle, and the correlation between degradation rate and variation is explained using basic principles. Then, mechanism-equivalence-based Wiener process models, including a basic model and a random-effects model, are proposed to characterize such degradation behavior of a product. Analytical solutions for both point estimation and interval estimation of unknown model parameters are obtained using the maximum likelihood estimation method and an expectation–maximization algorithm. An extension of the proposed model that is able to handle accelerated degradation tests is developed. A simulation study and two real-world applications are provided to illustrate the effectiveness of the proposed models in product reliability estimation based on degradation data.

Mechanism equivalence analysis, focusing on the underlying quantitative relationship between degradation model parameters under different stress levels when the accelerated failure mechanism remains unchanged, has been developed and adopted widely in accelerated degradation tests (ADTs) over recent years. For a specific degradation process, the mechanism equivalence conditions can be derived based on the acceleration factor invariant principle and further utilized to test whether the accelerated failure mechanism remains unchanged or not under different stress levels. In this paper, a unified form of the mechanism equivalence conditions for commonly-used stochastic process models is derived based on Tweedie exponential dispersion process. The unified form can cover the conditions of Wiener, Gamma and inverse Gaussian processes, etc. Based on this, a complete procedure for mechanism equivalence test of ADT is proposed through the joint application of normality test and parameter hypothesis tests. In this way, the availability of the ADT data can be distinguished before using them for lifetime prediction of products. In addition, the effects caused by degradation model mis-specification and ADT data misuse are further analyzed from the perspective of relative error. A simulation example and two real-world case studies are used to demonstrate the effectiveness of the proposed methods.