Modern products are usually designed with high reliability and have complex structures, and degradation analysis of the complex systems with two or multiple performance characteristics is still a challenge. In this paper, we propose a new bivariate degradation model based on the Wiener process. There are three main merits of the proposed model: it can describe the common factor affecting the degradation of the two performance characteristics and unit-to-unit variation simultaneously, the reliability functions of the system and the remaining useful life of the system have analytic forms, and the model parameters and the missing values can be estimated by the Bayesian method and data augmentation. The simulation study and data analysis show that the Bayesian method and the proposed model have satisfactory performance.

Degradation test is an effective method in assessing product reliability when measurements of degradation leading to failure can be observed. The accuracy of reliability inference in degradation analysis highly depends on the fitted model to the observed degradation data. Sometimes, observed degradation paths of the products exhibit multiphase pattern over the testing period. In this paper, we propose a change-point Wiener process with measurement errors (CPWPME) to fit two-phase degradation paths of organic light-emitting diodes (OLEDs). We assume the unit-specific parameters of the CPWPME model by using hierarchical Bayesian method. Based upon the proposed approach, the failure-time distribution and the remaining useful life distribution along with mean time to failure and mean residual life function are derived in closed form. A simulation study shows the utility of the proposed CPWPME model and the validity of the hierarchical Bayesian approach for the degradation data possessing two-phase degradation characteristics. In the analysis of OLED degradation data, the hierarchical Bayesian CPWPME model provides higher modeling flexibility and prediction power for future testing units than existing three degradation models.

In the field of reliability engineering, the gamma process plays an important role in modeling degradation processes. However, extracting lifetime information from product degradation observations has long been suffering from both ineffective modeling techniques and inefficient statistical inference methods. To overcome these challenges, we propose a reparameterized gamma process with random effects in this article. Compared with the classical gamma process, the proposed model has a more intuitive physical interpretation. In addition, statistical inference for the model can be readily done through the variational Bayesian algorithm. Combining with the Gauss–Hermite quadrature and the Laplace approximation, the algorithm yields closed-form variational posteriors for the proposed model. Its superiority over two other inference methods (expectation maximization and Monte Carlo Markov Chain) in terms of computational efficiency and estimation accuracy is demonstrated by simulation.