Degradation models and design of accelerated degradation testing plans

In this dissertation, we first develop a novel degradation-rate-based model called Geometric Brownian Motion Degradation Rate (GBMDR) model. The model enables us to predict the population reliability metric of a product using population degradation data. To this end, a three-step statistical inference procedure is developed to estimate the model parameters from the degradation data including measurement errors. The model and the inference procedure are also utilized to predict the residual life of an individual unit in service, which is very important for the determination of an optimal maintenance policy. Moreover, by relating the model parameters to the explanatory covariates (stresses), the model is extended to a new accelerated degradation testing (ADT) model, referred to as Accelerated Geometric Brownian Motion Degradation Rate (AGBMDR) model, which utilizes degradation data obtained in ADT experiments to predict the reliability under normal operating conditions.;Furthermore, the problem of the optimum design of ADT plans is investigated. The design of optimum ADT plans helps to improve estimation accuracy of a degradation model. We propose the first optimum degradation-rate-based ADT plan based on the AGBMDR model to further refine the reliability inference procedure. The proposed optimum testing plan belongs to a D-optimal plan, which is a general ADT plan for various engineering applications.;The fourth extensive study in this dissertation is motivated by the industry's need in predicting reliability accurately under the uncertainties of the field conditions. In general, the reliability of a product may not be robust to stress variations under use conditions. If the stochastic nature of use conditions is ignored, the estimation accuracy of a reliability model may be significantly influenced. Consequently, this will influence other analyses such as system reliability estimate and maintenance plans. We propose an approximation procedure that extends the Brownian motion with drift model and the AGBMDR model to incorporate the variations of stresses. Some aging properties of a product such as the acceleration effects under the stochastic stresses are also derived and verified by extensive simulation studies. The methodology is proved to be a powerful tool in relating ADT experiments to field applications.