Statistical inference and accelerated degradation testing plan for general use conditions

Accelerated degradation testing (ADT) is usually conducted to provide timely reliability information of a product without waiting for actual failures to occur. Based on an appropriate ADT model and carefully designed ADT experiments, failure time distribution can be statistically inferred. Subsequently, accurate reliability prediction under use conditions can be made as long as the use conditions are deterministic in time, or the product is robust to the stress variations in service. However, in numerous cases, an accurate prediction cannot be achieved if the stochastic nature of the field stresses is ignored either in the ADT model or in the experimental design procedure. The existing models and experimental design methodology in the literature are effective for estimating reliability indices under deterministic stress scenario but they are ineffective for field applications involving stochastic stresses. In this paper, we present an ADT model which extends the Brownian motion model to predict field reliability. The model takes into account the effects of the variations of applied stresses on products' degradation behavior. Several results regarding the accelerating effect and decelerating effect jointly determined by stress variations and acceleration models are addressed. Based on the degradation model, we demonstrate the methodology to infer field reliability. The effectiveness and robustness of the estimation procedure is validated by a simulation study where various distributions of field stresses are considered. In order to improve the efficiency of an ADT experiment, the problem of planning ADT experiment is investigated based on the proposed model. The presented optimum experimental design procedure distinguishes itself from those procedures that simply assume deterministic use conditions. It is the first ADT experimental design for general use conditions. Most importantly, it could be shown that considering the stochastic nature of general use conditions may lead to significantly different ADT plans, compared to those plans designed for deterministic use conditions. For demonstration, we design an optimum ADT plan that minimizes the asymptotic variance of the estimate of mean time to failure (MTTF) under general stochastic use conditions. Moreover, a case study is provided where light emitting diodes are tested under elevated temperature and applied electric current. It demonstrates the practical use of the proposed statistical inference and experimental design methodology in analyzing ADT.