Optimal design for step-stress accelerated test with random discrete stress elevating times based on gamma degradation process

摘要

Recently, a step-stress accelerated degradation test (SSADT) plan, in whichthe stress level is elevated when the degradation value of a product crosses apre-specified value, was proposed. The times of stress level elevating arerandom and vary from product to product. In this paper we extend this model toa more economic plan. The proposed extended model has two economical advantagescompared with the previous one. The first is that the times of stress levelelevating in the new model are identical for all products, which enable us touse only one chamber (oven) for testing all test units. The second is that, thenew method does not require continuous inspection and to elevate the stresslevel, it is not necessary for the experimenter to inspect the value of thedegradation continually. The new method decrease the cost of measurement andalso there is no need to use electronic sensors to detect the first passagetime of the degradation to the threshold value in the new method. We assumethat the degradation path follows a gamma process. The stress level is elevatedas soon as the measurement of the degradation of one of the test units, at oneof the specified times, exceeds the threshold value. Under the constraint thatthe total experimental cost does not exceed a pre-specified budget, the optimalsettings including the optimal threshold value, sample size, measurementfrequency and termination time are obtained by minimizing the asymptoticvariance of an estimated quantile of the lifetime distribution of the product.A case study is presented to illustrate the proposed method.