Reliability analysis for step-stress accelerated degradation test subject to AR(1) measurement errors

The autocorrelation among measurement errors has been usually ignored in the traditional accelerated degradation modeling procedure. For this problem, a step-stress accelerated degradation model is proposed by simultaneously considering a first-order autoregressive (AR(1)) measurement error series for reliability analysis. The Wiener process is utilized to describe the performance degradation procedure, and an AR(1) model is adopted for modeling the measurement error term. In addition, the relation function between the drift parameter and the accelerated stress is also constructed. Meanwhile, a parameter in the accelerated relation function is randomized to characteristic the individual variation. Then, under the concept of the first hitting time, closed-forms of the probability density function and the distribution function are derived. Moreover, the maximum likelihood estimation method is used for estimating unknown parameters in the proposed model. Finally, a real application involving the GaAs laser is conducted to illustrate the validity and efficiency of the proposed model. Results show that compared with the reference methods, the proposed model shows a better fitting goodness and an enhanced accuracy, and so that it can provide a strong support for further maintenance decision making.