Degradation Models With Wiener Diffusion Processes Under Calibrations

In this paper, two degradation models are developed in terms of degradation signals of systems with some Wiener diffusion processes under pre-specified periodical calibrations. Some detailed results on two models are given by solving some recursive equations. The system reliability is defined as the probability that the degradation signals do not exceed a threshold value by time t. Two methods for getting the system reliability are presented: one is a stochastic process-based method in terms of recent results on the distribution of the first passage time, and the other is based on partial differential equations with absorbing boundary conditions. The moments of lifetime (first passage time) also are given based on both methods. Some extended questions and results are discussed for more general situations, and finally discussions and conclusions are presented.