Reliability analysis based on a random-effect Wiener process degradation model

In engineering practice, the initial performance degradation value of many products shows indeterminacy. In such a situation, a random-effect Wiener process degradation model, which simultaneously considers the initial degradation value and the drift coefficient as random variables, is proposed for reliability analysis. Then, on the concept of the first hitting time, the analytic expressions of the probability distribution function and the probability density function are derived. Moreover, maximum likelihood estimations of the parameters in the proposed model are constructed. Finally, an illustrate example involving magneto-optical data storage disk is adopted to illustrate the reasonability and efficiency of the proposed model. Meanwhile, for comparison, the path degradation model with random effects is considered as the reference method, and the comparative results demonstrate that the estimation accuracy of the proposed model is higher and the modeling procedure is more reasonable.