Reliability Inference for the Wiener Degeneration Model with Measurement Errors

This paper mainly studies the accurate reliability inference of Wiener process with measurement errors. A test statistic is proposed to judge whether there is measurement error among the population. By constructing some pivotal quantities, the exact confidence intervals of diffusion parameters, the generalized confidence intervals of other model parameters, and the quantiles of life and reliability function are given. Furthermore, the generalized prediction interval of future degradation level is derived. In order to evaluate the performance of the proposed inference method, some simulation results are studied. Finally, two examples are given to illustrate the applicability of the proposed procedure.