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In this paper we propose an objective Bayesian method to analyze the accelerated degradation model based on the new Wiener process stated in Ye, Chen, and Shen (Reliab. Eng. Syst. Safe., 2015, 139: 58–67). The Jeffreys prior and reference priors are derived after reparameterization, and the posterior properties under each prior are validated. A Metropolis random walk algorithm is then employed to generate samples from the posterior distributions, and a simulation study is carried out to reveal the frequentist properties of these priors. Finally, we apply the approach to a real data and obtain the mean-time-to-failure (MTTF) under the usage condition. [ABSTRACT FROM AUTHOR]