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With the increasing requirement of safety and economy of equipment operation, more and more attention is paid to the prediction of remaining useful life(RUL). Scholars in various fields have conducted extensive research on this issue, including aerospace field [1, 17] , electronics [28], mechanical industrial [16, 22] , and many other fields [7, 20]. Most researchers devoted to improve the accuracy of the prediction results, and have investigated many effective methods for RUL prediction, including various neural networks (NN) [41], support vector regression (SVR) [34], stochastic process [13, 36], and other methods[3, 21]. Ramezani, Moini and Riahi [27] gives a comprehensive summary to various methods. However, the uncertainty of RUL prediction is still an inevitable problem remaining to be solved. For most mechanical systems, the actual degradation level is not directly observable and can only be inferenced by running data. Inescapably, uncertainty is infused to the resulting degradation status with the inference process, and makes RUL prediction result under the inferenced degradation status lack credibility in maintenance guiding. Considering this problem, scholars have studied and put forward some contributing methods[14, 24, 38]. Sankararaman and Goebel [30] suggests that the perfectly and precisely prediction of engineering systems behavior is not possible in practical engineering applications due to prognostics uncertainty, and divided the sources of uncertainty into four categories: present state uncertainty, future uncertainty, modeling uncertainty and prediction method uncertainty. Some researchers believe that the single value prediction of RUL is meaningless, even deceptive, what is really needed for decision-making is the prediction interval or probability distribution [11, 29, 32]. To reduce the uncertainty of RUL prediction, Sun, Zuo, Wang and Pecht [33] proposed a state space degradation model based method with combining online monitoring data. To reduce the impact of prediction method uncertainty, Baraldi, Mangili and Zio [2] fused the predicted results of two methods with belief function theory. Actually, the present state uncertainty and future uncertainty is time dependent. Engel, Gilmartin, Bongort and Hess [9] have demonstrated that with the reduction of residual life, the accuracy of the prediction increases and the uncertainty decreases. To reduce the uncertainty of later prediction, Deng, Bucchianico and Pechenizkiy [6] applied surrogate Wiener propagation model to RUL prediction to make later prediction more accurate by sacrificing the early prediction accuracy. Keywords

Prognostics uncertainty reduction by right-time prediction of remaining useful life based on hidden Markov model and proportional hazard model