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With integrated equipment health prognosis,both physical models and condition monitoring data are utilized to achieve more accurate prediction of equipment remaining useful life (RUL).In this paper,an integrated prognostics method is proposed to account for two important factors which were not considered before,the uncertainty in crack initiation time (CIT) and the shock in the degradation.Prognostics tools are used for RUL prediction starting from the CIT.However,there is uncertainty in CIT due to the limited capability of existing fault detection tools,and such uncertainty has not been explicitly considered in the literature for integrated prognosis.A shock causes a sudden damage increase and creates a jump in the degradation path,which shortens the total lifetime,and it has not been considered before in the integrated prognostics framework either.In the proposed integrated prognostics method,CIT is considered as an uncertain parameter,which is updated using condition monitoring data.To deal with the sudden damage increase and reduction of total lifetime,a virtual gradual degradation path with an earlier CIT is introduced in the proposed method.In this way,the effect of shock is captured through identifying an appropriate CIT.Examples of gear prognostics are given to demonstrate the effectiveness of the proposed method.