Machine reliability is one major concern in manufacturing industries, which is affected by interior degradation and outside shocks simultaneously. Low-quality feedstocks, as one typical kind of shocks, may arrive randomly during the operation of a machine. However, due to the instability of environment and manufacturing factors, low-quality feedstocks may arrive in clusters in some specific batches. In this paper, we first proposed a reliability evaluation model for the repairable machine, accounting for machine degradation and shocks caused by low-quality feedstocks. Then, the cluster arrival of low-quality feedstocks is modeled by the Hawkes point process with the properties of self-exciting and history dependent. Moreover, considering the degradation and shocks, the mixture failure rate of a machine is modeled. Further, the expectation of remaining lifetime is derived. Finally, the simulation experiment is implemented to compare the performance between the machine when the arrival intervals of low-quality feedstocks follow the Poisson point process and the Hawkes point process. Experimental results show the effectiveness of the proposed model for machine reliability analysis.