## 1 Introduction
[15] established the joint optimization model of imperfect opportunistic maintenance based on dynamic time window and spare parts inventory. The effectiveness and superiority of the proposed method is demonstrated through a numerical example. [PERSON] et al. [16] considered both economic and structural dependencies when conducting opportunistic maintenance, and the first opportunistic maintenance threshold \(eR_{o}\) is defined to determine whether the component needs maintenance from the perspective of economic dependency. At the same time, the second opportunistic maintenance threshold \(sR_{o}\) is defined to determine whether components on the disassembly path need to be maintained through this opportunity. This threshold and opportunistic maintenance are considered from the perspective of structural dependency. The degradation of components is considered a gamma process, and disassembly can cause an impact on the components, resulting in a degradation increment. [PERSON] et al. [17] proposed an imperfect maintenance-opportunistic maintenance strategy and applied it to CNC lathe, using the decreasing service life factor and increasing failure rate factor to update the unit failure rate after maintenance. [PERSON] and [PERSON]. [18] considered the opportunistic maintenance strategy for power equipment. The article assumed that the deterioration of the power equipment transmission bay is a homogeneous Markov process. The expected costs were calculated based on this, and as the optimization objective, the optimal inspection rate was obtained. The case study in the article demonstrates that using the proposed opportunistic maintenance can save costs and improve availability. [PERSON] et al. [19] optimizes the opportunistic maintenance strategy for multi-unit systems, considering the heterogeneity of unit-level maintenance strategies and the imperfect nature of preventive maintenance. An optimization model for preventive opportunistic maintenance strategies is established, along with a Monte Carlo simulation-based optimization algorithm, offering a novel approach for maintenance strategy formulation of complex electromechanical equipment. The effectiveness and superiority of the proposed model in reducing maintenance costs are demonstrated through a case study on a CNC gear grinding machine. [PERSON] et al. [20] proposed an opportunistic maintenance strategy for a two-unit series system. The life distribution of component B follows an exponential distribution. Component A has a self-healing mechanism, and impact can cause its state to degrade. The failure of component B will create opportunities for component A to repair. The comparison between the strategy of using only preventive maintenance in the article proves that using opportunistic maintenance can save costs. [PERSON] et al. [21] studied the opportunistic maintenance of the catenary system of high-speed railways, with a focus on selecting proper reliability margins. [PERSON] and [PERSON] [22] started with the actual maintenance of offshore wind farms, considering the impact of wind speed on maintenance accessibility. Based on the traditional failure rate model, the wind turbine state is determined by the effective age. For opportunistic maintenance, event-based opportunistic maintenance generated by environmental impacts, failure-based opportunistic maintenance, and age-based opportunistic maintenance are included. All three types of opportunistic maintenance contribute to cost reduction. [PERSON] et al. [23] also studied the opportunistic maintenance strategy for offshore wind turbines and demonstrated the effectiveness of opportunistic maintenance. The above literature and other studies not mentioned have demonstrated the usefulness of opportunistic maintenance policies. This article aims to study the opportunistic maintenance strategy of machining centers in order to improve their availability, avoid frequent failures in the production process, and reduce operating costs.