## 2 Research Methodology
### Multistate Markov Chain Model
#### 2.1.2 Multistate Markov Chain Model of Electromechanical Systems  
The Markov chain, as a mathematical method, can play a role in equipment fault prediction and maintenance planning [23]. The key is to describe the transition between states and its corresponding probability [24]. In this study, the basic process of the Markov chain is applied to the field of highway mechanical and electrical equipment management,and the equipment state is divided into normal operation state, slight fault state, general fault state, and serious fault state. By considering the situation of daily maintenance and analyzing the transfer probability between equipment states, a Markov fault prediction model of multistate electromechanical systems, considering maintenance, is proposed. This model is used to analyze the probability of occurrence in various states of the electromechanical system in the future and to propose maintenance strategies. In the fault prediction of the mechanical and electrical equipment of expressways in the outer field, the Markov model of regular operation and faults can be used to simulate the operation process of the highways' mechanical and electrical equipment. This model is shown in Figure 2, where \(S_{0}\) represents the normal running state of the equipment; \(S_{\mathrm{F}}\) represents the failure status of the equipment; and \(\lambda\) and \(\mu\) represent the failure rate and repair completion rate of the equipment, respectively. According to the abovementioned model, the fundamental failure rate of the electromechanical system can be calculated. However, the process of operation and maintenance of highway mechanical and electrical equipment is not limited to simple regular operation and fault state. It may include parts maintenance (such as minor failure), overall equipment replacement (such as severe failure), and other situations. This study extends the Markov chain model of two basic states to a multistate model, as shown in Figure 3, to better reflect the operation and maintenance status of highway mechanical and electrical equipment. In the absence of any maintenance policy, the equipment state will follow the Markov chain transfer from \(S_{0}\) to \(S_{\mathrm{F}}\) until a severe failure occurs; that is, it enters the \(S_{\mathrm{F}}\) state. Measures such as maintenance and replacement are needed to restore the equipment to its intact state, \(S_{0}\). In Figure 4, \(S_{0}\) represents the normal state of electromechanical equipment, \(S_{1}\) and \(S_{2}\) represent the slight and general fault states of electromechanical equipment, and \(S_{\mathrm{F}}\) represents the serious fault state of highway electromechanical equipment, which requires the replacement of the main parts of the faulty equipment or the replacement of the entire equipment to restore the regular operation of the electromechanical system. \(I_{0}\), \(I_{1}\), and \(I_{2}\) represent the equipment in the state of inspection. In addition, in the state classification of equipment faults, safety elements need to be put in the first place, and if equipment failures can affect highway traffic safety, then no matter what state the equipment is in, it should be regarded as a serious fault state, so as to warn the staff to deal with it immediately. Furthermore, \(\lambda_{01}\), \(\lambda_{12}\), \(\lambda_{2F}\), \(\lambda_{1}\), \(\mu_{100}\), \(\mu_{110}\), \(\mu_{120}\), and \(\mu_{IF0}\) are the state transfer rates of  
Figure 3: Multistate Markov chain model of electromechanical equipment. Figure 2: Markov chain model of two states of highway mechanical and electrical equipment. mechanical and electrical equipment. This study assumes that two kinds of maintenance methods are adopted, minor maintenance and deep maintenance. The process from \(I_{1}\) to \(S_{0}\) is the process of minor maintenance, and \(\mu_{I10}\) represents the completion rate of minor maintenance. The process from \(I_{2}\) to \(S_{0}\) is the process of deep maintenance, and \(\mu_{I20}\) represents the completion rate of deep maintenance.