## 4 Formulation of an Operation and Maintenance Strategy for Equipment with a High Failure Rate
### Data Processing and Fault Prediction
#### 4.1.2 Operation and Maintenance Strategy Formulation  
Taking Formula (12) as the initial state, Formula (13) is calculated with MATLAB R2022a to calculate the steady-state probability of each failure state of the video surveillance equipment without considering the overmaintenance strategy, as shown in Equation (14):  
\[\Pi=[0.0346,0.0130,0.9514,0.0010,0,0,0] \tag{14}\]  
It can be seen that without implementing the maintenance strategy, only 3.46% of the video surveillance equipment in these sections can remain in a normal state over time. In comparison, 95.14% of the video surveillance equipment without regular maintenance will begin to have problems such as unstable signals, occasional stutters, and inability to transmit pictures, which will significantly affect the regular operation of the mechanical and electrical system and bring great trouble to the monitoring personnel. The corresponding time and resources must be invested when considering the maintenance situation. Subject to the standard working hours system, an individual staff member's total statutory working hours are approximately 176 h in a natural month. Video surveillance equipment can maintain the most efficient and regular operation by strictly following the maintenance strategy. This study adopts a step-by-step method, taking one person-hour (1 h) as the time unit and gradually increasing the frequency of maintenance until the most ideal maintenance measures are found to improve the operation efficiency of the equipment. According to different fault types and state changes, the video surveillance equipment's initial fault transfer rate can be obtained, from the normal to the fault state. As shown in Figure 7, the corresponding maintenance strategy solution matrix (15) is written as follows:\[P= \begin{bmatrix}1-(\lambda_{01}+\lambda_{I})&0.0275&0&0&\lambda_{I}&0&0\\ 0&1-(\lambda_{12}+\lambda_{I})&0.073&0&0&\lambda_{I}&0\\ 0&0&1-(\lambda_{2F}+\lambda_{I})&0.001&0&0&\lambda_{I}\\ 1&0&0&1-\mu_{F0}&0&0&0\\ 0.9725&0.0275&0&0&1-(\lambda_{01}+\mu_{100})&0&0\\ 0.927&0&0.0730&0&0&1-(\lambda_{12}+\mu_{10})&0\\ 0.999&0&0&0.001&0&0&1-(\lambda_{2F}+\mu_{I20})\end{bmatrix}  \tag{15}\]  
The ratio of monthly maintenance hours to monthly legal working hours is set as the inspection frequency of the maintenance strategy. Among them, the daily legal working hours \(T_{legal}\) is calculated according to the \"measures for the preparation of budgetary estimates for Highway Construction projects\" (JTG3830-2018), and the number of monthly working days is 22. That is,  
\[\lambda_{I}=\frac{t}{T_{legal}} \tag{16}\]  
By substituting Formula (16) into the strategic maintenance matrix of the video surveillance equipment and solving its steady-state value, it can be concluded that when the monthly maintenance time is 29 person-hours, that is, when the maintenance frequency is 0.1648, the standard running state value of the long-term operation of the video surveillance equipment reaches the peak, which is 71.31%. The trend of each state of this kind of equipment changing with the maintenance time is shown in Figure 8.  
Figure 8: Trend chart of the steady-state probability of video surveillance equipment. Figure 7: Initial state transfer rate diagram of video surveillance equipment. The state transition matrix under the inspection policy is shown in Table 4.  
The steady-state probability of each state under the maintenance strategy is as follows (Equation (17)):  
\[\Pi=[0.7131,0.0961,0.0493,0.0010,0.1175,0.0158,0.0081] \tag{17}\]  
Figure 8 shows that, in theory, when implementing the strategy of 29 person-hours per month for video surveillance equipment, not only can the operation stability of the video surveillance equipment reach the highest level under long-term operation, but also the probability of general failure (state \(S_{2}\)) of this kind of equipment can be significantly reduced.