## 2 Methods
\]  
The transition graph shown in Figure 2 and representing the system's degradation state was created considering the state transition probabilities of the matrix coefficients \([P]\):  
The system presents a gradual degradation, which means that the higher the state of the system, the probability of the system remaining in that state drops and the probability of it changing state increases. There are also several consecutive changes of states, for example, from state 2 to 4. There is less likelihood of this transition happening and is caused by several factors: emergencies that cause incidents during inspections or incidents that appear simultaneously before maintenance and that cause transitions to several states. In order to determine the most appropriate maintenance policy for healthcare centers, maintenance must be represented in a matrix form. [PERSON] et al. (2005) represented the maintenance strategy of the system in a matrix form ([PERSON] et al., 2005). They designed the maintenance policy for a seven-state Markov chain. So, the maximum allowed degradation state is state 4, from which the system degradation is not adequate. In addition, the selected maintenance strategy allows the system's degradation state to be improved to degradation state 2. Therefore, Equation (4) is expressed as follows:  
\[E_{n}=r\cdot\left(M\cdot P\right)^{n} \tag{4}\]  
Figure 1: Status transition matrix. Figure 2: System transition graph. This model is suitable, assuming that the maintenance is carried out soon after the inspection, without letting the system change state. Moreover, if the maintenance is not conducted, the system will enter an unacceptable state (Level 9), whereas if the relevant inspections and maintenance are carried out, the system should remain operative for long periods of time. Then, a study was conducted with Markov chains to choose the most suitable maintenance policy for each healthcare center. First, the maximum permitted degradation state was determined to reduce the array of options. For this study, a low degradation state was considered inappropriate for healthcare buildings. Therefore, the maximum state the system had to reach was 6, presenting a significant number of incidents as shown in Table 1. Healthcare centers are buildings designed to carry out Primary Health Care actions continuously 365 days a year. In this way, the state of degradation of a building should not damage the health and safety of the patients. For this reason, the maintenance policy selected must guarantee that the condition of the health centers does not reach state 6. The selection of the optimum maintenance policy for the system is focused on choosing state \(i\) that the system can reach, and once achieved, perform the corresponding maintenance to re-establish the ideal state \(j\). To this end, five maintenance policies were conducted, the results of which are collated in Table 2. Options 1 and 2 represent a maximum degradation state of 5 and 4, respectively, and after maintenance, the system returned to state 2. Options 3 and 4 admitted a maximum degradation state of 5 and 4 respectively, but these options returned to state 1 after maintenance. Lastly, option 5 considered the possibility of the system reaching the maximum degradation state of 5, but only returned to state 3 after maintenance.