## 1 Introduction  
Maintenance is one of the most critical activities in healthcare buildings since the safety of users and workers depends on its proper management [1]. It also entails considerable operating costs, mainly due to the high intensity of use of their facilities [2] and limits the productivity of an organization [3]. In addition, maintenance activities are an important source of knowledge management [4]. The Markov chain is a tool used to predict the degradation suffered by a system by simulating its stochastic degradation process [5]. The most appropriate maintenance policies for the systems studied can be determined with this tool [6]. Markov chains have been used as a simulation, decision making and engineering prediction technique [7]. However, despite being considered a suitable method for analysis, the hospital engineering sector does not appear to apply it that much [8]. Markov chains have also been useful in biomedical research in both animal and human experimentation, including but not limited to, blood pressure, the state of the patient during an illness and safety culture of health organizations [9], but have not been applied to the maintenance of healthcare buildings. Healthcare buildings are designed to develop promotion, prevention and rehabilitation actions related to primary healthcare, and differ from hospitals in that they do not have hospital beds and do not perform surgeries [10]; they are, therefore, smaller in size. These buildings are difficult to maintain [11] given their complex and costly facilities and equipment, the correct functioning of which conditionsthe quality of the services it provides [12]. Another factor is their locations, selected for their proximity to the patients they serve and consequently dispersed among them [13]. The operating status of these resources depends fundamentally on a suitable design of the facilities, the quality of construction, the use of electronic equipment and the efficiency of their maintenance [14]. The different locations of the healthcare buildings mean that the maintenance is conducted through patrol maintenance. This type of maintenance consists of a team of people who make periodic scheduled visits to each building and repair non-urgent breakdowns that have occurred between visits and perform preventive maintenance previously planned operations [15]. [PERSON], [PERSON], and [PERSON] (2007) applied the Markov chain to assess maintenance policies and reveal the best implementation method according to the outcome [16]. [PERSON], [PERSON], and [PERSON] (2016) analyzed the safety culture of a Mexican hospital using Markov chains but did not study the impact on maintenance [17]. [PERSON], et al. (2008) adapted the Markov model to the maintenance of facades made up of concrete panels [18]. [PERSON] and [PERSON] (2013) also conducted a study predicting the consumption of energy of the life cycle of a residential building using the stochastic modeling based on a Markovian model, optimizing different maintenance actions according to the replacement cost of the components based on a multi-objective index [19]. [PERSON] and [PERSON] (2016) determined the most suitable maintenance policy for medicinal gas distribution subsystems for the particular case of a general public hospital. They used Markov chains with the Measuring Attractiveness by a Categorical Based Evaluation Technique [20]. [PERSON] and [PERSON] (2005) suggested a semi-Markov decision process (SMDP) for the optimization of the preventive maintenance policy based on the condition, and they presented an approach for the joint optimization of the inspection rate and maintenance policy [21]. [PERSON], [PERSON], [PERSON], and [PERSON] (2019) developed a hidden Markov model with auto-correlated observations for the study of the degradation of the manufacturing systems and obtained more accurate predictive values by using auto-correlated observation. They also achieved an appropriate time evolution of the degradation processes [22].