## 2 Literature Review
The authors of [25] fit the condition observed for community buildings into a gamma distribution curve, and accordingly developed a stochastic model that predicts the reliability of building components and gets calibrated using incremental observations. Moreover, [26] implemented a Weibull distribution model to plot the failure survival curves of heating, ventilation and air conditioning (HVAC) equipment in hospital buildings in order to contribute to a minimization of the wastage expected in the assets' useful lives and accordingly guide facility management personnel towards decision-making on scheduling the actions to restore the condition of the equipment. On the other hand, state-based models estimate the probability of transition of the asset components from one state to another within a specific time frame. Markov chain-based methodologies are the most widely used within state-based deterioration prediction models due to their demonstrated validity in modeling complex settings such as building facilities [27]. Markovian models are described as being \"memoryless\" given their sole dependence on the current observed condition level to predict the future state of the asset component regardless of the previous states experienced. The probability of a building component transforming from state to another is determined by means of expert judgement and/or the accumulation of empirical observation instances often illustrated in a matrix format. The matrix obtained from the previously described procedure is called a \"Transition Probability Matrix (TPM)\". Consequently, a future condition for a building component can be deduced from the multiplication of its current condition vector and the TPM. The majority of the previously developed Markovian models assume time homogeneity to ease the design and calculations involved in developing the model, which entails that the transition probabilities remain unchanged over the service life of the asset which is not a realistic estimate. Nevertheless, a major advantage linked with the usage of Markovian models is their ability to tackle and decrease the uncertainties in the initial condition estimation as well as the errors in assessment and applied stresses on building components. Markovian models have been applied on a variety of asset types including complex hierarchical structures, such as buildings and healthcare facilities, as well as linear networks such as water networks, bridges and pavements [25]. On the contrary, drawbacks correlated with the usage of Markovian models include the subjectivity associated with the assumption of probability distributions [17], which is a limitation this study is aiming to overcome. In a building deterioration prediction context, [28] proposed a Markovian model to estimate the deterioration experienced in community buildings in Australia. They calibrated the transition probability matrices utilized as part of their model by using a nonlinear optimization to minimize the difference between the expected and observed values of building components' condition levels. Another model developed as part of the study by [25] uses the factors outlined in the International Standards Organization's (ISO) method as a base for designing a Markovian model that determines the effect of several variables on the building assets' deterioration patterns over a predetermined duration. Finally, [27] designed a semi-Markov model based on the condition assessment data gathered from the building assets owned by the U.S. Department of Defense (DoD) to estimate the future condition level anticipated, taking into account the previous observed condition state for each component as well as the time elapsed between inspections.