## 3 Literature Review  
Pipeline maintenance requires assessing the progression of defects followed by implementing optimal maintenance operations. The pipeline's condition at the time of maintenance is crucial in determining the type as well as the cost of operation. This maintenance policy is commonly referred to as condition-based maintenance (CBM) in the literature. [PERSON] et al. (2015) defined three different condition-based maintenance approaches based on the methods used to determine the pipe states: model-based (adopt a mathematical model), knowledge-based (leverage available data using different artificial intelligence algorithms), and parameter-based (measure the pipe's operational characteristics). The assessments can be performed on periodic or non-periodic time bases. The implementation of CBM using Markov processes has been observed in several studies. The existing model formulations considered corrosion processes, the resulting failure, maintenance/inspection intervals, and optimal maintenance operations to mitigate the damage due to corrosion. For example, [PERSON], et al. (2015) studied a pure birth process with Kolmogorov's forward equation to generate the transition probability for a Markov process modeling of pitting corrosion. [PERSON], et al. (2016) demonstrated the effectiveness of a Markov chain model in predicting pitting corrosion growth. The study compared the result of the model to a fitted distribution function for the pipeline deterioration historical data. [PERSON] and [PERSON] (2016) presented a pure birth Markov model to predict pit corrosion depth using negative binomial distribution for transition probability formulated based on different factors (pit depths, temperatures, CO2 partial pressures, pH, and flow rates). [PERSON], et al. (2014) modeled the cumulative damage due to the propagation of internal corrosion (formulated with exponential functions) using the Markov chain to predict failure. It adopted Bernoulli trials and probability to make transition decisions. [PERSON], [PERSON], and [PERSON] (2016) proposed a Markov model for determining the inspection interval of stormwater pipes. A Markov model was developed to emulate the pipe deterioration process, which was incorporated into a simulation model to run different maintenance planning scenarios. [PERSON], et al. (2017) presented a Markov chain sewer pipe degradation model with single and multi-transition chains. Sequential Least-Squares Programming optimized the parameter for the Markov chain model by minimizing the root mean weighted square error. [PERSON], et al. (2018) integrated a machine-learning algorithm with the Markov chain and set pair theory to determine the reliability of anticorrosion coating. The model evaluated the change in the properties of the coating layer to establish its grade and effectiveness. MDP and POMDP models have been recently adopted for maintenance-related optimization problems in the oil and gas industry. [PERSON], et al. (2016) and [PERSON], et al. (2016) proposed MDP models to optimize maintenance actions. The degradation of pipelines based on physical attributes was determined using Monte Carlo simulation and non-stationary Gamma distribution models, respectively. The articles employed ILI and simulation data pipeline states assessment. [PERSON], et al. (2019) discussed the application of unmanned vehicles as an inspection tool and implemented MDP as a maintenance optimization model. [PERSON], et al. (2018) and [PERSON], et al. (2017) demonstrated the implementation of the POMDP for two different optimization problems. [PERSON], et al. (2018) optimized maintenance action along with some economic analysis for gas transmission networks. [PERSON], et al. (2017) focused on the maintenance action considering partially observed states with ILI inspection errors. Most Markov-based maintenance optimization models assumed that the deterioration state of the pipeline could be accurately observed.