## 1 Introduction  
Pipelines transport a significant portion of the crude and refined products in the oil and gas industries. They constitute the major portion of assets in any organization operating in the industry since they are needed to transport products over a large span of distance. Due to the potential health and environmental hazards related to petroleum products, the integrity of pipelines must be maintained to the highest standards. Any pipeline damage would hinder the flow of products and affect the organization's earnings. Therefore, ensuring the proper operation and reliable state of the pipeline is essential, making inspection and maintenance operations crucial in the industry. Pipeline failure due to corrosion can be considered one of the major causes of integrity failures. Different inspection and maintenance operations are implemented to reduce the risk associated with these failures and prolong the service life of pipelines. These operations are optimized to meet the required safety level with the minimum cost, as they are not value-adding operations. This paper presents a continuous state partially observable Markov decision process (CSPOMDP) method to formulate a stochastic model for maintenance operations in the oil and gas industries. The MP has been adopted for modeling the pipeline corrosion process to predict the rate of degradation or failure [1; 2; 3; 4]. Extensions of this method, such as the Markov decision process (MDP) and partially observable Markov decision process (POMDP), have also been implemented to integrate maintenance operation optimization with corrosion degradation process formulation as well as deterioration rate (failure) prediction [5; 6; 7; 8]. In these Markov-based approaches, maintenance operations (actions) considered only the current deterioration state and not the event that led it. The transition probability matrix to the subsequent state is determined by the maintenance action selected. The reward is calculated based on the selected action to remedy the current state of the pipeline. In the case of MDP, the current state of the pipeline is defined with certainty, enabling a clear transition from one state to the next. When the pipeline's deterioration states can only be estimated (with some degree of accuracy), POMDP models are implemented to accommodate this constraint. States can be formulated as continuous or discrete values in MDP and POMDP. This study presents a CSPOMDP model to enhance the maintenance decision process for pipelines. First, it formulates the deterioration states of the pipeline as a defect depth expressed in the percentage of wall thickness. Actions comprise corrosion mitigation operations, including _inhibition_, _pigging_, _replacement_, and _do-nothing_. The source of uncertainty in determining the pipeline's current state is attributed to the errors emanating from the inspection method. Considering an inline inspection (ILI) method, detection, and false reading errors are integrated into the model. Specifically, these errors define the observation function, which formulates the variation (uncertainty) in reading the actual state of pipeline degradation due to corrosion. The cost of maintenance actions under different states describes the reward function of the model. Second, two algorithms, the partially observable Monte Carlo planning (POMCP) and anytime regularized determinized sparse partially observable tree (ARDESPOT), are selected to formulate and solve the problem. Numerical examples are presented to demonstrate the solution search and reporting protocols using Julia-based POMDP solvers [9]. Finally, the performance of different maintenance policies is evaluated using the model (example) to support decision-making. The proposed model applies stochastic attributes to POMDP elements to better represent the maintenance environments and decision-making process.