## 1 Introduction  
Pipeline networks are the most economical method of transporting oil and gas products at different stages of the production process [1]. They carry different products, which include crude oil, natural gas, and semi-processed and finished oil and gas products. These products are not only health hazards (flammable, poisonous) but also pose a serious environmental risk in the case of pipeline damage. Some of the causes for pipeline damage include corrosion, cracks, improper operation and maintenance, physical damage (accidents as a result of excavation, vehicle operation), and natural disasters. Corrosion ranks as one of the major causes of failure. According to the Association for Materials Protection and Performance (AMPP), the oil and gas industry loses $1.372 billion per year, of which $589 million (43%) is related to the pipeline distribution network [2]. A three-step procedure can be adopted to implement corrosion maintenance to pipelines in the industry [3]. The first step is to detect and identify corrosion by performing inspections, monitoring, or analysis. Information on the extent of the corrosion is collected using technical personnel, inline inspection (ILI) tools, non-destructive tests, and other evaluation methods. ILI, the most commonly used corrosion detection method, includes magnetic flux leakage (MFL--either circumferential or triaxial), Ultrasonic Tools (UTs), electromagnetic acoustic technology (EMAT), and eddy current testing (EC) [4]. In the second step, the pipeline's failure time is forecasted using corrosion growth rate (degradation) estimation methods. These methods comprise deterministic (such as single-value, linear, and nonlinear corrosion growth rate) and probabilistic (such as the Markov model--Markov process (MP), (partially observable) Markov decision process ((PO)MDP), Monte-Carlo simulation, time-dependent/independent generalized extreme value distribution, Gamma process, and Wiener process) models [4; 5]. Finally, maintenance objectives are optimized, including determining the best inspection intervals and efficient repair or replacement operations. Optimization tools include mathematical (exact) methods, heuristics and metaheuristics, and machine learning. [PERSON], [PERSON], and [PERSON] [6], [PERSON] et al. [7], and [PERSON] et al. [8] presented MDP models, whereas [PERSON] et al. [9] discussed a POMDP model for oil and gas pipeline-network-related problems. [PERSON], [PERSON], and [PERSON] [6] and [PERSON] et al. [7] proposed Monte Carlo simulation and non-stationary Gamma distribution models, respectively, for determining the degradation of pipelines based on physical attributes. These articles formulated pipeline states using data collected from ILI or simulation models. The MDP model was used to optimize the maintenance actions based on these states. [PERSON] et al. [8] discussed the implementation of the MDP models, where the states of the pipeline were determined by using unmanned vehicles for inspection. The research focused on the vehicles' proficiency in detecting corrosion along with its severity. [PERSON] et al. [9] demonstrated the implementation of the POMDP in the maintenance of gas transmission networks. It considered the network as a system with different states (defined by the degradation and future load of nodes in the network) that cannot be directly observed at any given time. Maintenance actions were optimized in addition to some economic analysis based on the accuracy of the model. This paper presents a model for the optimization of maintenance actions where ILI methods detect corrosion defects while the POMDP formulates the deterioration rate and respective maintenance action. The corrosion data collected through ILI is used to determine the transition intensity rates for equally spaced deterioration states. The intensity rate is used to calculate the transition probability, where [PERSON]'s forward equations for a pure birth process is applied to construct the transition of deterioration from one state to the next.