## 6 Conclusions and Future Work  
Pipelines constitute a significant portion of assets in the oil and gas industries. They have a substantial impact on product flow throughout the supply chain. Ensuring pipelines' safe operation is paramount in the industry, as evidenced by past catastrophic accidents. Effective maintenance functions can guarantee the continuous and reliable operation of pipelines. This study aims to contribute toward this goal. Corrosion maintenance is performed by first inspecting the state of the pipeline using ILI methods. Based on the inspection output, the maintenance operation is optimized to minimize costs and prolong the service life. Since corrosion is a continuous process, it requires a continuous function to model better the defects it causes in pipelines. Furthermore, most ILI methods come with inherent reading errors, and addressing these errors inside the optimization model is very important to assess the effectiveness of ILI methods. Particularly, investigating the systemic error of the inspection method is essentialto understand its overall impact on maintenance decision-making. The POMDP model proposed in this paper addressed a continuous state formulation while accounting for the observational variation due to inspection error. The state of the proposed CSPOMDP model defined the deterioration level as a fraction of wall thickness. An upper bound for deterioration has been set to avoid the pipeline's failure while in service. Corrosion mitigation methods such as adding inhibitors and pigging were formulated as actions. No maintenance action and total replacement have also been added to the action set to provide more decision options. The observation function has been fitted to the behavior of the ILI method, including the systemic error that the methods embody. Since most methods report the pipeline state as discrete values, the observations were formulated accordingly. The reward, defined as the cumulative cost related to a maintenance operation, was comprised of service and inspection costs. Hence, the objective of the optimization problem was to identify the least costly maintenance policy for the pipeline's partially observed initial state. POMCP and DESPOT, sample-based algorithms, were used to formulate a numerical test model to assess the CSPOMDP model's performance. Compared to the discrete state model formulation, the continuous state showed slight variation in solution search proficiency and run-time. It showed better policy analysis due to the more elaborate definition of the states. However, optimal results cannot be obtained even in small-size problems. Experimental runs showed that the POMDP model could be adopted to compare maintenance policies defined by practitioners or obtained from solvers. This could help identify the best options, including those that may have been overlooked in the modeling process. The discounted total cost of the maintenance campaign may differ between the CS and DS models implementing the same solver, as well as between different solvers for the same model. Most of the model runs were completed within a very short time. This is especially true for predefined policy runs. As the model size increased, the solvers took longer times to report results. One extension of this study involves testing the proposed model on real pipeline maintenance scenarios. Most of the data used in constructing the experiment were obtained from the literature, which may not accurately represent the actual cases in the industry. The data were also restricted to small and medium-sized models. Pipelines in the industry consist of diverse types of pipelines, several corrosion mitigation methods, multiple inspections and monitoring systems, and other maintenance optimization factors. These can be incorporated into the proposed approach to convert it into a more practical optimization tool for the industry.