## 3 Literature Review
In practice, accurate observation is challenging due to the dynamic nature of corrosion and the inherent error of inspection methods. [PERSON], et al. (2017) addressed this problem by formulating a discrete state partially observable Markov decision process (DSPOMDP) model that considers observational errors and inaccuracies. This study extends the DSPOMDP approach by formulating the state as a continuous function to integrate the uncertainty without any discretization step. Better model fidelity can be achieved with this continuous state approach. Exploring the POMDP model application is ongoing in several other industries and fields of study. Some of the most recently accomplished studies include [PERSON] et al. (2018), who integrated POMDP in maintenance planning optimization (with a case study for lead battery maintenance); [PERSON] et al. (2018), who combined dynamic Bayesian networks with POMDPs to formulate a framework for the optimization of inspection and maintenance planning; and [PERSON] & [PERSON] (2018) who optimized inspection interval for maintenance operation using POMDP model with Baum-Welch algorithm for parameters estimation. The choice of the solver is one of the most crucial aspects of adopting MDP and POMDP models. Value iteration or policy iteration methods can be considered for small-size (less than thousands of states) and discrete MDP and POMDP models. However, these methods cannot be effectively applied to large-size (more than a hundred thousand states) or continuous space models. For POMDP models, [PERSON] (2018) presented a systematic review of sample-based solvers based on the attributes of modeling components. The review covered most of the popular solvers. For models with a large state space (some continuous state), the study recommended adopting algorithms such as point-based value iteration (PBVI--samples beliefs from a set of beliefs constructed from a reachable belief from a given initial belief), Perseus (sampling beliefs and backup operation performed independently), heuristic search value iteration (HSVI--employs an \(\alpha\)-vector policy representation and point-based backup), successive approximations of the reachable space under optimal policies (SARSOP--a belief sample method using \(\alpha\)-vector policy representation and point-based backup), and Monte Carlo value iteration (MCVI--a policy based algorithm where the total expected value is computed at a given point in a defined state and action). Monte Carlo tree search (MCTS--combination approach of random sampling and tree search in a balanced effort between exploitation and exploration (2018)), and determined sparse partially observable tree (DESPOT--for each iteration, the algorithm searches the sample space for the best policy for a belief state (2018)) were proposed for continuous state (large state) POMDP models. Perseus and guided cluster sampling (an algorithm that optimizes on a subset of continuously updating sampling space) were suggested for continuous action POMDP models. Partially observable Monte Carlo planning (POMCP) and partially observable Monte Carlo planning with observation widening (POMCPOW--extensions of MCTS by adding Monte Carlo updating procedure for belief state to MCTS search in the present state (2018)) have been proposed for POMDP models with a large number of observations. In addition, the review has presented several algorithms for long planning horizons and complex dynamic problem models. Even though the model elements encompassed in all algorithms are the same, the detailed formulation, solving procedures, effectiveness, and the final solution quality can differ. The proposed CSPOMDP model adopts the POMCP and DESPOT solvers to search for the best maintenance policies.