In comparison with the well‐researched field of analysis and design of structural systems, the life‐cycle performance prediction of these systems under no maintenance as well as under various maintenance scenarios is far more complex, and is a rapidly emergent field in structural engineering. As structures become older and maintenance costs become higher, different agencies and administrations in charge of civil infrastructure systems are facing challenges related to the implementation of structure maintenance and management systems based on life‐cycle cost considerations. This article reviews the research to date related to probabilistic models for maintaining and optimizing the life‐cycle performance of deteriorating structures and formulates future directions in this field.

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Maintenance optimization is the problem of determining cost‐optimal maintenance decisions for a system or structure to ensure a safe and economic operation. An important concept in maintenance optimization is that of life‐cycle costing, where the total costs of design, building, maintenance, and demolition are considered over the entire life span of the system or structure in question. In optimizing maintenance, the uncertainties in the time to failure and/or the deteriorating condition should be taken into account. Proper stochastic deterioration models are Markov processes with independent increments (e.g., gamma processes) and Markov decision processes. This chapter reviews mathematical decision models to optimize time‐based maintenance (e.g., in terms of age‐ and block‐replacement intervals) and condition‐based maintenance (e.g., in terms of inspection intervals). Using renewal theory, optimal maintenance decisions under uncertain deterioration can be determined for which the expected nondiscounted cost per unit time or the expected discounted cost over an unbounded time horizon is minimal. Using Bayesian statistics, these optimal maintenance decisions can be adapted on the basis of observations.

Maintenance optimization is the problem of determining cost‐optimal maintenance decisions for a system or structure to ensure a safe and economic operation. An important concept in maintenance optimization is that of life‐cycle costing, where the total costs of design, building, maintenance, and demolition are considered over the entire life span of the system or structure in question. In optimizing maintenance, the uncertainties in the time to failure and/or the deteriorating condition should be taken into account. Proper stochastic deterioration models are Markov processes with independent increments (e.g., gamma processes) and Markov decision processes. This chapter reviews mathematical decision models to optimize time‐based maintenance (e.g., in terms of age‐ and block‐replacement intervals) and condition‐based maintenance (e.g., in terms of inspection intervals). Using renewal theory, optimal maintenance decisions under uncertain deterioration can be determined for which the expected nondiscounted cost per unit time or the expected discounted cost over an unbounded time horizon is minimal. Using Bayesian statistics, these optimal maintenance decisions can be adapted on the basis of observations.