The performance of the Prognostics and Health Management (PHM) depends both on the functioning of the measurement acquisition system and on the actual state of the system being monitored. The dependencies between these systems must be considered when developing optimal inspection and maintenance strategies. This paper presents a methodology to support the definition maintenance strategies for PHM-equipped industrial systems. The methodology employs influence diagrams when seeking to maximize the expected utility of system operation. The optimization problem is solved by mixed-integer linear programming, subject to budget and technical constraints. Chance constraints can be also included, for instance to curtail risks based on measures such as the Value at Risk (VaR) and the Conditional Value at Risk (CVaR) of system operation. The viability of the methodology is demonstrated by optimizing the inspection and maintenance strategy for a gas turbine equipped with PHM solution. The computation of the Value of Perfect Information (VoPI) provides additional insights on maintenance management. •The methodology optimizes maintenance strategies for PHM-equipped industrial systems.•Influence diagrams models the multi-stage decisions to maximize the expected utility.•The optimization problem is solved by mixed-integer linear programming.•The Value of Perfect Information provides insights into improving the PHM solution.•The methodology is illustrated by optimizing the maintenance strategy of gas turbines.