An opportunistic maintenance policy based on a semi-Markov decisionprocess is presented for the critical component in a multicomponent system.Opportunistic maintenance is maintenance planning for the target (i.e. critical)component in which replacement is determined on the basis of maintenanceopportunities provided by other components. The transition of the deteriorationstate of the target component follows a semi-Markov process while the occurrenceof maintenance opportunities follows a Poisson process. Sensorsare used to continuously monitor the target component to enable immediatedetection of a state transition, but since the underlying state cannot be knownexactly, the decision maker obtains information on the deterioration stateprobabilistically from sensor results. The focus here is on one critical component in asystem, and the decision-making problem isformulated as a partially observable semi-Markov decision process. The cost structureis composed of operating cost and two types of replacement costs. Theproperties of an optimal policy minimizing the expected total discounted costover an infinite horizon are analytically investigated. Sufficient conditionsare derived under which the objective function for policy optimization isnondecreasing in each deterioration state and the optimal policy is determinedby a threshold. A property indicating the presence or absence of a maintenanceopportunity is presented that is based on the relationship between thresholdsfor optimal actions in a deterioration state.