This paper investigates inspection strategies for a finite-state continuous-time Markovian deteriorating system. Two inspection strategies are considered: sequential inspection and continuous inspection. Unlike many previous efforts, the inspection times for the sequential inspection strategy are assumed to be non-negligible. The replacement times and costs for both strategies are non-negligible and state dependent. Our objective here is to minimize the expected long-run cost rate. Iterative algorithms are provided to derive the optimal policies for both strategies. The structures of these optimal policies and their corresponding optimal cost rates are discussed and compared.
