Abstract: The optimal inspection period for a degradation system subject to compound damages is investigated.The operational dynamic environment of the system is modeled as a continuous time discrete state Markov process,the system degrades gradually on conditions of continuous wear and discrete shocks damages.In order to compute an optimal inspection period and corresponding limiting average availability,a nonlinear programming model is formulated.The inspection period is optimized by genetic algorithms.In the end,the feasibility of the model and algorithm is verified through a numerical example.