Abstract: The problem of decision-making on functional inspection for a component with delayed repair is studied.The models of failures and life cycle cost are developed using probability and stochastic process.An optimal policy of inspection is presented with an economic objective,and the property of solution to the intervals of inspection is studied.The model is applicable to analyze maintenance policy under non-periodic inspection,and optimize the inspection intervals and the delay of repair together.An algorithm for optimizing the policy is presented using the method of iteration,and procedure for using the methodology is also presented.At last,an example is given to show the process of solving the problem and verification of the algorithm.