Abstract: During the operation of the system, it can effectively reduce the serious consequences of failure to discover the defective state of the system through inspection and perform preventive maintenance in advance. Inspections are generally imperfect and probabilities of inspection errors are non-constant. When the system is indicated to be defective, minimal repair is carried out, and the number of minimal repairs is limited. Inspection-based replacement will be performed when the inspections reveal the defects for several times. In addition, age-based replacement is scheduled at the specified time interval, and replacement can renew the system. The expected cost and the expected length per renewal cycle are derived by using a recursive method. The cost rate over an infinite time horizon is formulated based on the renewal reward theorem. The inspection interval, the upper limit of the number of minimal repairs and the age-based replacement interval are jointly optimized through the optimization algorithm. The steel converter system is provided to illustrate the performance and applicability of the proposed maintenance policy. The sensitivity analysis results show that the upper limit of the number of minimal repairs is only sensitive to the cost of minimal repair and preventive replacement. To show the advantages of the proposed method, the policies not considering minimal repair and not limiting the number of minimal repairs are separately presented for comparison. Simulation algorithm is introduced to verify the correctness of the method.

Key words: delay time model, non-constant probabilities of inspection errors, minimal repair, hybrid preventive maintenance policy