The availability of a periodic inspection system under mixed maintenance policies is studied in this paper.To accom-modate the characteristic of multiple failure modes for complex systems,the system failures can be divided into two failure modes:hard failure and soft failure.When hard failure occurs,the corresponding corrective maintenance will be performed,taking a random time under the perfect maintenance policy;in contrast,if the soft failure is found,the corresponding preven-tive maintenance will be performed,taking a random time under the imperfect maintenance policy.The dynamic age setback model is adopted for imperfect maintenance,which can accu-rately reflect the fault characteristics of the degraded system.Then an analytical model for system steady state availability and instantaneous availability are derived.Moreover,the optimal method to maximize the system steady-state availability through adjusting the inspection interval is researched.According to the above research,the optimization of system unit time cost,pre-ventive maintenance intervals and availability is researched.Fi-nally,the developed approach is demonstrated by a numerical example.