A complex system has the properties of multi-component, multi-function and multi-failure mode, and its failure may cause serious consequence in terms of safety and economy loss. Based on the properties of complex systems, a model was developed to optimise the inspection schedule for a multi-defect component using a probability and random process. The inspections were intended to detect any defect in the components, which may be imperfect. The situation of imperfect inspections and non-constant inspection intervals were considered. An algorithm was presented to optimise the intervals of inspections in order to maximize the reliability of the components. A case study was carried out where the proposed model was used to schedule the rail inspection at a high speed railway network. 