Maintenance plays a key role in industry. Compared with the prevailing maintenance policies such as time-based maintenance and condition-based maintenance, the delay time concept, considering the failure process as a two-stage process, effectively captures the reason why successive inspections are an important part of a preventive maintenance program by determining the state of component through inspections. Since periodic inspection is a common practice for its managerial convenience, to determine the inspection interval emerges as a key problem for the optimal maintenance decision. Many works on determining the inspection interval generally assumed that the time of inspection span and the time of failure renewal are negligible y. However, in realistic cases, the above time should not be negligible, and they may be overlapped. To model the effect of the possible overlapping of inspection span with failure downtime on determining the optimal inspection interval, two inspection models for a single component based on delay time concept are proposed. That is, the age based inspection policy and the block based inspection policy. The developed models are also demonstrated by numerical example.