We present a model for inspection and maintenance of a system under two types of failures. Early failures (type I), affecting only a proportion p of systems, are due to a weak critical component detected by inspection. Type II failures are the result of the system ageing and preventive maintenance is used against them. The two novelties of this model are: (1) the use of a defective distribution to model strong components free of defects and thus immune to early failures. (2) the removal of the weak critical part once it is detected with no other type of rejuvenation of the system which constitutes an alternative to the minimal repair. We study the conditions under which this model outperforms, from a cost viewpoint, other two classical age-replacement models. The analysis reveals that inspection is advantageous if the system can function with the critical component in the defective state for a long enough time. The proportion of weak units and the quality of inspections also determine the optimum policy. The results about the range of application of the model are useful for decision making in actual maintenance. A case study concerning the timing belt of a four-stroke engine illustrates the model
