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The inspection activities are often carried out to detect possible indication of failures in plant systems.This paper considers a single unit system subject to two types of failures,where one failure mode is the traditional 0-1 logic failure and the other failure mode is described by a two-stage failure process.Adjustable inspections are used to detect the defective stage of the latter.We assume that the inspection duration gets shorter and shorter with a constant ratio.At the same time,preventive replacement is used to avoid the possible failure due to the former failure mode.The renewal process of this system is analyzed and the expected long-run cost per unit time (ELRCUT) is derived.The optimal inspection period and the preventive replacement interval to minimize ELRCUT are studied.At last,a numerical example is presented to illustrate the proposed model.