A Hazardous-Inspection Model

This paper deals with the determination of optimal inspection policies when inspections have the potential of being harmful to the device under consideration. The device operates throughout a number of periods and in each period is subject to failure. Failure of the device is directly observable. Prior to failure the device enters a state in which it is functioning, but in an impaired manner. This state can be detected only by performing an inspection. Once the device is known to be in die impaired state, appropriate action may be taken to prolong its remaining life. In this respect inspection is valuable. However the act of inspecting die device when it is not~impaired may itself cause it to become impaired. In this respect inspection is hazardous. This paper determines inspection policies which maximize the expected lifetime of the device. The optimal inspection policies are shown to generally be of only two possible forms, the choice of which depends upon the model parameters.