Inspection models and their application

Inspection involves examining deteriorating systems to try to identify their state, in order to effect some repair, replacement, or maintenance action. In many cases, one is able to monitor the system at no extra cost and with no interference to the system, and so one has a continuous costless inspection process. In other cases, such as health care, inspection involves stopping the normal running of the system to carry out some costly procedures. Another division is between inspections that are able to give a perfect diagnosis of the state of the system and those that give only partial information on the system. This paper derives the properties for a number of related inspection models, not discussed elsewhere in the literature, varying only in the quality and cost of inspection. It then points out how existing models in the literature could be classified similarly by emphasizing the inspection costs and whether the inspection is perfect or not.