Imperfect Inspection of a System With Unrevealed Failure and an Unrevealed Defective State

This paper proposes a model of inspection of a protection system in which the inspection outcome provides imperfect information of the state of the system. The system itself is required to operate on demand typically in emergency situations. The purpose of inspection is to determine the functional state of the system and consequently whether the system requires replacement. The system state is modeled using the delay time concept in which the failed state is preceded by a defective state. Imperfect inspection is quantified by a set of probabilities that relate the system state to the outcome of the inspection. The paper studies the effect of these probabilities on the efficacy of inspection. The analysis indicates that preventive replacement mitigates low-quality inspection and that inspection is cost-effective provided the imperfect inspection probabilities are not too large. Some derivative policies in which replacement is postponed following a positive inspection are also studied. An isolation valve in a utility network motivates the modeling.