Modelling inspection and replacement quality for a protection system

An inspection and replacement policy for a protection system is described by a mathematical model that incorporates multiple aspects of maintenance quality. A three-state component failure model is assumed, with a defective state preceding failure. The quality of maintenance intervention is modelled by supposing that inspections may misclassify defects (false positives and false negatives) and further that an inspection may induce a defect. The quality of replacement is modelled by supposing that a component arises from a heterogeneous population, composed of weak and strong items and with the mixing parameter determining quality. Isolation valves used in water distribution systems motivate the model development, and a case study is considered in this context. We evaluate the impact of these aspects of the quality of maintenance upon cost and production losses. Defect induction is found to be a key determinant of the cost-optimal policy. The proposed model allows us to verify conditions that justify investment in higher quality maintenance, and thus to provide guidance for prioritization of this investment.