Modified-opportunistic inspection and the case of remote, groundwater well-heads

We develop a model of a maintenance policy in which inspections are partly opportunistic and partly scheduled. Opportunities for inspection occur at random, and the system is inspected at such an opportunity only if the system is aged at least S. Further, once the system reaches age T, an emergency inspection is performed. The purpose of inspection is to determine whether the system is in the defective state, which acts as a warning stage prior to failure. The policy represents a reality in which flexible inspections prioritise production or missions or convenience, subject to statutory or safety regulations. The model is a generalization of the delay time model. Inspection of pumps at groundwater well-heads, which are geographically remote, motivates the model. Main-tenance interventions at other nearby installations are opportunities. Policy outcomes (cost-rate, mean time between operational failures) are studied numerically for a range of values of the parameters of the model. The model is useful for practice because it quantifies the benefit and disbenefit of flexibility in the inspection policy. We show that in some circumstances making better use of opportunities can simultaneously reduce cost and increase reliability.