Optimal periodic condition inspection and replacement policy for a binary monotone system using a counting process approach

This paper considers a binary monotone system consisting of n components. The system failure process is given by a counting process whose intensity at all times is adapted to information about the system state and at periodic inspection times it is adapted also to information about the component states and their underlying conditions. A parametric policy is introduced prescribing replacement of the entire system either when it enters the failed state, which is observed immediately, or when upon an inspection the intensity is found to have reached a predefined threshold. Costs are associated with inspections, replacements, and system failures, and the periodic inspection interval and intensity threshold that jointly minimize the expected long run cost per unit of time are determined. A numerical example is also included.