An optimal inspection strategy for randomly failing equipment

This paper addresses the problem of generating optimal inspection strategies for randomly failing equipment where imminent failure is not obvious and can only be detected through inspection. Inspections are carried out following a condition-based procedure. The equipment is replaced if it has failed or if it shows imminent signs of failure. The latter state is indicated by measuring certain predetermined control parameters during inspection. Costs are associated with inspection, idle time and preventive or corrective actions. An optimal inspection strategy is defined as the inspection sequence minimizing the expected total cost per time unit over an infinite span. A mathematical model and a numerical algorithm are developed to generate an optimal inspection sequence. As a practical example, the model is applied to provide a machine tool operator with a time sequence for inspecting the cutting tool. The tool life time distribution and the trend of one control parameter defining its actual condition are supposed to be known.