Problem
A large bearing can be inspected visually with some minor machine dismantling. The inspection costs $400 and it is considered that visual indication of damage to cage, races or rollers will be evident at least 4 months before failure. As the inspection requires a skilled technician and it is not possible to be inspect all features of the bearing the inspection is believed to be about 90% effective. If the bearing fails there is a loss to the business of $50,000 in addition to the normal replacement cost. The machine could be expected to achieve an average life of 15 years and it is considered that this bearing will determine the life. Is the inspection efficient? What is the optimal inspection interval?