AbstractThis paper considers the problem of optimally controlling a finite state production process subject to deterioration where the decisions available to the inspector are: produce without inspection, produce with inspection, and repair. The state of the production process is perfectly observed at times of inspection and completely unobserved otherwise. If the production process has an increasing failure rate and if certain reasonable assumptions are satisfied by the cost structure, it is shown that optimal strategies for the finite horizon, discounted cost, and average cost cases have certain structural properties which correspond to the well-known four-region description of the optimal policy presented by Ross for the two-state case. These results are also shown to be similar to those recently determined by Rosenfield and are proven under weaker assumptions.