An Optimal Policy for Machine Tool Replacement

This paper presents a new optimal policy for machine tool replacement. The method used is based on the assumption that, as the tool is used longer, the number of defective items produced by the machine will increases due to the malfunction of the tool. On the other hand, if maintenance or corrective actions are applied to the tool more frequently, the number of defectives produced is expected to decrease. The objective, therefore, is to determine the optimal length of time that should elapse before maintenance or corrective actions are applied to the tool. This would be such as to give a balance between the conflicting costs of maintaining the tool and of reworking and/or scrapping the defective items. Two types of maintenance actions are applied to the tool: (1) replacement, and (2) sharpening or adjustment. The procedure assumes that the application of either of these actions would restore the tool to its original condition It is also assumed that these maintenance actions are applied at equally spaced intervals of time, as predetermined from optimal results. The type of maintenance to be applied is decided on either a deterministic or a probabilistic basis. This paper also proposes an approximate for solving the integral equation which determines the value of the decision variable of the problem.