Optimal tool replacement based on the surface roughness in finish machining

This paper studies tool-replacement models based on the surface roughness in finish machining in a mass-production setting. The optimal tool-replacement interval is obtained by minimizing the expected average cost per unit time. Two kinds of cost are considered in the models: the tool-replacement cost and the quality cost due to growth in surface roughness expressed by either Taguchi's quadratic loss functions or the classical loss function. A random-coefficient regression model is used to represent the growth in surface roughness which is generally characterized by an increasing mean and increasing variance. The estimation procedures for the unknown parameters in the regression model are discussed, and it is shown that the optimal tool-replacement time can be found for both loss functions by solving a nonlinear equation.