The drilling problem: A stochastic modeling and control example in manufacturing

A machining economics problem is considered where feed rate selection and tool replacement policies are to be determined. A new stochastic model for tool wear, called a diffusion-threshold model, is proposed. This tool wear model allows the machining economics problem to be formulated as a stochastic optimal control problem incorporating measurement feedback of tool wear. Two types of control policies are described. One is a traditional machining economics policy and the other utilizes tool wear feedback and allows on-line decision making. The optimal policy is described for both types. An example problem based on actual data is worked out that compares the two approaches and demonstrates the utility of information feedback and on-line control.