A stochastic model for a machining cell with tool failure and tool replacement considerations

This paper presents a stochastic model for analyzing machining cells with arbitrary demand, production, tool failure, and tool replacement processes, and a finite output buffer. Expressions are developed for the transition probabilities among the different states, the proportion of transitions that take the process to a particular state, the probabilities that the process is in a particular state, and the expected state residence times. Also, expressions are developed for some quantities of interest, like average inventory and percentage of lost sales. Applications are discussed for various demand, production, tool failure and replacement processes, and numerical examples are presented. Finally suggestions are made for utilizing the proposed model in a serial production line environment.