Setup adjustment for discrete-part manufacturing processes with asymmetric cost functions

This paper presents a feedback adjustment rule for discrete-part manufacturing processes that experience errors at the setup operation which are not directly observable due to part-to-part variability and measurement error. In contrast to previous work on setup adjustment, the off-target cost function of the process is not symmetric around its target. Two asymmetric cost functions—constant and quadratic functions—are considered in this paper. By introducing a bias term in the feedback adjustment rule, the process quality characteristic converges to the optimal steady-state target from the lower cost side of the cost function. This minimizes the off-target loss incurred during the transient phase of adjustment. A machining application is used to illustrate the proposed adjustment procedure and to demonstrate the savings generated by the proposed feedback adjustment rule compared to an adjustment rule due to Grubbs and to an integral controller. It is shown that the advantage of the proposed rule is significant when the cost of the items is high, items are produced in small lot sizes and the asymmetry of the cost function is large.