Optimal guard bands for gauges in series

In many manufacturing settings, a series of gauges is used to screen product before it is shipped to the customer. Semiconductor manufacturing is an example of an industry where this type of serial inspection is used. A common problem is determining the target for each gauge so that gauge losses (good units classified as defective by the system of gauges) and defect levels (defective units passed by the system of gauges and sent to the customer) are at appropriate levels. These gauge targets are called guard bands. This article develops general models for defect levels and gauge losses for systems of gauges and shows how response surface models can be used to optimize the system by appropriate selection of the guard bands.