Elizabeth J Kelly

This article presents a method for determining an optimal quality control (QC) inspection frequency for a manufacturing process where a specified number of items will be produced and where, if the process goes out of control and generates a defective item, it stays out of control. In addition, there is a QC inspection procedure than can detect a defective item. The frequency of inspection is based on minimizing the total cost. The total cost includes the cost of QC inspections plus the cost of manufacturing defective items. In this application the cost of manufacturing defective items is, after identifying a defective item, the cost of checking previously manufactured items until it is determined when the process went out of control, i.e., until a good item is found.

Design and analysis of factorial experiments with randomization restrictions has received considerable attention in recent years; motivated by studies of multi-stage processes or systems. This has given rise to seemingly unrelated methods of design construction, specific to the layout (e.g., split-plot, split-lot, strip-plot designs). We develop a general approach to this problem that includes most approaches in the literature as special cases, and is easily adaptable to designs which are combinations of different layouts.