Optimal inspection of a finite population

ABSTRACT

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.

KEYWORDS:

• cost optimality
• finite population
• optimal inspection frequency
• quality control

About the authors

E. J. Kelly is a Scientist at Los Alamos National Laboratory and holds a Ph.D. in Biostatistics from UCLA. She is a Fellow of the American Statistical Association.

M. S. Hamada is a Scientist at Los Alamos National Laboratory and holds a Ph.D. in Statistics from the University of Wisconsin-Madison. He is a Fellow of the American Statistical Association.

S. A. Vander Wiel is a Scientist at Los Alamos National Laboratory and holds a Ph.D. in Statistics from the Iowa State University. He is a Fellow of the American Statistical Association.

R. D. Ryne is a Scientist at Lawrence Berkeley National Laboratory and holds a Ph.D. in Physics from the University of Maryland.

Acknowledgments

We thank an anonymous referee for insightful comments on an earlier version that helped improve this article.