Determining Optimal Number of Samples for Constructing Multivariate Control Charts

Abstract

Normally, an average run length (ARL) is used as a measure for evaluating the detecting performance of a multivariate control chart. This has a direct impact on the false alarm cost in Phase II. In this article, we first conduct a simulation study to calculate both in-control and out-of-control ARLs under various combinations of process shifts and number of samples. Then, a trade-off analysis between sampling inspection and false alarm costs is performed. Both the simulation results and trade-off analysis suggest that the optimal number of samples for constructing a multivariate control chart in Phase I can be determined.

Keywords:

• Average run length
• Multivariate control chart
• Standard deviation run length

Mathematics Subject Classification:

• 65C05
• 65C60

Acknowledgments

The authors gratefully acknowledge financial supports from both National Science Council of Taiwan and Landmark Program of the NCKU Top University Project. Special thanks also go to the Editor and two anonymous reviewers for their valuable comments and suggestions.

Notes

Note: The number in bracket is a standard error of the estimated ARL.