Profile Monitoring Using Nonparametric Bootstrap T² Control Chart

Abstract

In certain statistical process control applications, performance of a product or process can be monitored effectively using a linear profile or a linear relationship between a response variable and one or more explanatory variables. In this article, we design a nonparametric bootstrap control chart for monitoring simple linear profiles based on T ² statistic. We evaluate the performance of the proposed method in phase II. The average and standard deviation of the run length under different shifts in the intercept, slope, and standard deviation are considered as the performance measures. Simulation results show that the performance of the proposed bootstrap control chart improves as the size of the available data increases.

Keywords:

• Average run length
• Bootstrap
• Linear profile monitoring
• Nonparametric control chart
• Statistical process control

Mathematics Subject Classification:

• Primary 62G08
• Secondary 62F40

Acknowledgments

The authors acknowledge the valuable comments of the anonymous reviewer. The authors also wish to thank Professor Ronald J.M.M. Does from University of Amsterdam, Kamran Peynabar from University of Michigan, and Dr. Amirhossein Amiri from Shahed University for their help on this article.

Notes

¹IC: In-Control