An optimization method for change-point monitoring in finite samples sequence

Abstract

This article proposes a method of optimizing control chart (sequential test) to detect an abnormal change in a sequence of finite or even small samples with the unknown change-point and the unknown post-change probability distribution. We not only introduced a performance measure for a given charting statistic to evaluate the detection effect of a control chart, but also constructed an optimal control chart under the measure. The effect of optimization method was illustrated by numerical simulations of three optimized Shewhart, CUSUM and EWMA control charts, and a real data example.

Keywords:

• Optimization of control chart
• change-point detection
• finite samples

MSC 2010 Subject Classifications:

• Primary 62L10
• secondary 62L15

Acknowledgments

We sincerely thank the two reviewers for their precious comments on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by RGC Competitive Earmarked Research Grants and National Natural Science Foundation of China (11531001).