Outlier detection in non-parametric profile monitoring

Abstract

The robustness of the various profile monitoring methods that can perform poorly in the presence of outliers has been heavily debated. To contribute to this strand of the literature, we propose a two-stage outlier detection scheme for non-parametric profile monitoring that can control type-I error rates as well as identify outlier profiles. In the first stage, we define an outlier detection measure by using a non-parametric test statistic and extend the well-known least trimmed squares algorithm to find a clean profile set. Then, in the second stage, the detection of outlying profiles is deemed as a hypothesis testing problem, where the thresholding rule is obtained from the asymptotic distribution of the proposed measure. Furthermore, to enhance efficiency, a one-step refinement algorithm is proposed to determine whether a data point is a real outlying profile. Simulation studies show that the proposed procedure can control type-I error rates, while maintaining reasonably high outlier detection power values. Finally, we apply the proposed approach to a real data analysis to demonstrate the effectiveness of our method. Our approach responds to the fact that in the profile monitoring of statistical process control problems, the dimensionality and complexity of the relationship between the response and explanatory variables can increase the possibility that a profile is outlying and such outlying profiles may influence the data analysis markedly.

Keywords:

• Asymptotic normality
• nonparametric regression
• nonparametric test statistic
• outlier detection
• profile monitoring

2020 Mathematics Subject Classifications:

• 62G86
• 62H30
• 62G10

Acknowledgements

The authors are grateful to the editor, the associate editor and two anonymous referees for their comments that have greatly improved this paper. The authors also gratefully acknowledge Professor Zhaojun Wang, Professor Changliang Zou of Nankai University and Professor Zhongyi Zhu of Fudan University for their guidance and suggestions on this paper.

Disclosure statement

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

Additional information

Funding

This work was supported by National Nature Science Foundation of China [11926347, 11926350, 11971197], Natural Science Foundation of the Higher Education Institutions of Jiangsu of China [21KJD110003], Jiangsu Government Scholarship Program [2019-43], and Qinglan Project of Jiangsu Province of China [2022].