A General Framework for Robust Monitoring of Multivariate Correlated Processes

Abstract

Statistical process control (SPC) charts provide an important analytic tool for online monitoring of sequential processes. Conventional SPC charts are designed for cases when in-control (IC) process observations are independent and identically distributed at different observation times and the IC process distribution belongs to a parametric (e.g., normal) family. In practice, however, these model assumptions are rarely valid. To address this issue, there have been some existing discussions in the SPC literature for handling cases when the IC process distribution cannot be described well by a parametric form, and some nonparametric SPC charts have been developed based on data ranking and/or data categorization. However, both data ranking and data categorization would lose information in the original process observations. Consequently, the effectiveness of the nonparametric SPC charts would be compromised. In this article, we make another research effort to handle this problem by developing a general process monitoring framework that is robust to the IC process distribution and short-ranged serial correlation. The new method tries to preserve as much information in the original process observations as possible. Instead of using data ranking and/or data categorization, it is based on intensive data pre-processing, including data decorrelation, data transformation, and data integration. Because the distribution of the pre-processed data can be approximated well by a parametric distribution, the design and implementation of the new method is relatively simple. Numerical studies show that it is indeed robust to the IC process distribution and effective for online monitoring of multivariate processes with short-ranged serial correlation.

KEYWORDS:

• Data decorrelation
• Recursive computation
• Robustness
• Self-starting charts
• Sequential learning
• Transformation

Supplementary Materials

ComputerCodesAndData.zip: This zip file contains some computer codes to implement the proposed method and the real data used in the article.

supplement.pdf: This supplementary file contains the proof of the result in Proposition 1.

Acknowledgments

The authors thank the editor, the associate editor, and four referees for many constructive comments and suggestions which improved the quality of the article greatly.

Additional information

Funding

This research is supported in part by an NSF grant.