A new multivariate CUSUM chart using principal components with a revision of Crosier's chart

ABSTRACT

In this article, we introduce a new multivariate cumulative sum chart, where the target mean shift is assumed to be a weighted sum of principal directions of the population covariance matrix. This chart provides an attractive performance in terms of average run length (ARL) for large-dimensional data and it also compares favorably to existing multivariate charts including Crosier's benchmark chart with updated values of the upper control limit and the associated ARL function. In addition, Monte Carlo simulations are conducted to assess the accuracy of the well-known Siegmund's approximation of the average ARL function when observations are normal distributed. As a byproduct of the article, we provide updated values of upper control limits and the associated ARL function for Crosier's multivariate CUSUM chart.

KEYWORDS:

• Average run length
• Crosier's multivariate CUSUM chart
• Multivariate CUSUM
• Multivariate statistical process control

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62N05
• Secondary 62L05

Acknowledgments

Jiaqi Chen's research is supported by National Natural Science Foundation of China, No. 11501147.

Additional information

Funding

National Natural Science Foundation of China(11501147, 10.13039/501100001809)