A Variable Dimension Covariance Matrix Control Chart

ABSTRACT

Monitoring more than two correlated quality variables simultaneously is essential in industrial manufacturing and service processes. Consequently, multivariate statistical process control (MSPC) has become an important and widely studied research area. This paper aims to develop a new standardized exponentially weighted moving average (ZEWMA) control chart with variable‐dimension (VD) quality variables for monitoring the process covariance matrix of multivariate normal processes. The proposed VD ZEWMA charting statistic is designed not to be influenced by shifts in the process mean vector, thereby enabling accurate detection of changes in the covariance matrix. Based on this statistic, a VD ZEWMA control chart is constructed to effectively identify out‐of‐control conditions in the process covariance matrix. The statistical properties of the proposed chart, as well as its out‐of‐control detection performance, are thoroughly investigated. Compared with the existing fixed‐dimension ZEWMA covariance matrix control chart, the proposed VD ZEWMA chart offers greater flexibility when some quality variables are difficult or costly to measure. In addition, it demonstrates superior detection performance while reducing sampling and measurement cost. Finally, a semiconductor data set is used to illustrate the practical applicability of the proposed VD ZEWMA control chart.