MHWMA Control Charts for Monitoring Multivariate Multiple Linear Profiles

Document Type : Research Paper

Authors

1 PhD Graduate in Industrial Engineering, Department of Industrial and system Engineering, Faculty of Engineering, Isfahan University of Technology (IUT), Isfahan, Iran

2 Assistant Professor, Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran

10.22084/ier.2025.31437.2211

Abstract

In many industrial processes, quality can be characterized using a multivariate multiple linear profile model, which describes the regression relationships between response variables and explanatory variables. This paper proposes three control schemes based on the Multivariate Homogeneously Weighted Moving Average (MHWMA) chart for monitoring multivariate multiple linear profiles. These charts utilize a uniformly weighted moving average structure, enabling the detection of shifts in the profile parameters. The proposed methods—MHWMA, Extended MHWMA, and MHWMA/χ²—are designed to monitor the regression coefficients and covariance matrix of the profiles. The performance of these methods was evaluated using the CVRL metric in a simulation study, and the results showed that the MHWMA/χ² method outperforms other methods in detecting deviations. Additionally, a sensitivity analysis was conducted to assess the impact of design parameters, such as the smoothing constant and sample size, on the change detection. Furthermore, the effect of parameter estimation in Phase I on the performance of the control charts in Phase II was investigated. The simulation results indicated that parameter estimation in Phase I can significantly affect the ability to detect shifts in Phase II. Finally, a practical application of the new control chart is illustrated using a real case study.

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Main Subjects

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Journal of Industrial Engineering Research in Production Systems
Volume 13, Issue 26
September 2025
Pages 183-196

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