System Engineering and Productivity

System Engineering and Productivity

Double Sampling-based Ridge Penalized Likelihood Ratio Control Charting Scheme for Detecting the Covariance Matrix Disturbances

Document Type : Research Paper

Authors
Zeinab Iji 1
Mohammad Reza Maleki 2
Hossein Eghbali 3
1 Ph.D. Student, Department of Industrial Engineering, Faculty of Industrial Engineering, University of Eyvanekey, Eyvanekey, Iran
2 Corresponding author: Assistant Professor, Department of Industrial Engineering,, Golpayegan College of Engineering, Isfahan University of Technology, Golpayegan, Iran
3 Assistant Professor, Department of Industrial Engineering, Faculty of Industrial Engineering, University of Eyvanekey, Eyvanekey, Iran
10.22034/sep.2025.2046743.1238
Abstract
Given the manufacturer's obligation to meet expectations and financial constraints, monitoring a large number of quality characteristics with a limited sample size poses a significant challenge for researchers in statistical quality control. According to recent research, multivariate charts based on double sampling are developed under the assumption that the number of quality characteristics is less than the sample size. The objective of this paper is to monitor the dispersion matrix of high-dimensional processes using a combination of the ridge penalized likelihood ratio statistic and double sampling method. To evaluate the performance of the proposed chart, we first introduce seven out-of-control scenarios, which include three combined diagonal/non-diagonal patterns, two diagonal patterns, and two non-diagonal patterns. We then extract the run length properties and the expected value of the sample size associated with the proposed chart through simulation experiments. The simulation results indicate that, across all three pattern categories mentioned, the proposed chart's sensitivity in detecting disturbances in the covariance matrix improves as the magnitude of shifts in its components increases. The simulation results further indicate that as the number of components influenced by the assignable cause in the covariance matrix decreases, the proposed control chart can detect process disturbances over a longer period.

Highlights

  • Monitoring the dispersion matrix of high-dimensional processes in phase 2
  • Equipping the edge-compensated likelihood ratio diagram for double sampling
  • Discovery of any dichotomy of sparse and non-scattered changes of the covariance matrix

Keywords
Statistical quality control
Double sampling
Covariance matrix
High dimensional data
Ridge penalized likelihood ratio
Subjects

Copyright © Zeinab Iji. Mohammad Reza Maleki. Hossein Eghbali

 

License

This article is released under the Creative Commons Attribution (CC BY 4.0) license. Anyone is free to copy, share, translate, and adapt this article for any purpose, whether commercial or non-commercial, as long as proper citation is given to the authors and original publication.

 

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System Engineering and Productivity
Volume 5, Issue 1 - Serial Number 14
Serial No. 14, Spring Quarterly
Spring 2025
Pages 51-64

  • Receive Date 25 November 2024
  • Revise Date 20 December 2024
  • Accept Date 25 January 2025
  • First Publish Date 25 January 2025
  • Publish Date 22 May 2025