Title: Multivariate exponentially weighted moving sample covariance control chart for monitoring covariance matrix
Authors: Seyed A. Vaghefi; E. Hassan Nayebi; Mona Ayoubi; Amirhossein Amiri
Addresses: Lighthouse Data and Analytics, KPMG LLP, Ignition Center, 1001 17th Street, Suite 200, Denver, CO 80202, USA ' Department of Industrial Engineering, Iran University of Science and Technology, Tehran 16844, Iran ' Department of Industrial Engineering, Islamic Azad University, West Tehran Branch, Tehran, Iran ' Department of Industrial Engineering, Shahed University, Tehran, Iran
Abstract: In this paper, a control chart is proposed to detect changes in the covariance matrix of a multivariate normal process, when sample size is one. The proposed chart statistic is constructed based on the exponentially weighted form of sample covariance matrix given by individual observation over time. Distance between the values of variance and covariance components in this multivariate exponentially weighted moving sample covariance matrix and, the in-control corresponding elements of process variance-covariance matrix provides a basis for process variability monitoring. The statistical performance of the proposed method is evaluated through the use of a Monte Carlo simulation. The results show the superiority of the proposed control chart performance especially in the case of incremental changes in covariance matrix.
Keywords: average run length; ARL; covariance matrix; multivariate exponentially weighted moving sample covariance; MEWMSC control charts; smoothing parameters; statistical process control; SPC; Monte Carlo simulation.
International Journal of Quality Engineering and Technology, 2016 Vol.6 No.1/2, pp.20 - 39
Received: 09 Apr 2016
Accepted: 29 Jun 2016
Published online: 17 Jan 2017 *