Bekker, Andriette, 1958-Ferreira, Johannes TheodorusHuman, Schalk WilliamAdamski, Karien2023-03-062023-03-062022-01-13Bekker, A.; Ferreira, J.T.; Human S.W.; Adamski, K. Capturing a Change in the Covariance Structure of a Multivariate Process. Symmetry 2022, 14, 156. https://DOI.org10.3390/sym14010156.10.3390/sym140101562073-8994 (online)https://repository.up.ac.za/handle/2263/89962This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift.en© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Generalised bimatrix variate beta type II distributionMeijer’s G-functionRun-lengthSequentialShiftArticle