{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:41:55Z","timestamp":1740156115067,"version":"3.37.3"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"RDP","award":["296\/2019"]},{"DOI":"10.13039\/501100001321","name":"National Research Foundation","doi-asserted-by":"publisher","award":["SRUG190308422768 nr. 120839","71199"],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"This 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.<\/jats:p>","DOI":"10.3390\/sym14010156","type":"journal-article","created":{"date-parts":[[2022,1,14]],"date-time":"2022-01-14T08:14:56Z","timestamp":1642148096000},"page":"156","source":"Crossref","is-referenced-by-count":1,"title":["Capturing a Change in the Covariance Structure of a Multivariate Process"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4793-5674","authenticated-orcid":false,"given":"Andriette","family":"Bekker","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0002, South Africa"},{"name":"Centre of Excellence in Mathematical and Statistical Sciences, Johannesburg 2000, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5945-6550","authenticated-orcid":false,"given":"Johannes T.","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0002, South Africa"},{"name":"Centre of Excellence in Mathematical and Statistical Sciences, Johannesburg 2000, South Africa"}]},{"given":"Schalk W.","family":"Human","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0002, South Africa"}]},{"given":"Karien","family":"Adamski","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0002, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1080\/00224065.1991.11979327","article-title":"SPC Q charts for start-up processes and short or long runs","volume":"23","author":"Quesenberry","year":"1991","journal-title":"J. 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