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All Journal Jurnal Matematika
Alfred Ayo Ayenigba
Ajayi Crowther University, Oyo
Mathematics

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Hotelling’s T² Control Chart for Monitoring Correlated Wine Quality in Small-Scale Production Alfred Ayo Ayenigba; Deborah Ayomide Adegboye; Dorcas Omobola Folarin; James Serumun Ivande
Jurnal Matematika Vol. 16 No. 1 (2026)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Udayana University Gedung UKM, Ruang UKM 8 Lt 1, Kampus Bukit Jimbaran, Badung-Bali.

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2026.v16.i01.p198

Abstract

This research papers investigates the use of Hotelling's T² control charts for monitoring correlated quality features in a small-scale wine production process with small samples. Analysis of physicochemical data obtained from 50 red wine samples (fixed acidity, volatile acidity, alcohol content, residual sugar) for multivariate process stability demonstration and comparison made to standard univariate Shewhart charts. The correlation analysis exhibited significant relationships, including a relatively high, positive correlation between alcohol and residual sugar (r = 0.668) and a moderate negative correlation of fixed and volatile acidity (r = -0.435). Hotelling’s T² charts reveal four out-of-control samples, while univariate charts only detect two, failing to recognise coordinated multivariate deviations. The T² chart signals a 40 action detection with no monitoring of univariate charts by signals under the coordinated 1.5sigma shift simulated. The sample-to-variable ratio of 12.5:1 supported robust covariance estimation. The results show that Hotelling's T² has greater sensitivity to joint process deviations, provides control of inflated family-wise error rates, and gives actionable diagnostic information. This framework provides small wine producers with a practical and data-based approach for enhancing product consistency and enabling early detection of multivariate deviations, even with limited production data.
Co-Authors Deborah Ayomide Adegboye Dorcas Omobola Folarin James Serumun Ivande