A Statistical Variance Decomposition Framework for Cotton Yarn Quality Engineering: From Fibre Properties to Final Yarn

Yarn quality in cotton textile manufacturing is conventionally assessed through single-point metrics such as mean tenacity or evenness CV%. This approach, while operationally convenient, fails to identify where within the production system quality variation originates — making targeted improvement impossible. This article proposes and demonstrates a rigorous additive variance decomposition model for ring-spun cotton yarn, decomposing observed yarn tenacity variance (Var_Yarn) into six independent, physically meaningful components: within-fibre properties, fibre-to-fibre variation, within-yarn fibre arrangement, spinning process variation, measurement system error (MSA), and testing method variation. Each component is quantified using published research data from USDA crop statistics, USTER Statistics 2018, and peer-reviewed journal sources. For 30 Ne carded ring-spun cotton, within-yarn fibre arrangement emerges as the dominant source (26.8%), followed by fibre-to-fibre properties (21.1%) and spinning process (19.7%). Critically, combined observational variance accounts for 25.4% of total variance — exceeding the AIAG MSA acceptance threshold of 10%, revealing systematic and correctable inflation of apparent yarn variability. The model provides a statistically grounded, actionable framework for quality engineers to prioritise improvement initiatives, set evidence-based reduction targets, and separate real process variation from measurement artefact.