Modeling Yarn Structural Heterogeneity via Generalized Poisson and Gamma Mixture Distributions

This study investigates the applicability of finite mixture models (FMMs) for accurately modeling yarn structural quality parameters in 28/1 Ne ring-spun polyester/viscose yarns, focusing on yarn hairiness and twist. The research addresses the need for advanced statistical modeling techniques to better capture the inherent heterogeneity in textile production data. To this end, the Poisson mixture model is employed to represent the twist parameter, while the gamma mixture model is used to model the continuous hairiness indices (S3 CV% and H). Model parameters are estimated using the expectation–maximization (EM) algorithm, and model selection is guided by the Akaike and Bayesian information criteria (AIC and BIC). The results reveal that a two-component mixture distribution provides the optimal fit varies by parameter: twist is best represented by a two-component generalized Poisson mixture, which preserves the integer support of the measurements while relaxing the equidispersion restriction of the ordinary Poisson distribution, whereas hairiness (S3 CV%, H) is best described by two- and three-component gamma mixture distributions, respectively. Model adequacy is assessed by a parametric bootstrap with re-estimation on each replicate. The two-component gamma mixture for S3 CV% is not rejected, whereas residual departures remain for H and, more substantially, for twist, where the concentration of the variable on six recorded levels limits the adequacy of any continuous or semi-continuous specification. These findings highlight the robustness of FMMs in capturing complex distributional patterns in yarn data, extending previous work on yarn imperfections and mechanical properties, and demonstrating their potential in enhancing quality assessment and process control in the textile industry.