# Finite Mixture Model-Based Analysis of Yarn Quality Parameters
## 1 Introduction
Although such white spots are visible when fabrics are dyed with lighter colors, these spots or specks are especially visible in fabrics dyed with darker colors. Once these marks and specks are present in the fabric, they can lead to downgrading or rejection because there is no cost-effective method of concealing them [24]. Because these imperfections can significantly degrade the quality of both the yarn and the resulting fabric, understanding the probability distribution of yarn imperfections is crucial for predicting these properties, ensuring quality control, and optimizing production. This knowledge also contributes to a better understanding of variations in yarn properties and enables the rapid identification of potential issues. In addition to the imperfection parameters of the yarn, the mechanical properties, including tenacity and elongation, have also been considered in the scope of the study. Tenacity and elongation are two crucial quality parameters that directly impact the overall performance and suitability of textile fibers and yarns for various applications [25; 26; 27; 28; 29; 30]. Tenacity, also known as tensile strength, refers to the ability of a fiber or yarn to withstand tensile stress before breaking [26; 27]. This property is essential in high-speed weaving and other fabric manufacturing processes where the yarn is subjected to high stresses imposed by various machine elements. Yarns with higher tenacity are less prone to breakage during these dynamic processes, leading to improved efficiency and reduced waste [31]. The elongation of a fiber or yarn represents its maximum extension before rupture [29; 30]. This property is closely related to the fabric's deformability and elasticity, which are important for the comfort and fit of the final textile products. Fabrics with higher elongation can better accommodate user movements and stresses, enhancing the overall user experience [32]. In the literature, studies on this subject have generally focused on identifying the factors influencing the yarn tenacity and elongation parameters. Overall, the tenacity and elongation of textile fibers are crucial parameters that determine the suitability and performance of the final textile products. Understanding these factors is essential for optimizing the quality and performance of textile materials. Finally, this study aims to evaluate the applicability and effectiveness of FMMs in analyzing yarn imperfections--specifically thin places, thick places, and reps--as well as yarn mechanical properties, including tenacity and elongation. By leveraging Poisson and gamma mixture distributions, this work highlights a novel approach for characterizing these quality parameters, offering practical insights for quality control and process optimization in the textile industry. To provide a clear understanding of the research process and findings, the structure of this paper is outlined as follows: Section 2 provides the methodology employed in this study, including data collection procedures and the theorical background of specific FMMs utilized for analyzing imperfections and yarn mechanical properties. Section 3 presents the results of the analysis, discussing the findings in detail. Finally, Section 4 concludes the study by summarizing the key findings, discussing their implications for the textile industry, and outlining potential avenues for future research.