Stochastic Modelling of Pilling Degree Changes During the Pilling Process of Wool Fabrics

Year 2022, Volume: 32 Issue: 1, 65 - 76, 29.03.2022

Özge Elmastaş Gültekin , Aslı Kılıç , Gonca Özçelik Kayseri

https://doi.org/10.32710/tekstilvekonfeksiyon.974026

Abstract

As a fabric surface defect, pilling gives clothes an unpleasant appearance and is often characterized with small, complex clusters of fibres attaching to the surface of the garment caused by the fibre migration from yarns to the fabric surface as the fabric rubs against itself, another fabric, or even the skin. In this study, a Markov chain model was built based on the pilling propensity of wool fabrics, evaluated with a scale ranging from 1 (severe pilling) to 5 (non-pilling). These grades were defined as the state space of Markov chain. The numerical values of the transition probability matrix related to the pilling degrees were obtained by maximum likelihood estimation (MLE). Based on the matrix, it was intended to model the changes in the pilling process of woven wool fabrics. Furthermore, given that the fabric will eventually be in state 1, 2 or 3, accepted as unpleasant appearance; the conditional mean first passage times for any transient state to enter any recurrent state for the first time were determined.

Keywords

wool fabric, pilling process, Markov processes, stochastic modelling, maximum likelihood estimation

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