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

Yıl 2022, Cilt: 32 Sayı: 1, 65 - 76, 29.03.2022

Özge Elmastaş Gültekin , Aslı Kılıç , Gonca Özçelik Kayseri

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• Özçelik K.G., & Kirtay, E. (2015). Part 1. Predicting the pilling tendency of the cotton interlock knitted fabrics by regression analysis. Journal of Engineered Fibers and Fabrics, 10 (3), 110-120.
• Beltran R., Wang L., & Wang X. (2006). Predicting the pilling tendency of wool knits. Journal of Textile Institute, 97 (2), 129-136.
• Beltran R., Wang L., & Wang X., (2006). Measuring the influence of fiber-to-fabric properties on the pilling of wool fabrics. Journal of Textile Institute, 97 (3), 197-204.
• Hearle, J.W.S., Wilkins, A.H. (2006). Mechanistic modelling of pilling. Part I: Detailing of mechanisms. Journal of the Textile Institute, 97 (4), 359 - 368.
• Schindler, W.D, Hauser, P.J. (2004). Chemical finishing of textiles. Cambridge, Woodhead Publishing Ltd, (Chapter 11).
• Taylor, H.M., Karlin, S. (1998). An introduction to stochastic modeling. 3rd Ed., Academic Press, USA, 631 p.
• Kay, R. (1986). A Markov model for analysing cancer markers & disease states in survival studies. Biometrics, 42 (4), 855-865.
• Craig, B.A., Sendi, P.P. (2002). Estimation of the transition matrix of a discrete-time Markov chain. Health Economics, 11, 33–42.
• Jackson, C.H., Sharples, L.D., Thompson, S.G., Duffy, S.W., & Couto, E. (2003). Multistate Markov models for disease progression with classification error. The Statistician, 52 (2), 193–209.
• Yaesoubi, R., Cohen,T (2011). Generalized Markov models of infectious disease spread: A novel framework for developing dynamic health policies. European Journal of Operations Research, 215 (3), 679–687.
• Malik, M., Thomas, L. C. (2012). Transition matrix models of consumer credit ratings. International Journal of Forecasting, 28, 261–272.
• Shi, Q., Zheng, Y.B., Wang, R.S., Li, Y.W. (2011). The study of a new method of driving cycles construction. Procedia Engineering, 16, 79–87.
• Chierichetti, F., Kumar, R., Raghavan, P., & Sarlós, T. (2012). Are Web users really Markovian? Proceedings of the 21st International Conference on World Wide Web, (609-618), ACM. Lyon, France.
• Paras, M.K., Pal, R. (2018). Application of Markov chain for LCA: A study on the clothes ‘reuse’ in Nordic countries. Int. J. Adv. Manuf. Technol., 94, 191-201.
• Kumar, R., Tewari, P.C., Khanduja, D. (2018). Parameters optimization of fabric finishing system of a textile industry using teaching-learning-based optimization algorithm. International Journal of Industrial Engineering Computations, 9, 221-234.
• Baycan, I.O., Yildirim, G. (2016). Analysing the nonlinear dynamics of the Turkish textile and apparel industries. Tekstil ve Konfeksiyon, 26 (4), 345-350.
• Badea, L., Grigorescu, A., Constantinescu, A., & Visileanu, E. (2016). Time optimization of the textile manufacturing process using the stochastic process. Industria Textila, 67(2), 205-209.
• Kumar, R., Tewari, P.C. Khanduja, D. (2016). Performance modeling and availability analysis of the fabric finishing system of a textile industry. International Journal of Engineering Science and Computing, 6(8), 2563-2567.
• Afrinaldi, F. (2020) Exploring product lifecycle using Markov chain. Procedia Manufacturing. 43, 391-398.
• EN ISO 12945-2 Determination of fabric propensity to surface fuzzing & to pilling - Part 2: Modified Martindale method.
• Furferi R., Governi L., Volpe Y. (2015). Machine Vision-Based Pilling Assessment: A Review. Journal of Engineered Fibers and Fabrics, 10 (3), 79-93
• Jackson, T., Keyes, N.M., Harris, P., Holden, J.B., (2005). A preliminary report: Fuzz & pilling surface changes on cotton fabrics measured by linetech industries' image analysis system, Beltwide Cotton Conferences, New Orleans, Louisiana - January 4 – 7, 2219-2228
• Zhang J., Wang X., Palmer, S. (2007). Objective grading of fabric pilling with wavelet texture analysis. Textile Research Journal, 77 (11), 871–879.
• Winston, W.L., Goldberg, J.B. (2004). Operations research: Applications and algorithms, 4th edition, California, Thomson Brooks/Cole.
• Singer, P., Helic, D., Taraghi, B. Strohmaier, M. (2014). Deteching memory and structure in human navigation patterns using Markov chain models of varying order, Plos one, 9 (7), DOI: 10.1371/journal.pone.0102070.
• Sheskin, T.J., (2011). Markov chains and decision processes for engineers and managers. USA, CRC Press.
• Sheskin, T.J. (2013). Conditional mean first passage time in a Markov chain. International Journal of Management Science and Engineering Management, 8 (1), 32-37.