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Abstrakty
In this paper, we consider a nonparametric Shewhart chart for fuzzy data. We utilize the fuzzy data without transforming them into a real-valued scalar (a representative value). Usually fuzzy data (described by fuzzy random variables) do not have a distributional model available, and also the size of the fuzzy sample data is small. Based on the bootstrap methodology, we design a nonparametric Shewhart control chart in the space of fuzzy random variables equipped with some L2 metric, in which a novel approach for generating the control limits is proposed. The control limits are determined by the necessity index of strict dominance combined with the bootstrap quantile of the test statistic. An in-control bootstrap ARL of the proposed chart is also considered.
Rocznik
Tom
Strony
389--401
Opis fizyczny
Bibliogr. 37 poz., tab.
Twórcy
autor
- Department of Statistics, School of Economics and Statistics, Guangzhou University, 230 Waihuanxi Road, Guangzhou, 510006, PR China
autor
- Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland
Bibliografia
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- [9] Gil, M., López-Diaz, M. and Ralescu, D.A. (2006). Overview on the development of fuzzy random variables, Fuzzy Sets and Systems 157(19): 2546–2557.
- [10] Grzegorzewski, P. and Hryniewicz, O. (2000). Soft methods in statistical quality control, Control and Cybernetics 29(1): 119–140.
- [11] Gülbay, M. and Kahraman, C. (2006). Development of fuzzy process control charts and fuzzy unnatural pattern analysis, Computational Statistics and Data Analysis 51(1): 433–451.
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- [17] Körner, R. (1997). On the variance of fuzzy random variables, Fuzzy Sets and Systems 92(1): 83–93.
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- [30] Shu, M.-H. andWu, H.-C. (2011). Fuzzy X and r control charts: Fuzzy dominance approach, Computers & Industrial Engineering 61(3): 676–685.
- [31] Taleb, H. (2009). Control charts applications for multivariate attribute processes, Computers & Industrial Engineering 56(1): 399–410.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
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