<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 L<sub>2</sub> 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.</p></abstract>

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.

A fuzzy nonparametric Shewhart chart based on the bootstrap approach

Department of Statistics, School of Economics and Statistics Guangzhou University, 230 Waihuanxi Road, Guangzhou, 510006, PR China

Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A fuzzy nonparametric Shewhart chart based on the bootstrap approach"}

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...

A fuzzy nonparametric Shewhart chart based on the bootstrap approach

Published Online: Jun 25, 2015

Page range: 389 - 401

Received: Oct 24, 2013

DOI: https://doi.org/10.1515/amcs-2015-0030

© by Olgierd Hryniewicz

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.