A fuzzy nonparametric Shewhart chart based on the bootstrap approach

Dabuxilatu Wang; Olgierd Hryniewicz

International Journal of Applied Mathematics and Computer Science (2015)

  • Volume: 25, Issue: 2, page 389-401
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Dabuxilatu Wang, and Olgierd Hryniewicz. "A fuzzy nonparametric Shewhart chart based on the bootstrap approach." International Journal of Applied Mathematics and Computer Science 25.2 (2015): 389-401. <http://eudml.org/doc/270744>.

@article{DabuxilatuWang2015,
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.},
author = {Dabuxilatu Wang, Olgierd Hryniewicz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Shewhart control chart; fuzzy data; bootstrap; average run length; average run length (ARL)},
language = {eng},
number = {2},
pages = {389-401},
title = {A fuzzy nonparametric Shewhart chart based on the bootstrap approach},
url = {http://eudml.org/doc/270744},
volume = {25},
year = {2015},
}

TY - JOUR
AU - Dabuxilatu Wang
AU - Olgierd Hryniewicz
TI - A fuzzy nonparametric Shewhart chart based on the bootstrap approach
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 2
SP - 389
EP - 401
AB - 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.
LA - eng
KW - Shewhart control chart; fuzzy data; bootstrap; average run length; average run length (ARL)
UR - http://eudml.org/doc/270744
ER -

References

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