Percentile‐based X-bar and R Control Charts for Triangular Fuzzy Quality

Document Type : Research Paper

Authors

1 عضو هییت علمی

2 Bahonar University Of Kerman

3 Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

4 Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman

Abstract

Process monitoring using control charts is a common quality control method to plot the manufacturing process data and compare it to the control limits in the manufacturing process. Construction of the statistical control charts is recently suggested on the basis of the flexible triangular fuzzy quality rather than common interval-valued quality. Two new percentile-based approaches are investigated in this paper to construct mean and range control charts for the degree of belonging observations to the triangular fuzzy quality. A real-world case study about automobile engine piston rings is presented to show the performance of the proposed control charts.

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Main Subjects

References

[1] H. M. Alizadeh, S. M. T. Fatemi Ghomi, Fuzzy development of mean and range control charts using statistical
properties of different representative values, Journal of Intelligent and Fuzzy Systems, 22 (2011), 253-265. https:
//doi.org/10.3233/IFS-2011-0487
[2] V. Amirzadeh, M. Mashinchi, A. Parchami, Construction of p-charts using degree of nonconformity, Information
Sciences, 179(2) (2009), 150-160. https://doi.org/10.1016/j.ins.2008.09.010
[3] Y. C. Chen, A tutorial on kernel density estimation and recent advances, Biostatistics Epidemiology, 1 (2017),
161-187. https://doi.org/10.1080/24709360.2017.1396742
[4] M. H. Fazel Zarandi, I. B. Turksen, A. H. Kashan, Fuzzy control charts for variable and attribute quality characteristics, Iranian Journal of Fuzzy Systems, 3(1) (2006), 31-44.
[5] H. Iranmanesh, M. Jabbari Nooghabi, A. Parchami, Robust yield test for a normal production process, Quality
Engineering, 36(2) (2024), 273-286. https://doi.org/10.1080/08982112.2023.2202727
[6] H. Iranmanesh, A. Parchami, M. Jabbari Nooghabi, Testing capability index Cpk with its application in automobile
engine manufacturing industry, Quality Engineering, 35(1) (2022), 48-55. https://doi.org/10.1080/08982112.
2022.2087042
[7] H. Iranmanesh, A. Parchami, B. Sadeghpour Gildeh, A case study on quality test based on fuzzy specification
limits, International Conference on Intelligent and Fuzzy Systems, (2021), 636-643. https://doi.org/10.1007/
978-3-030-85577-2-75
[8] H. Iranmanesh, A. Parchami, B. Sadeghpour-Gildeh, Statistical testing quality and its Monte Carlo simulation based
on fuzzy specification limits, Iranian Journal of Fuzzy Systems, 19(3) (2022), 1-17. https://doi.org/10.22111/
IJFS.2022.6940
[9] D. C. Montgomery, Introduction to statistical quality control, John Wiley and Sons, New York, 2001.
[10] A. Parchami, H. Iranmanesh, B. Sadeghpour Gildeh, Simulation testing of fuzzy quality with a case study in
pipe manufacturing industries, International Conference on Intelligent and Fuzzy Systems, (2021), 630-635. https:
//doi.org/10.1007/978-3-030-85577-2-74
[11] A. Parchami, H. Iranmanesh, B. Sadeghpour-Gildeh, Monte Carlo statistical test for fuzzy quality, Iranian Journal
of Fuzzy Systems, 19(1) (2022), 115-124. https://doi.org/10.22111/IJFS.2022.6555
[12] A. Parchami, M. Mashinchi, A new generation of process capability indices, Journal of Applied Statistics, 37(1)
(2010), 77-89. https://doi.org/10.1080/02664760802695785
[13] A. Parchami, B. Sadeghpour-Gildeh, M. Mashinchi, Why fuzzy quality?, International Journal for Quality Research,
10(3) (2016), 457-470. https://doi.org/10.18421/IJQR10.03-01
[14] W. L. Pearn, S. Kotz, Encyclopedia and handbook of process capability indices: A comprehensive exposition of
quality control measures, World Scientific, Singapore, 2006.
[15] B. Sadeghpour Gildeh, Comparison of Cp, Cpk and Cp-tilde process capability indices in the case of measurement
error occurrence, IFSA World Congress, Istanbul, Turkey, (2003), 563-567.
[16] L. Scrucca, qcc: An R package for quality control charting and statistical process control, R News, 4(1) (2004),
11-17.
[17] T. R. Tsai, Skew normal distribution and the design of control charts for averages, International Journal of Reliability, Quality and Safety Engineering, 14(1) (2007), 49-63. https://doi.org/10.1142/S0218539307002507
[18] C. Yongting, Fuzzy quality and analysis on fuzzy probability, Fuzzy Sets and Systems, 83 (1996), 283-290. https:
//doi.org/10.1016/0165-0114(95)00383-5
Iranian Journal of Fuzzy Systems
Volume 21, Issue 3
May and June 2024
Pages 91-101

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