Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Applying the Skew-Normal Distribution in Designing Fuzzy Mean and Range Quality Control Charts

Document Type : Original Article

Authors
Hamideh Iranmanesh 1
Abbas Parchami 2
Vahid Amirzade 3
Fateme Ghaderi 4
1 Department of Statistics, Faculty of Mathematical Sciences, Shahid Bahonar University of Kerman, Kerman, Iran
2 University of Kerman
3 Shahid Bahonar University of Kerman
4 Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
10.22034/jfsa.2026.552371.1288
Abstract
Control charts are considered important tools for monitoring and controlling statistical processes and play an effective role in enhancing and improving quality. In recent years, instead of the conventional quality definition approach, the use of flexible triangular fuzzy quality in designing control charts has been proposed. In this paper, novel approaches for designing $\bar{X}$ and $R$ control charts based on triangular fuzzy quality are introduced and investigated. For this purpose, conventional statistical methods, including the method of moments and maximum likelihood estimation, are used to fit the skew-normal distribution to the membership degrees of the triangular fuzzy quality. Then, two control charts based on different quantiles are presented to simultaneously monitor the mean and range of the membership degrees. To evaluate and compare the performance of the proposed and previous approaches, a real case study in the automotive industry (automobile engine piston rings) is employed, and supplementary simulations are also designed. The results indicate that the proposed control charts, relying on fuzzy quality membership functions, possess more flexibility and efficiency compared to conventional approaches.
Keywords
Quality Control Chart
Triangular Fuzzy Quality
Skew-Normal Distribution
Method of Moments Estimation
Maximum Likelihood Estimation

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Fuzzy Systems and its Applications
Volume 9, Issue 1 - Serial Number 18
Open Access Statement
June 2026
Pages 37-62

  • Receive Date 10 October 2025
  • Revise Date 19 February 2026
  • Accept Date 03 May 2026