10.57647/cna.2025.86c8

Construction of α-cut fuzzy X¯ control charts based on standard deviation and range using fuzzy triangular numbers

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  • Ezzatallah Baloui Jamkhaneh*1,
  1. Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Received: 2025-01-28

Revised: 2025-03-30

Accepted: 2025-06-05

Published in Issue 2025-12-30

Copyright (c) 2025 Ezzatallah Baloui Jamkhaneh (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Construction of α-cut fuzzy X¯ control charts based on standard deviation and range using fuzzy triangular numbers. (2025). Communications in Nonlinear Analysis, 13(2). https://doi.org/10.57647/cna.2025.86c8

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Abstract

Control charts are one of the fundamental tools in the field of statistical process control (SPC) that lead to improve quality processes. It is well known that conventional control charts require data to be exactly known, whereas there are many quality characteristics that cannot measured as exact number. In this paper, control charts have been extended using the fuzzy sets associated with uncertain into measuring of quality characteristics. We study two different approaches to construct control chart, when the observations are fuzzy number. Two methods of defuzzification for calculating the value representing sample means and for determining the control chart limits are presented. In the second approach α-cut control chart for variable are developed using upper control limits and lower control limits. The article also presents a fuzzy decision for in control or out of control of the process, in which membership degrees of in and out of control states of process mean is computed.

Keywords

  • Statistical process control,
  • Control charts,
  • Quality control,
  • α-cut fuzzy control charts,
  • Fuzzy number,
  • Fuzzy decision,
  • MSC 2020: 62A86, 62P30
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