CONTROL LIMITS OF THE G CHART BASED ON FAST DOUBLE BOOTSTRAP WITH GENERALIZED KULLBACK-LEIBLER DIVERGENCE PARAMETER ESTIMATION

  • Muhammad Yahya Matdoan Department of Statistics, Faculty of Science and Technology, Universitas Pattimura, Indonesia https://orcid.org/0000-0001-6185-9300
  • Muhammad Mashuri Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia https://orcid.org/0000-0001-9348-4507
  • Muhammad Ahsan Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia https://orcid.org/0000-0003-3444-2766
DOI: https://doi.org/10.30598/barekengvol20iss3pp1807-1820
Keywords: Control limit, Fast double bootstrap, g-chart, Generalized Kulullback Leibler (GKL) divergence

Abstract

The g chart is a type of attribute control chart that is effective for monitoring processes with low defect rates. If the process parameters on the g chart are unknown, parameter estimation is performed. The most effective parameter estimation method for data contaminated with outliers is GKL divergence. This parameter estimation was developed to avoid the limitations of previous robust methods, namely the truncation method and the truncation method. However, in practice, the g chart developed from the GKL divergence parameter estimator has weaknesses, especially if there are no nonconforming items in the phase I sample, which causes a lack of sensitivity at the control limits. To overcome this problem, a bootstrap-based and double bootstrap-based control limit approach was developed. However, this approach requires high accuracy, a long time, and high computational costs. Therefore, the purpose of this study is to develop a g chart with fast double bootstrap-based control limits. The data used in this study were simulation data with contaminated and non-contaminated outliers and empirical data sourced from PT. X. regarding container weight measurements. This study found that the control limits of the g chart based on fast double bootstrap were more sensitive than the conventional and bootstrap approaches. The results indicate that the container weighing process is still under control.

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Published
2026-04-08
How to Cite
[1]
M. Y. Matdoan, M. Mashuri, and M. Ahsan, “CONTROL LIMITS OF THE G CHART BASED ON FAST DOUBLE BOOTSTRAP WITH GENERALIZED KULLBACK-LEIBLER DIVERGENCE PARAMETER ESTIMATION”, BAREKENG: J. Math. & App., vol. 20, no. 3, pp. 1807-1820, Apr. 2026.
Issue
Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2026 Muhammad Yahya Matdoan, Muhammad Mashuri, Muhammad Ahsan

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