BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application

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)
Muhammad Mashuri (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia)
Muhammad Ahsan (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia)



Article Info

Publish Date
08 Apr 2026

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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Journal Info

Abbrev

barekeng

Publisher

Subject

Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

Description

BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure ...