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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Muhammad Mashuri
Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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CONTROL LIMITS OF THE G CHART BASED ON FAST DOUBLE BOOTSTRAP WITH GENERALIZED KULLBACK-LEIBLER DIVERGENCE PARAMETER ESTIMATION Muhammad Yahya Matdoan; Muhammad Mashuri; Muhammad Ahsan
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss3pp1807-1820

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.
Co-Authors Muhammad Ahsan Muhammad Yahya Matdoan