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Improved bootstrap control chart for non-normally distributed data.

Sukma Adi Perdana1,2, Muhammad Mashuri1, Muhammad Ahsan1

  • 1Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia.

Methodsx
|February 25, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces an improved bootstrap method for control charts, enhancing accuracy and stability for non-normal data. The novel approach ensures reliable average run length (ARL) values, outperforming classic methods.

Keywords:
Bootstrap control chartControl chartsImproved Bootstrap Control ChartImproved bootstrap control chartNon-normal data

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Area of Science:

  • Statistical Process Control
  • Quality Management

Background:

  • Bootstrap control charts are crucial for data monitoring but can lack accuracy and stability with non-normal data.
  • Average run length (ARL) results from traditional bootstrap methods may not consistently achieve desired performance metrics.

Purpose of the Study:

  • To propose a novel improved bootstrap method for constructing control charts specifically designed for non-normal data.
  • To enhance the accuracy and stability of control chart performance by ensuring desired average run length (ARL₀) values.

Main Methods:

  • Development of a novel improved bootstrap methodology.
  • Construction of control limits using the improved bootstrap technique to achieve precise ARL₀ values.
  • Comparative performance analysis against existing methods like Bajgier and Liu Tang bootstrap control charts.

Main Results:

  • The proposed improved bootstrap method demonstrates superior accuracy compared to classic bootstrap control chart techniques.
  • The novel method effectively addresses the variability and potential inaccuracies in ARL results associated with traditional bootstrap control charts.
  • Ensured that the Upper Control Limit (UCL) and Lower Control Limit (LCL) precisely yield the target ARL₀ value.

Conclusions:

  • The novel improved bootstrap method offers a more accurate and stable approach for implementing control charts with non-normal data.
  • This advancement in statistical process control provides enhanced reliability for quality monitoring systems.
  • The proposed method successfully improves upon existing bootstrap control chart techniques for non-normal data analysis.