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A parametric bootstrap control chart for Lindley Geometric percentiles.

Muthanna Ali Hussein Al-Lami1,2, Hossein Jabbari Khamnei1, Ali Akbar Heydari1

  • 1Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran.

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Summary
This summary is machine-generated.

This study introduces a new control chart for monitoring skewed data, specifically the Lindley geometric (LG) distribution. Parametric bootstrap methods enhance quality control by effectively tracking LG distribution percentiles in industrial settings.

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Area of Science:

  • Industrial Engineering
  • Statistical Quality Control
  • Reliability Engineering

Background:

  • Traditional control charts (e.g., Shewhart charts) are often inadequate for skewed distributions like the Lindley geometric (LG) distribution.
  • The LG distribution is critical for modeling material strength and failure, particularly in structural design where lower percentiles signify reduced tensile strength.

Purpose of the Study:

  • To develop and evaluate a novel control chart utilizing parametric bootstrap techniques for monitoring percentiles of the LG distribution.
  • To provide a more effective quality control method for processes exhibiting skewed distributions.

Main Methods:

  • Extensive simulations were conducted to assess the proposed control chart's performance.
  • The study considered various factors including LG distribution parameters, percentile values, Type I error rates, and sample sizes.

Main Results:

  • The new control chart demonstrates high sensitivity to changes in LG distribution parameters and consistent performance across different percentiles.
  • Findings indicate that subgroup size, percentile choice, and significance levels significantly influence control limits, emphasizing the need for careful parameter selection.

Conclusions:

  • The proposed control chart offers a robust and practical solution for industrial quality control applications involving the LG distribution.
  • Further research in real-world production environments is recommended to validate its efficiency and reliability.