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A parametric bootstrap control chart for Lindley Geometric percentiles

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  • Muthanna Ali Hussein Al-Lami
  • Hossein Jabbari Khamnei
  • Ali Akbar Heydari

Abstract

Control charts are vital for quality control and process monitoring, helping businesses identify variations in production. Traditional control charts, like Shewhart charts, may not work well for skewed distributions, such as the Lindley geometric distribution (LG). This study introduces a new control chart that uses parametric bootstrap techniques to monitor percentiles of the LG distribution, providing a more effective quality control method. The LG distribution is useful for modeling material strength and failures, especially in structural design, where lower percentiles indicate reduced tensile strength. We conducted extensive simulations to assess the proposed control chart’s effectiveness, considering various distribution parameters, percentile values, Type I error rates, and sample sizes. Our findings highlight how subgroup size, percentiles, and significance levels affect control limits, stressing the need for careful parameter selection in monitoring processes. The results show that the new control chart is highly sensitive to changes in LG distribution parameters and performs consistently across different percentiles. This suggests its practical relevance and robustness for industrial applications in quality control. Future research should explore its performance in real-world production settings to confirm its efficiency and reliability.

Suggested Citation

  • Muthanna Ali Hussein Al-Lami & Hossein Jabbari Khamnei & Ali Akbar Heydari, 2025. "A parametric bootstrap control chart for Lindley Geometric percentiles," PLOS ONE, Public Library of Science, vol. 20(2), pages 1-29, February.
    • Handle: RePEc:plo:pone00:0316449
    DOI: 10.1371/journal.pone.0316449
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Giovanna Capizzi & Guido Masarotto, 2009. "Bootstrap-based design of residual control charts," IISE Transactions, Taylor & Francis Journals, vol. 41(4), pages 275-286.
    3. Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
    4. Waleed Ahmed Hassen Al-Nuaami & Ali Akbar Heydari & Hossein Jabbari Khamnei, 2023. "The Poisson–Lindley Distribution: Some Characteristics, with Its Application to SPC," Mathematics, MDPI, vol. 11(11), pages 1-16, May.
    5. Teyarachakul, Sunantha & Chand, Suresh & Tang, Jen, 2007. "Estimating the limits for statistical process control charts: A direct method improving upon the bootstrap," European Journal of Operational Research, Elsevier, vol. 178(2), pages 472-481, April.
    6. Krishna, Hare & Kumar, Kapil, 2011. "Reliability estimation in Lindley distribution with progressively type II right censored sample," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 281-294.
    7. Oliveira, Ricardo P. & Achcar, Jorge A. & Mazucheli, Josmar & Bertoli, Wesley, 2021. "A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    8. Rashid Mehmood & Muhammad Riaz & Ronald Does, 2013. "Efficient power computation for r out of m runs rules schemes," Computational Statistics, Springer, vol. 28(2), pages 667-681, April.
    9. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    10. Yuancheng Si & Saralees Nadarajah, 2020. "Lindley Power Series Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 242-256, February.
    11. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
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