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<p>This paper proposes a control chart for monitoring percentiles of a process that follows a truncated beta distribution, utilizing a studentized parametric bootstrap method to account for the case when in-control parameters are unknown. To evaluate the in-control performance, extensive Monte Carlo simulations are conducted across various combinations of percentiles, false alarm rates, and sample sizes, with performance measured in terms of the average run length. The out-of-control performance is thoroughly assessed by introducing shifts in the distributional parameters and comparing the proposed chart with the conventional beta-based chart. The effectiveness and practical applicability of the proposed chart is illustrated through real-world examples from environmental data.</p>

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Studentized bootstrap control chart for percentiles of truncated beta distributed environmental data

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Bidhan Modok,
  • Amarjit Kundu,
  • Shovan Chowdhury

摘要

This paper proposes a control chart for monitoring percentiles of a process that follows a truncated beta distribution, utilizing a studentized parametric bootstrap method to account for the case when in-control parameters are unknown. To evaluate the in-control performance, extensive Monte Carlo simulations are conducted across various combinations of percentiles, false alarm rates, and sample sizes, with performance measured in terms of the average run length. The out-of-control performance is thoroughly assessed by introducing shifts in the distributional parameters and comparing the proposed chart with the conventional beta-based chart. The effectiveness and practical applicability of the proposed chart is illustrated through real-world examples from environmental data.