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<p>This paper develops a comprehensive statistical framework for analyzing sequential order statistics (SOS) from heterogeneous populations that follow the Al-Hussaini family of distributions. We establish maximum likelihood estimation procedures for key parameters and derive a generalized likelihood ratio test for population homogeneity. The proposed Bayesian approach introduces a novel family of posteriors and constructs highest posterior density credible sets. Our simulation studies demonstrate that estimation accuracy improves with increasing sample size and number of observed failures, while the Bayesian credible sets provide more precise interval estimates than traditional confidence intervals. The methodology is applied to real-world reliability data, showing superior performance in modelling sequential failure times.</p>

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Statistical Inference for Load-Sharing Systems with Heterogeneous Populations Using Sequential Order Statistics

  • 期刊论文

  • 发表日期：

    2026年1月13日

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  • Majid Hashempour,
  • Morteza Mohammadi,
  • Mahdi Doostparast

摘要

This paper develops a comprehensive statistical framework for analyzing sequential order statistics (SOS) from heterogeneous populations that follow the Al-Hussaini family of distributions. We establish maximum likelihood estimation procedures for key parameters and derive a generalized likelihood ratio test for population homogeneity. The proposed Bayesian approach introduces a novel family of posteriors and constructs highest posterior density credible sets. Our simulation studies demonstrate that estimation accuracy improves with increasing sample size and number of observed failures, while the Bayesian credible sets provide more precise interval estimates than traditional confidence intervals. The methodology is applied to real-world reliability data, showing superior performance in modelling sequential failure times.