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<p>This paper introduces the Bivariate Harmonic Vitality Function (<i>BHVF</i>), a continuous-time measure for analyzing dependence between component lifetimes in multivariate reliability systems. A conditional version (<i>CHVF</i>) evaluates the expected reciprocal lifetime of one component given the survival of another. We establish key properties and develop empirical and kernel-based estimators, whose performance is assessed through simulations and real data applications. A biomedical study of infection recurrence in kidney patients undergoing portable dialysis demonstrates the ability of the <i>CHVF</i> to capture risk patterns, with kernel estimators showing improved accuracy. An engineering application to the NASA turbofan engine dataset further illustrates its usefulness in modeling degradation and predicting failures. Overall, the proposed vitality-based framework provides a practical tool for medical and industrial reliability analysis.</p>

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On Bivariate Harmonic Vitality Function with Applications in Biomedical and Engineering Reliability

  • 期刊论文

  • 发表日期：

    2026年6月27日

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  • E. I. Abdul Sathar,
  • T. S. Athira

摘要

This paper introduces the Bivariate Harmonic Vitality Function (BHVF), a continuous-time measure for analyzing dependence between component lifetimes in multivariate reliability systems. A conditional version (CHVF) evaluates the expected reciprocal lifetime of one component given the survival of another. We establish key properties and develop empirical and kernel-based estimators, whose performance is assessed through simulations and real data applications. A biomedical study of infection recurrence in kidney patients undergoing portable dialysis demonstrates the ability of the CHVF to capture risk patterns, with kernel estimators showing improved accuracy. An engineering application to the NASA turbofan engine dataset further illustrates its usefulness in modeling degradation and predicting failures. Overall, the proposed vitality-based framework provides a practical tool for medical and industrial reliability analysis.