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Empirical likelihood ratio tests for homogeneity of component lifetime distributions based on system lifetime data

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  • Jingjing Qu

    (Southern Methodist University)

  • Hon Keung Tony Ng

    (Bentley University)

  • Chul Moon

    (Southern Methodist University)

Abstract

In system reliability, practitioners may be interested in testing the homogeneity of the component lifetime distributions based on system lifetimes from multiple data sources for various reasons, such as identifying the component supplier that provides the most reliable components. In this paper, we develop distribution-free hypothesis testing procedures for the homogeneity of the component lifetime distributions based on system lifetime data when the system structures are known. Several nonparametric testing statistics based on the empirical likelihood method are proposed for testing the homogeneity of two or more component lifetime distributions. The computational approaches to obtain the critical values of the proposed test procedures are provided. The performances of the proposed empirical likelihood ratio test procedures are evaluated and compared to the nonparametric Mann–Whitney U test and some parametric test procedures. The simulation results show that the proposed test procedures provide comparable power performance under different sample sizes and underlying component lifetime distributions, and they are powerful in detecting changes in the shape of the distributions.

Suggested Citation

  • Jingjing Qu & Hon Keung Tony Ng & Chul Moon, 2024. "Empirical likelihood ratio tests for homogeneity of component lifetime distributions based on system lifetime data," Computational Statistics, Springer, vol. 39(6), pages 3007-3029, September.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:6:d:10.1007_s00180-023-01421-w
    DOI: 10.1007/s00180-023-01421-w
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    References listed on IDEAS

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    1. Jorge Navarro & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2012. "Parametric inference for component distributions from lifetimes of systems with dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 487-496, October.
    2. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
    3. Hon Ng & Jorge Navarro & Narayanaswamy Balakrishnan, 2012. "Parametric inference from system lifetime data under a proportional hazard rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 367-388, April.
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    6. Jian Zhang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2015. "Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 550-563, October.
    7. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, July-Dece.
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    9. Narayanaswamy Balakrishnan & Hon Ng & Jorge Navarro, 2011. "Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 741-752.
    10. Song Chen & Ingrid Van Keilegom, 2009. "Rejoinder on: A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 468-474, November.
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