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Testing for Equality of Parameters from Different Load-Sharing Systems

Author

Listed:
  • Stefan Bedbur

    (Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany)

  • Udo Kamps

    (Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany)

Abstract

In reliability, sequential order statistics serve as a model for the component lifetimes of k -out-of- n systems, which are operating as long as k out of n components are operating. In contrast to modelling with order statistics, load-sharing effects and other impacts of failures on the performance of the remaining components may be taken into consideration. Inference for associated load-sharing parameters, as well as for the underlying baseline distribution, is then of particular interest. In a setup of multiple samples of sequential order statistics modelling the component lifetimes of possibly differently structured k -out-of- n systems, we provide exact statistical tests to check for common load-sharing or common baseline-distribution parameters. In the two-sample case, critical values for the corresponding test statistics are tabulated for small sample sizes, and the asymptotic distributions of the test statistics under the null hypotheses are derived. Based on a simulation study, power comparisons are addressed. The proposed tests may be applied to detect significant differences between systems or to decide whether a meta-analysis of the data may be conducted to increase the performance of subsequent inferential procedures.

Suggested Citation

  • Stefan Bedbur & Udo Kamps, 2019. "Testing for Equality of Parameters from Different Load-Sharing Systems," Stats, MDPI, vol. 2(1), pages 1-19, January.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:1:p:6-88:d:201692
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    References listed on IDEAS

    as
    1. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    2. Balakrishnan, N. & Beutner, E. & Kamps, U., 2008. "Order restricted inference for sequential k-out-of-n systems," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1489-1502, August.
    3. Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    4. Erhard Cramer & Udo Kamps, 2001. "Estimation with Sequential Order Statistics from Exponential Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 307-324, June.
    5. Erhard Cramer & Udo Kamps, 1996. "Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 535-549, September.
    6. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
    7. N. Balakrishnan & U. Kamps & M. Kateri, 2012. "A sequential order statistics approach to step-stress testing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 303-318, April.
    8. Eric Beutner, 2008. "Nonparametric inference for sequential k-out-of-n systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 605-626, September.
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