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Minimal repair under a step-stress test

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  • Balakrishnan, N.
  • Kamps, U.
  • Kateri, M.

Abstract

In the one- and multi-sample cases, in the context of life-testing reliability experiments, we introduce minimal repair processes under a simple step-stress test, based on exponential distributions and an associated cumulative exposure model, and then develop likelihood inference for such a model.

Suggested Citation

  • Balakrishnan, N. & Kamps, U. & Kateri, M., 2009. "Minimal repair under a step-stress test," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1548-1558, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:13:p:1548-1558
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    References listed on IDEAS

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    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. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
    3. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    4. Raqab, Mohammad Z. & Balakrishnan, N., 2008. "Prediction intervals for future records," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1955-1963, September.
    5. Belzunce, Félix & Shaked, Moshe, 2001. "Stochastic comparisons of mixtures of convexly ordered distributions with applications in reliability theory," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 363-372, July.
    6. Khaledi, Baha-Eldin & Shojaei, Roohollah, 2007. "On stochastic orderings between residual record values," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1467-1472, July.
    7. Lugtigheid, Diederik & Banjevic, Dragan & Jardine, Andrew K.S., 2008. "System repairs: When to perform and what to do?," Reliability Engineering and System Safety, Elsevier, vol. 93(4), pages 604-615.
    8. Belzunce, Félix & Mercader, José A. & Ruiz, José M., 2003. "Multivariate aging properties of epoch times of nonhomogeneous processes," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 335-350, February.
    9. Wang, Hongzhou & Pham, Hoang, 2006. "Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1706-1722, November.
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    Cited by:

    1. Georgios Psarrakos & Antonio Di Crescenzo, 2018. "A residual inaccuracy measure based on the relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 37-59, January.
    2. Navarro, Jorge & Arriaza, Antonio & Suárez-Llorens, Alfonso, 2019. "Minimal repair of failed components in coherent systems," European Journal of Operational Research, Elsevier, vol. 279(3), pages 951-964.
    3. M. Burkschat & J. Navarro, 2014. "Asymptotic behavior of the hazard rate in systems based on sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 965-994, November.
    4. Zantek, Paul F. & Hanson, Timothy & Damien, Paul & Popova, Elmira, 2015. "A decision dependent stochastic process model for repairable systems with applications," Operations Research Perspectives, Elsevier, vol. 2(C), pages 73-80.
    5. Mahdi Salehi & Jafar Ahmadi, 2014. "Record ranked set sampling scheme," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 351-365, October.

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