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Multivariate Imperfect Repair

Author

Listed:
  • Moshe Shaked

    (University of Arizona, Tucson, Arizona)

  • J. George Shanthikumar

    (University of California, Berkeley, California)

Abstract

In this paper, we consider models of systems whose components have dependent lifelengths and are imperfectly repaired upon failure until they are scrapped. First, assuming that no more than one component can fail at a time, we study two models that describe imperfect repairs, and derive the resulting density and other probabilistic quantities of interest. We then generalize the models to cover applications in which more than one component can fail at the same time, and obtain various properties of the resulting distributions. Finally, we illustrate the theory through some examples.

Suggested Citation

  • Moshe Shaked & J. George Shanthikumar, 1986. "Multivariate Imperfect Repair," Operations Research, INFORMS, vol. 34(3), pages 437-448, June.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:3:p:437-448
    DOI: 10.1287/opre.34.3.437
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    Citations

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    Cited by:

    1. Balakrishnan, Narayanaswamy & Belzunce, Félix & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 45-54.
    2. Tanwar, Monika & Rai, Rajiv N. & Bolia, Nomesh, 2014. "Imperfect repair modeling using Kijima type generalized renewal process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 24-31.
    3. Richard Arnold & Stefanka Chukova & Yu Hayakawa, 2016. "Failure distributions in multicomponent systems with imperfect repairs," Journal of Risk and Reliability, , vol. 230(1), pages 4-17, February.
    4. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
    5. Zhang, Lin & Chen, Xiaohui & Khatab, Abdelhakim & An, Youjun, 2022. "Optimizing imperfect preventive maintenance in multi-component repairable systems under s-dependent competing risks," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    6. Li, Haijun & Xu, Susan H., 2001. "Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 63-89, January.
    7. 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.
    8. Cha, Ji Hwan & Kim, Jae Joo, 2001. "On availability of Bayesian imperfect repair model," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 181-187, June.
    9. Torrado, Nuria & Arriaza, Antonio & Navarro, Jorge, 2021. "A study on multi-level redundancy allocation in coherent systems formed by modules," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    10. Rajiv N Rai & Nomesh Bolia, 2014. "Availability-based optimal maintenance policies for repairable systems in military aviation by identification of dominant failure modes," Journal of Risk and Reliability, , vol. 228(1), pages 52-61, February.
    11. Félix Belzunce & Carolina Martínez-Riquelme, 2015. "Some results for the comparison of generalized order statistics in the total time on test and excess wealth orders," Statistical Papers, Springer, vol. 56(4), pages 1175-1190, November.
    12. Haijun Li & Susan H. Xu, 2004. "On the Coordinated Random Group Replacement Policy in Multivariate Repairable Systems," Operations Research, INFORMS, vol. 52(3), pages 464-477, June.
    13. 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.
    14. José Pablo Arias‐Nicolás & Félix Belzunce & Olga Núñez‐Barrera & Alfonso Suárez‐Llorens, 2009. "A multivariate IFR notion based on the multivariate dispersive ordering," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 339-358, May.
    15. Félix Belzunce & Julio Mulero & José María Ruíz & Alfonso Suárez-Llorens, 2015. "On relative skewness for multivariate distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 813-834, December.

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