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Optimal allocation of minimal repairs in parallel and series systems

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  • Yiying Zhang
  • Peng Zhao

Abstract

In reliability engineering, the concept of minimal repair describes that the repair brings the failed unit (eg, system or component) to the situation which is same as it was just before the failure. With the help of the well‐known Gamma‐Poisson relationship, this paper investigates optimal allocation strategies of minimal repairs for parallel and series systems through implementing stochastic comparisons of various allocation policies in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orderings. Numerical examples are presented to illustrate these findings as well. These results not only strengthen and generalize some known ones in the seminal work of Shaked and Shanthikumar, but also solve the open problems proposed by Chahkandi et al.'s study and Arriaza et al.'s study.

Suggested Citation

  • Yiying Zhang & Peng Zhao, 2019. "Optimal allocation of minimal repairs in parallel and series systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 517-526, September.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:6:p:517-526
    DOI: 10.1002/nav.21865
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    References listed on IDEAS

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    1. Peng Zhao & Yiying Zhang, 2014. "On the maxima of heterogeneous gamma variables with different shape and scale parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 811-836, August.
    2. Antonio Arriaza & Jorge Navarro & Alfonso Suárez‐Llorens, 2018. "Stochastic comparisons of replacement policies in coherent systems under minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 550-565, September.
    3. E. Arjas & I. Norros, 1989. "Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 355-361, May.
    4. Jorge Navarro, 2018. "Stochastic comparisons of coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 465-482, May.
    5. Zhao, Peng & Zhang, Yiying & Li, Long, 2015. "Redundancy allocation at component level versus system level," European Journal of Operational Research, Elsevier, vol. 241(2), pages 402-411.
    6. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
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    8. Valdés, José E. & Zequeira, Rómulo I., 2003. "On the optimal allocation of an active redundancy in a two-component series system," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 325-332, July.
    9. Zhao, Peng & Chan, Ping Shing & Ng, Hon Keung Tony, 2012. "Optimal allocation of redundancies in series systems," European Journal of Operational Research, Elsevier, vol. 220(3), pages 673-683.
    10. Zhang, Yiying, 2018. "Optimal allocation of active redundancies in weighted k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 110-117.
    11. Zhao, Peng & Zhang, Yiying & Chen, Jianbin, 2017. "Optimal allocation policy of one redundancy in a n-component series system," European Journal of Operational Research, Elsevier, vol. 257(2), pages 656-668.
    12. M. Chahkandi & J. Ahmadi & S. Baratpour, 2014. "Some results for repairable systems with minimal repairs," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(2), pages 218-226, March.
    13. Bo H. Lindqvist & Francisco J. Samaniego, 2015. "On the signature of a system under minimal repair," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(3), pages 297-306, May.
    14. Yeo, Wee Meng & Yuan, Xue-Ming, 2009. "Optimal warranty policies for systems with imperfect repair," European Journal of Operational Research, Elsevier, vol. 199(1), pages 187-197, November.
    15. Nakagawa, Toshio & Kowada, Masashi, 1983. "Analysis of a system with minimal repair and its application to replacement policy," European Journal of Operational Research, Elsevier, vol. 12(2), pages 176-182, February.
    16. Brito, Gerandy & Zequeira, Romulo I. & Valdés, José E., 2011. "On the hazard rate and reversed hazard rate orderings in two-component series systems with active redundancies," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 201-206, February.
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    Cited by:

    1. Hui Xiao & Kunxiang Yi & Gang Kou & Liudong Xing, 2020. "Reliability of a two‐dimensional demand‐based networked system with multistate components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(6), pages 453-468, September.

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