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Replacement policies for age and working numbers with random life cycle

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  • Xufeng Zhao
  • Satoshi Mizutani
  • Toshio Nakagawa

Abstract

It has been modeled for several replacement policies in literatures that the whole life cycle or operating interval of an operating unit should be finite rather than infinite as is done with the traditional method. However, it is more natural to consider the case in which the finite life cycle is a fluctuated parameter that could be used to estimate replacement times, which will be taken up in this article. For this, we first formulate a general model in which the unit is replaced at random age U, random time Y for the first working number, random life cycle S, or at failure X, whichever occurs first. The following models included in the general model, such that replacement done at age T when variable U is a degenerate distribution, and replacement done at working numbers N summed by number N of variable Y, are optimized. We obtain the total expected cost until replacement and the expected replacement cost rate for each model. Optimal age T, working number N, and a pair of (T, N) are discussed analytically and computed numerically.

Suggested Citation

  • Xufeng Zhao & Satoshi Mizutani & Toshio Nakagawa, 2017. "Replacement policies for age and working numbers with random life cycle," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6791-6802, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:14:p:6791-6802
    DOI: 10.1080/03610926.2015.1136416
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    Cited by:

    1. Yongjun Du & Lijun Shang & Qingan Qiu & Li Yang, 2022. "Optimum Post-Warranty Maintenance Policies for Products with Random Working Cycles," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    2. Jiang, Tao & Liu, Yu, 2020. "Selective maintenance strategy for systems executing multiple consecutive missions with uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. Lin, Chen & Xiao, Hui & Peng, Rui & Xiang, Yisha, 2021. "Optimal defense-attack strategies between M defenders and N attackers: A method based on cumulative prospect theory," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

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