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Opportunity-based age replacement with a one-cycle criterion

Author

Listed:
  • P Coolen-Schrijner

    (Durham University)

  • S C Shaw

    (University of Bath)

  • F P A Coolen

    (Durham University)

Abstract

In this paper age replacement (AR) and opportunity-based age replacement (OAR) for a unit are considered, based on a one-cycle criterion, both for a known and unknown lifetime distribution. In the literature, AR and OAR strategies are mostly based on a renewal criterion, but in particular when the lifetime distribution is not known and data of the process are used to update the lifetime distribution, the renewal criterion is less appropriate and the one-cycle criterion becomes an attractive alternative. Conditions are determined for the existence of an optimal replacement age T * in an AR model and optimal threshold age T opp * in an OAR model, using a one-cycle criterion and a known lifetime distribution. In the optimal threshold age T opp *, the corresponding minimal expected costs per unit time are equal to the expected costs per unit time in an AR model. It is also shown that for a lifetime distribution with increasing hazard rate, the optimal threshold age is smaller than the optimal replacement age. For unknown lifetime distribution, AR and OAR strategies are considered within a nonparametric predictive inferential (NPI) framework. The relationship between the NPI-based expected costs per unit time in an OAR model and those in an AR model is investigated. A small simulation study is presented to illustrate this NPI approach.

Suggested Citation

  • P Coolen-Schrijner & S C Shaw & F P A Coolen, 2009. "Opportunity-based age replacement with a one-cycle criterion," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1428-1438, October.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:10:d:10.1057_jors.2008.99
    DOI: 10.1057/jors.2008.99
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    References listed on IDEAS

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    1. Coolen-Schrijner, P. & Coolen, F.P.A., 2007. "Nonparametric adaptive age replacement with a one-cycle criterion," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 74-84.
    2. Coolen, F. P. A. & Coolen-Schrijner, P., 2003. "A nonparametric predictive method for queues," European Journal of Operational Research, Elsevier, vol. 145(2), pages 425-442, March.
    3. P Coolen-Schrijner & F P A Coolen & S C Shaw, 2006. "Nonparametric adaptive opportunity-based age replacement strategies," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 63-81, January.
    4. P Coolen-Schrijner & F. P. A. Coolen, 2006. "On Optimality Criteria for Age Replacement," Journal of Risk and Reliability, , vol. 220(1), pages 21-29, June.
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    Citations

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    Cited by:

    1. Frank PA Coolen & Tahani Coolen-Maturi & Abdullah H Al-nefaiee, 2014. "Nonparametric predictive inference for system reliability using the survival signature," Journal of Risk and Reliability, , vol. 228(5), pages 437-448, October.
    2. Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2015. "Predictive inference for system reliability after common-cause component failures," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 27-33.
    3. Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V., 2017. "A study of postponed replacement in a delay time model," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 70-79.
    4. Rebecca M. Baker & Tahani Coolen-Maturi & Frank P. A. Coolen, 2017. "Nonparametric predictive inference for stock returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1333-1349, June.
    5. Aboalkhair, Ahmad M. & Coolen, Frank P.A. & MacPhee, Iain M., 2013. "Nonparametric predictive reliability of series of voting systems," European Journal of Operational Research, Elsevier, vol. 226(1), pages 77-84.
    6. Melis, Kristina & Campo, Katia & Lamey, Lien & Breugelmans, Els, 2016. "A Bigger Slice of the Multichannel Grocery Pie: When Does Consumers’ Online Channel Use Expand Retailers’ Share of Wallet?," Journal of Retailing, Elsevier, vol. 92(3), pages 268-286.
    7. Hamidi, Maryam & Szidarovszky, Ferenc & Szidarovszky, Miklos, 2016. "New one cycle criteria for optimizing preventive replacement policies," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 42-48.
    8. Truong Ba, H. & Cholette, M.E. & Borghesani, P. & Zhou, Y. & Ma, L., 2017. "Opportunistic maintenance considering non-homogenous opportunity arrivals and stochastic opportunity durations," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 151-161.
    9. Sheu, Shey-Huei & Tsai, Hsin-Nan & Sheu, Uan-Yu & Zhang, Zhe George, 2019. "Optimal replacement policies for a system based on a one-cycle criterion," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

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