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Nonparametric adaptive opportunity-based age replacement strategies

Author

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  • P Coolen-Schrijner

    (University of Durham)

  • F P A Coolen

    (University of Durham)

  • S C Shaw

    (University of Bath)

Abstract

We consider opportunity-based age replacement (OAR) using nonparametric predictive inference (NPI) for the time to failure of a future unit. Based on n observed failure times, NPI provides lower and upper bounds for the survival function for the time to failure Xn+1 of a future unit which lead to upper and lower cost functions, respectively, for OAR based on the renewal reward theorem. Optimal OAR strategies for unit n+1 follow by minimizing these cost functions. Following this strategy, unit n+1 is correctively replaced upon failure, or preventively replaced upon the first opportunity after the optimal OAR threshold. We study the effect of this replacement information for unit n+1 on the optimal OAR strategy for unit n+2. We illustrate our method with examples and a simulation study. Our method is fully adaptive to available data, providing an alternative to the classical approach where the probability distribution of a unit's time to failure is assumed to be known. We discuss the possible use of our method and compare it with the classical approach, where we conclude that in most situations our adaptive method performs very well, but that counter-intuitive results can occur.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:1:d:10.1057_palgrave.jors.2601954
    DOI: 10.1057/palgrave.jors.2601954
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    References listed on IDEAS

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    1. P Coolen-Schrijner & F P A Coolen, 2004. "Adaptive age replacement strategies based on nonparametric predictive inference," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1281-1297, December.
    2. Percy, David F., 2002. "Bayesian enhanced strategic decision making for reliability," European Journal of Operational Research, Elsevier, vol. 139(1), pages 133-145, May.
    3. S Apeland & P A Scarf, 2003. "A fully subjective approach to capital equipment replacement," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 371-378, April.
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    Citations

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    Cited by:

    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. Houlding, B. & Coolen, F.P.A., 2012. "Nonparametric predictive utility inference," European Journal of Operational Research, Elsevier, vol. 221(1), pages 222-230.
    3. 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.
    4. T F Lipi & J-H Lim & M J Zuo & W Wang, 2012. "A condition- and age-based replacement model using delay time modelling," Journal of Risk and Reliability, , vol. 226(2), pages 221-233, April.
    5. P Coolen-Schrijner & F P A Coolen & I M MacPhee, 2008. "Nonparametric predictive inference for system reliability with redundancy allocation," Journal of Risk and Reliability, , vol. 222(4), pages 463-476, December.
    6. 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.
    7. 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.
    8. 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.
    9. V. J. Roelofs & F. P. A. Coolen & A. D. M. Hart, 2011. "Nonparametric Predictive Inference for Exposure Assessment," Risk Analysis, John Wiley & Sons, vol. 31(2), pages 218-227, February.

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