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Stochastic ordering for populations of manufactured items

Author

Listed:
  • Nil Kamal Hazra

    (University of the Free State)

  • Maxim Finkelstein

    (University of the Free State
    ITMO University)

  • Ji Hwan Cha

    (Ewha Womans University)

Abstract

We develop a theory of stochastic orders for the age and the residual (remaining) lifetime for populations of manufactured identical items. The obtained theoretical results can be used by manufacturers or users for the justified decisions with respect to, e.g., the increase or decrease in the production rate or with respect to the necessary maintenance actions. Specifically, we show that if the random age of a population is smaller (resp. larger) in some stochastic sense than the defined equilibrium age, then it is also smaller (resp. larger) than the corresponding residual lifetime with respect to different stochastic orders. We discuss various stochastic comparisons between the random age and the residual lifetime for one or more populations. Some ageing properties of the random age and the residual lifetime have also been studied.

Suggested Citation

  • Nil Kamal Hazra & Maxim Finkelstein & Ji Hwan Cha, 2018. "Stochastic ordering for populations of manufactured items," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 173-196, March.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-017-0539-1
    DOI: 10.1007/s11749-017-0539-1
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    References listed on IDEAS

    as
    1. Khaledi, Baha-Eldin & Shaked, Moshe, 2010. "Stochastic comparisons of multivariate mixtures," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2486-2498, November.
    2. Maxim Finkelstein & James Vaupel, 2015. "On random age and remaining lifetime for populations of items," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(5), pages 681-689, September.
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    Citations

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    Cited by:

    1. Maxim Finkelstein & Ji Hwan Cha, 2021. "On degradation-based imperfect repair and induced generalized renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1026-1045, December.
    2. Finkelstein, Maxim & Cha, Ji Hwan & Bedford, Tim, 2023. "Optimal preventive maintenance strategy for populations of systems that generate outputs," Reliability Engineering and System Safety, Elsevier, vol. 237(C).

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