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On random age and remaining lifetime for populations of items

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  • Maxim Finkelstein
  • James Vaupel

Abstract

We consider items that are incepted into operation having already a random (initial) age and define the corresponding remaining lifetime. We show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we develop the population studies approach to the problem and generalize the setting in terms of stationary and stable populations of items. We obtain new stochastic comparisons for the corresponding population ages and remaining lifetimes that can be useful in applications. Copyright © 2014 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmbi:v:31:y:2015:i:5:p:681-689
    DOI: 10.1002/asmb.2073
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    Cited by:

    1. 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).
    2. Boardman, Nicholas T. & Sullivan, Kelly M., 2024. "Approximate dynamic programming for condition-based node deployment in a wireless sensor network," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    3. Francisco Villavicencio & Tim Riffe, 2016. "Symmetries between life lived and left in finite stationary populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 35(14), pages 381-398.
    4. Arijit Patra & Chanchal Kundu, 2021. "Stochastic comparisons and ageing properties of residual lifetime mixture models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 123-143, August.
    5. 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.

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