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On lifetimes influenced by a common environment

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  • Çinlar, Erhan
  • Shaked, Moshe
  • Shanthikumar, J. George

Abstract

Consider the lifelengths T1,..., Tk of k components subjected to a randomly varying environment. They are dependent on each other because of their common dependence of the environment. The parameters of the model are the distribution of the random process which describes the environment and a set of rate functions which determine the probability law of Ti,..., Tk as a function of the distribution of the environment. We find conditions on the parameters of the model which imply that T1,..., Tk are associated. Other conditions which imply that T1,..., Tk have the multivariate aging properties IHR (increasing hazard rate) and NBU (new better than used) are also described. Also two such models are compared. In particular, we characterize the parameters of these models so that stochastic ordering between the two vectors of resulting lifetimes can be obtained.

Suggested Citation

  • Çinlar, Erhan & Shaked, Moshe & Shanthikumar, J. George, 1989. "On lifetimes influenced by a common environment," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 347-359, December.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:2:p:347-359
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    Citations

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    Cited by:

    1. Yeek-Hyun Kim & Lyn Thomas, 2013. "Training and repair policies for stand-by systems," Annals of Operations Research, Springer, vol. 208(1), pages 469-487, September.
    2. Moshe Shaked & Fabio Spizzichino, 1998. "Positive Dependence Properties of Conditionally Independent Random Lifetimes," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 944-959, November.
    3. Y-H Kim & L C Thomas, 2006. "Repair strategies in an uncertain environment: Markov decision process approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(8), pages 957-964, August.
    4. Kuban Altinel, I. & Ozekici, Suleyman, 1998. "Optimum component test plans for systems with dependent components," European Journal of Operational Research, Elsevier, vol. 111(1), pages 175-186, November.
    5. Jeffrey P. Kharoufeh & Dustin G. Mixon, 2009. "On a Markov‐modulated shock and wear process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 563-576, September.
    6. Ozekici, Suleyman, 1995. "Optimal maintenance policies in random environments," European Journal of Operational Research, Elsevier, vol. 82(2), pages 283-294, April.

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