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Necessary and sufficient conditions for stochastic orders between (n − r + 1)-out-of-n systems in proportional hazard (reversed hazard) rates model

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  • Narayanaswamy Balakrishnan
  • Ghobad Barmalzan
  • Abedin Haidari
  • Amir T. Payandeh Najafabadi

Abstract

Consider two (n − r + 1)-out-of-n systems, one with independent and non-identically distributed components and another with independent and identically distributed components. When the lifetimes of components follow the proportional hazard rates model, we establish a necessary and sufficient condition for the usual stochastic order to hold between the lifetimes of these two systems. For the special case of r = 2, some generalized forms of this result to the hazard rate, dispersive and likelihood ratio orders are also obtained. Moreover, for the case when the lifetimes of components follow the proportional reversed hazard rates model, we derive some similar results for comparing the lifetimes of two systems . Applications of the established results to different situations are finally illustrated.

Suggested Citation

  • Narayanaswamy Balakrishnan & Ghobad Barmalzan & Abedin Haidari & Amir T. Payandeh Najafabadi, 2018. "Necessary and sufficient conditions for stochastic orders between (n − r + 1)-out-of-n systems in proportional hazard (reversed hazard) rates model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(23), pages 5854-5866, December.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:23:p:5854-5866
    DOI: 10.1080/03610926.2017.1406517
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    Cited by:

    1. Alimohammadi, Mahdi & Esna-Ashari, Maryam & Cramer, Erhard, 2021. "On dispersive and star orderings of random variables and order statistics," Statistics & Probability Letters, Elsevier, vol. 170(C).

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