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Exponentiated models preserve stochastic orderings of parallel and series systems

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  • Narayanaswamy Balakrishnan
  • Ghobad Barmalzan
  • Abedin Haidari

Abstract

In this paper, we establish that the usual stochastic, hazard rate, reversed hazard rate, likelihood ratio, dispersive and star orders are all preserved for parallel systems under exponentiated models for lifetimes of components. We then use the multiple-outlier exponentiated gamma models to illustrate this result. Finally, we consider the dual family with exponentiated survival function and establish similar results for series systems. The results established here extend some well-known results for series and parallel systems arising from different exponentiated distributions such as generalized exponential and exponentiated Weibull, established previously in the literature.

Suggested Citation

  • Narayanaswamy Balakrishnan & Ghobad Barmalzan & Abedin Haidari, 2020. "Exponentiated models preserve stochastic orderings of parallel and series systems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(7), pages 1592-1602, April.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:7:p:1592-1602
    DOI: 10.1080/03610926.2018.1532007
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    Cited by:

    1. Luigi-Ionut Catana & Vasile Preda, 2022. "A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes," Mathematics, MDPI, vol. 11(1), pages 1-14, December.

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