Stochastic Comparisons of Series and Parallel Systems arising from Lomax Components with ‎Archimedean Copula

Document Type : Original Paper

Authors

1 Department of Statistics, University of Zabol, Zabol, Iran

2 Department of Mathematics, University of Zabol, Zabol, Iran

Abstract

‎This paper studies the usual stochastic‎, ‎star ‎and ‎‎convex transform orders of both series and parallel systems comprised of heterogeneous‎ (and dependent) components‎. ‎Sufficient conditions are established for the star ordering between the lifetimes of series and parallel systems consisting of dependent‎
‎components having multiple-outlier lomax model‎.
‎We also prove that‎, ‎without any restriction on the parameters‎, ‎the lifetime of a parallel or series systems‎
‎with dependent heterogeneous components is smaller than that with dependent‎
‎homogeneous components in the sense of the convex transform order‎.‎

Keywords


David, H.A. and Nagaraja, H.N. (2003). Order Statistics, 3rd Ed.,
John Wiley, Hoboken, New Jersey.
 Lehmann, E. (1955). Ordered Families of Distributions. The Annals
of Mathematical Statistics, 26, 399-419.
 Khaledi, B.E. and Kochar, S.C. (2006). Weibull Distribution: Some
Stochastic Comparisons Results. Journal of Statistical Planning
and Inference, 136, 3121-3129.
Kochar, S.C. and Xu, M. (2007a). Some Recent Results on
Stochastic Comparisons and Dependence among Order Statistics in
the case of PHR Model. Journal of the Iranian Statistical Society,
6, 125-140.
[Kochar, S.C. and Xu, M. (2007b). Stochastic Comparisons of
Parallel Systems when Components Have Proportional Hazard
Rates. Probability in the Engineering and Informational Sciences,
21, 597-609.
Fang, L. and Zhang, X. (2013). Stochastic Comparison of Series
Systems with Heterogeneous Weibull Components. Statistics and
Probability Letters, 83, 1649-1653.