Some new results on stochastic comparisons of parallel systems Article

Khaledi, BE, Kochar, S. (2000). Some new results on stochastic comparisons of parallel systems . JOURNAL OF APPLIED PROBABILITY, 37(4), 1123-1128. 10.1239/jap/1014843091

cited authors

  • Khaledi, BE; Kochar, S

authors

abstract

  • Let X1, …, Xn be independent exponential random variables with Xi having hazard rate λi, i = 1, …, n. Let Y1, …, Yn be a random sample of size n from an exponential distribution with common hazard rate λ = (Πni=1 λi)1/n, the geometric mean of the λis. Let Xn:n = max(X1, …, Xn). It is shown that Xn:n is greater than Yn:n according to dispersive as well as hazard rate orderings. These results lead to a lower bound for the variance of Xn:n and an upper bound on the hazard rate function of Xn:n in terms of λ. These bounds are sharper than those obtained by Dykstra et al. ((1997), J. Statist. Plann. Inference 65, 203-211), which are in terms of the arithmetic mean of the λis. Furthermore, let X∗1, …, X∗n be another set of independent exponential random variables with X∗i having hazard rate λ∗i, i = 1 …, n. It is proved that if (log λ1, …, log λn) weakly majorizes (log λ∗1, …, log λ∗n), then Xn:n is stochastically greater than X∗n:n. © 2000 Applied Probability Trust.

publication date

  • January 1, 2000

published in

Digital Object Identifier (DOI)

start page

  • 1123

end page

  • 1128

volume

  • 37

issue

  • 4