COMPARISONS OF ORDER STATISTICS AND OF SPACINGS FROM HETEROGENEOUS DISTRIBUTIONS11Research sponsored by the Air Force Office of Scientific Research, AFSC, USAF, under Grant No. AFOSR-71-2058 and the National Science Foundation under Grant GU 2612. The United States Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation hereon.
1971; Elsevier BV; Linguagem: Inglês
10.1016/b978-0-12-604550-5.50011-0
AutoresGordon Pledger, Frank Proschan,
Tópico(s)Software Reliability and Analysis Research
ResumoGiven two sets of independent, possibly unlike, components, conditions involving majorization are given which insure that any k-out-of-n system constructed of components in the first set will have reliability at least as great as that of a corresponding system constructed of components in the second set. Since the ordered failure times of the components represent order statistics from heterogeneous distributions, we obtain stochastic comparisons between the order statistics from one set of underlying distributions {F1, …, Fn} and those from another set{F1*, …, Fn*} under both parametric and nonparametric assumptions. As a sample result, if one vector of component hazards (−log[1 −F1 (t)], …, −log[1 − Fn (t)]) majorizes a second such vector (−log[1 − F1*(t)], …, −log[1 − Fn*(t)]) for each t ≥ 0, then for k = 1, …, n, the k-th order statistic from the set {F1, …, Fn} is stochastically larger than the k-th order statistic from the set {F1*, …, Fn*}. Results of this type can be used to find bounds for the reliability of a k-out-of-n system of unlike components in terms of a k-out-of-n system of like components.
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