Stochastic Comparisons of Order Statistics, with Applications in Reliability.
Abstract
This paper surveys recent advances in stochastic comparisons of order statistics along with reliability applications. Section 2 presents inequalities for linear combinations of order statistics from restricted families. Comparisons of linear combinations of order statistics from distributions F and G are obtained for/G F convex and for/G F starshaped. These results yield conservative upper and lower tolerance limits. For G exponential and F IFR or IFRA, stochastic comparisons are presented for the total time on test, used in life testing. Section 3 presents stochastic comparisons of order statistics from underlying heterogeneous distributions. Given two sets of independent components (possibly unlike), majorization conditions are given which insure that any k-out-of-n system constructed from components in the first set will have reliability at least as great as that of a corresponding system constructed from components in the second set. Since the ordered failure times of the components represent order statistics from heterogeneous distributions, the order statistics from one set of underlying distributions (F1,...,Fn) can be compared stochastically with those from another set (F1,...,Fn).
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1987
- Accession Number
- ADA189408
Entities
People
- Frank Proschan
- Jayaram Sethuraman
- Jee S. Kim
Organizations
- Florida State University