Order statistics, Poisson processes and repairable systems
Keyword(s):
Necessary and sufficient conditions are presented under which the point processes equivalent to order statistics of n i.i.d. random variables or superpositions of n i.i.d. renewal processes converge to a non-degenerate limiting process as n approaches infinity. The limiting process must be one of three types of non-homogeneous Poisson process, one of which is the Weibull process. These point processes occur as failure-time models in the reliability theory of repairable systems.
1976 ◽
Vol 13
(03)
◽
pp. 519-529
◽
2009 ◽
Vol 29
(3)
◽
pp. 563-576
◽
1972 ◽
Vol 4
(01)
◽
pp. 151-176
◽
1993 ◽
Vol 30
(03)
◽
pp. 602-615
◽
1988 ◽
Vol 25
(02)
◽
pp. 423-427
◽
1993 ◽
Vol 30
(04)
◽
pp. 877-888
◽
1984 ◽
Vol 21
(04)
◽
pp. 720-729
◽