Failure rates of regenerative systems with heavy tails |
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Authors: | S Asmussen V Kalashnikov |
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Institution: | (1) Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden;(2) Institute of Systems Analysis, Prospect 60 let Oktyabrya, 9, 117312 Moscow, Russia |
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Abstract: | Let ξt be a regenerative process and assume that, at each state x, the process can fail with intensity α(x). If the inter-regeneration
times have a finite exponential moment orinf
xα(x)>0, then α(ξt) tends to some limiting positive intensity as t→∞ (under mild additional restrictions). This fact is widely used in engineering
because the limiting intensity can be employed in various calculations, say, in reliability theory. The paper contains a variety
of examples showing that α(ξt) provided that inter-regeneration time has no exponential moment andinf
x α(x)=0. The speed of convergence depends, in general, on both the tail of inter-regeneration time and α(x).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part III. |
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