Moments and Blackwell Convergence for Repairable Systems with Heavy Tailed Lifetimes

G. Last, R. Szekli

2001, v.7, №3, 469-490

ABSTRACT

In this paper we prove convergence of polynomial moments of a continuous time Markov process describing a repairable system. We also establish polynomial rates of this convergence. The obtained results describe in particular asymptotic properties of repairable systems working under heavy tailed lifetime distributions. The underlying failure point process is shown to obey a Blackwell type result with a polynomial speed of convergence. The results are illustrated by classical examples of repair policies, for example by the age dependent imperfect repair policy.

Keywords: imperfect repair,repairable systems,point process,stochasticintensity,compensator,Markov process,generator,convergence of moments,ergodicity,stationarity,Blackwell's theorem

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