Showing papers by "Tamás F. Móri published in 1992"
TL;DR: In this paper, the authors studied the distribution properties of a random sum of i.i.d. non-negative random variables, where the number of terms is geometrically distributed and not independent of the summands.
Abstract: We study some distribution properties of a random sum of i.i.d. non-negative random variables, where the number of terms is geometrically distributed and not independent of the summands. The results are applied to the system failure time of a one-unit system with a single spare and repair facility. In such a system when the operating unit fails it is immediately replaced by the spare and sent to the repair facility. The system continues operating until the first time when the failed unit has not yet been repaired by the failure of the operating unit. Certain ageing properties such as NBU, NWU, NBUE, NWUE, HNBUE, HNWUE, L+ and L– are shown to be inheritable from the working time of the operating unit to the system lifetime.
6 citations
TL;DR: This time it is proved that these waiting times are getting independent as n -> oo, which is used for applying the converse part of the Borel-Cantelli lemma to problems connected with such waiting times, yielding thus improvements on some known theorems.
Abstract: For every n consider a subset Hn of the patterns of length n over a fixed finite alphabet. The limit distribution of the waiting time until each element of Hn appears in an infinite sequence of independent, uniformly distributed random letters was determined in an earlier paper. This time we prove that these waiting times are getting independent as n → ∞. Our result is used for applying the converse part of the Borel–Cantelli lemma to problems connected with such waiting times, yielding thus improvements on some known theorems.
5 citations
TL;DR: In this paper, the authors characterized all pairs of random variables (X1, X2) for which there exist no Borel measurable injections f1, f 2 such that f1(X1) and f2(X2) are uncorrelated.
3 citations
TL;DR: In this article, the authors considered the waiting time until each pattern of lengthk over a fixed alphabet of sizen appears at least once in an infinite sequence of independent, uniformly distributed random letters.
Abstract: For everyk≥1 consider the waiting time until each pattern of lengthk over a fixed alphabet of sizen appears at least once in an infinite sequence of independent, uniformly distributed random letters. Lettingn→∞ we determine the limiting finite dimensional joint distributions of these waiting times after suitable normalization and provide an estimate for the rate of convergence. It will turn out that these waiting times are getting independent.
1 citations
01 Jan 1992
TL;DR: In this paper, the authors studied some distribution properties of the solution of the renewal equation, where V and W are non-negative probability distributions, 0 < p < 1, and the results are applied in several reliability models to derive known or new properties.
Abstract: We study some distribution properties of the solution of the renewal equation, where V and W are non-negative probability distributions, 0 < p < 1, and. The results are applied in several reliability models to derive known or new theorems. Certain aging properties such as NBU, NWU, NBUE, NWUE, HNBUE, HNWUE, L+ and L- are shown to be preserved under different conditions by the geometric convolution, the failure time of a one unit system with spare and repair facility, the system lifetime in certain random shock models and the blocking time in a queuing system with an unreliable server.