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Conference Object Citation - WoS: 9Citation - Scopus: 12Stochastic Comparisons Between Lifetimes of Reliability Systems With Exchangeable Components(Springer, 2016) Koutras, Markos V.; Triantafyllou, Ioannis S.; Eryilmaz, SerkanIn this article we present several results pertaining to the stochastic comparison of the lifetimes of two reliability systems with exchangeable components. More specifically, we provide signature-based sufficient and necessary conditions for establishing hazard rate and reverse hazard rate orderings. Finally, focusing on the class of consecutive-type systems, we illustrate how the general results can be exploited to deduce several stochastic orderings among members of this class.Editorial Special Issue: International Workshop in Applied Probability 2014(Springer, 2016) Eryilmaz, S.; Koutras, Markos V.[No Abstract Available]Article Citation - WoS: 44Citation - Scopus: 52Signature Based Analysis of m-consecutive-k< f Systems With Exchangeable Components(Wiley-blackwell, 2011) Eryilmaz, Serkan; Koutras, Markos V.; Triantafyllou, Ioannis S.In this article, we study reliability properties of m-consecutive-k-out-of-n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature-based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m-consecutive-k-out-of-n: F systems. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 344-354, 2011Article Citation - WoS: 14Citation - Scopus: 17Compound Geometric Distribution of Order k(Springer, 2017) Koutras, Markos V.; Eryilmaz, SerkanThe distribution of the number of trials until the first k consecutive successes in a sequence of Bernoulli trials with success probability p is known as geometric distribution of order k. Let T (k) be a random variable that follows a geometric distribution of order k, and Y (1),Y (2),aEuro broken vertical bar a sequence of independent and identically distributed discrete random variables which are independent of T (k) . In the present article we develop some results on the distribution of the compound random variable Y-t.
