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Article On the Definition of Sequential Consistency(Elsevier Science Bv, 2005) Sezgin, A; Gopalakrishnan, GThe definition of sequential consistency is compared with an intuitive notion of correctness. That the definition is not strong enough is illustrated through a hypothetical memory system which is clearly incorrect, yet sequentially consistent. It is claimed that the reason for this is the absence of a relation between what actually happens (temporal order) and what seems to happen (logical order). A stronger version of sequential consistency is proposed. (c) 2005 Elsevier B.V. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3On the Mean Number of Remaining Components in Three-State k-out-of-n< System(Elsevier Science Bv, 2015) Eryilmaz, Serkan; Eryılmaz, Serkan; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringA three-state k-out-of-n system with n independent components is considered, where the vector k of integers is determined by given fixed scalars k(1) and k(2) such that k(1), k(2) <= n. The mean number of components of each type either in a perfect functioning state or in a partially working state at the time of the system failure and at a time while the system is working are studied. An optimization problem concerned with the most economical value of n is also formulated. (C) 2015 Elsevier B.V. All rights reserved.Article Citation - WoS: 61Citation - Scopus: 72Generalized δ-shock model via runs(Elsevier Science Bv, 2012) Eryilmaz, SerkanAccording to the delta-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold delta. This model has a potential application in various fields such as inventory, insurance and system reliability. In this paper, we study run-related generalization of this model such that the system fails when k consecutive interarrival times are less than a threshold delta. The survival function and the mean value of the failure time of the system are explicitly derived for exponentially distributed interarrival times. We also propose a new combined shock model which considers both the magnitudes of successive shocks and the interarrival times. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 12The Behavior of Warm Standby Components With Respect To a Coherent System(Elsevier Science Bv, 2011) Eryilmaz, SerkanThis paper is concerned with a coherent system consisting of active components and equipped with warm standby components. In particular, we study the random quantity which denotes the number of surviving warm standby components at the time of system failure. We represent the distribution of the corresponding random variable in terms of system signature and discuss its potential utilization with a certain optimization problem. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1On Unfair Permutations(Elsevier Science Bv, 2018) Arslan, Ilker; Islak, Umit; Pehlivan, CihanIn this paper we study the inverse of so-called unfair permutations. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave very much alike in case of locally dependent random variables. As an example of a globally dependent statistic we use the number of inversions, and show that this statistic satisfies a central limit theorem after proper centering and scaling. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 8Citation - Scopus: 11Joint Distribution of Run Statistics in Partially Exchangeable Processes(Elsevier Science Bv, 2011) Eryilmaz, SerkanLet {X-i}(i >= 1) be an infinite sequence of recurrent partially exchangeable random variables with two possible outcomes as either "1" (success) or "0" (failure). In this paper we obtain the joint distribution of success and failure run statistics in {X-i}(i >= 1). The results can be used to obtain the joint distribution of runs in ordinary Markov chains, exchangeable and independent sequences. (C) 2010 Elsevier B.V. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4On Success Runs in a Sequence of Dependent Trials With a Change Point(Elsevier Science Bv, 2018) Eryilmaz, SerkanLet {X-i}(i=1)(n) be a sequence of n dependent binary trials such that the first n(1) in {X-i}(i=1)(n) are of type 1 and follow an exchangeable joint distribution denoted by L-1, and the last n2 elements in {X-i}(i=1)(n) are of type 2 and follow an exchangeable joint distribution denoted by L-2, where n(1) + n(2) = n. That is, the trials within the same group are exchangeable dependent, and the trials in different groups are dependent in a general sense. The exact distributions of the number of success runs of length k in {X-i}(i=1)(n) are obtained under nonoverlapping and at least schemes. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 2Sets of Random Variables With a Given Uncorrelation Structure(Elsevier Science Bv, 2001) Ostrovska, SLet xi (1),...,xi (n) be random variables having finite expectations. Denote i(k) := # {(j(1),...,j(k)): 1 less than or equal to j(1) < ... < j(k) less than or equal to n and E (l=1)pi (k) xi (fi) = (l=1)pi (k) E xi (h)}, k = 2,...,n. The finite sequence (i(2),...,i(n)) is called the uncorrelation structure of xi (1),...,xi (n). It is proved that for any given sequence of nonnegative integers (i(2),...,i(n)) satisfying 0 less than or equal to i(k) less than or equal to ((n)(k))and any given nondegenerate probability distributions P-1,...,P-n there exist random variables eta (1),...,eta (n) with respective distributions P-1,...,P-n such that (i(2),...,i(n)) is their uncorrelation structure. (C) 2001 Elsevier Science B.V. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 13Geometric Distribution of Order k With a Reward(Elsevier Science Bv, 2014) Eryilmaz, SerkanIn this paper, we introduce and study geometric distribution of order k with a reward. In a sequence of binary trials, suppose that each time a success occurs a random reward is received. The distribution of the number of trials until the sum of consecutive rewards is equal to or exceeds the level k is called geometric distribution of order k with a reward. We obtain expressions for the probability mass function of this distribution. (C) 2014 Elsevier B.V. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3q-stieltjes Classes for Some Families of q-densities(Elsevier Science Bv, 2019) Ostrovska, Sofiya; Turan, MehmetThe Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly infinite families of probability densities with the same sequence of moments. In this paper, the notion of q-moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either q-moment determinate or indeterminate in terms of its q-density have been obtained. Also, a q-analogue of Stieltjes classes is defined for q-distributions and q-Stieltjes classes have been constructed for a family of q-densities of q-moment indeterminate distributions. (C) 2018 Elsevier B.V. All rights reserved.
