10 results
Search Results
Now showing 1 - 10 of 10
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: 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: 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: 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 - Scopus: 5Component Importance in Coherent Systems With Exchangeable Components(Applied Probability Trust, 2015) Eryilmaz,S.This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results. © 2015 Applied Probability Trust.Article Citation - WoS: 5Citation - Scopus: 8Discrete Scan Statistics Generated by Exchangeable Binary Trials(Cambridge Univ Press, 2010) Eryilmaz, SerkanLet {X-i}(i=1)(n) be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable S-n,S-m to be the maximum number of Is within any m consecutive trials in {X-i}(i=1)(n). The random variable S-n,S-m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {X-i}(i=1)(n) consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of S-n,S-m for 2m >= n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.Article Citation - WoS: 11Citation - Scopus: 12Discrete Time Shock Models Involving Runs(Elsevier Science Bv, 2015) Eryilmaz, SerkanIn this paper, three different discrete time shock models are studied. In the first model, the failure occurs when the additively accumulated damage exceeds a certain level while in the second model the system fails upon the local damage caused by the consecutively occurring shocks. The third model is a mixed model and combines the first and second models. The survival functions of the systems under these models are obtained when the occurrences of the shocks are independent, and when they are Markov dependent over the periods. (C) 2015 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: 66Citation - Scopus: 77Generalized 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: 4Citation - Scopus: 5A New Class of Lifetime Distributions(Elsevier Science Bv, 2016) Eryilmaz, SerkanIn this paper, a new class of lifetime distributions which is obtained by compounding arbitrary continuous lifetime distribution and discrete phase-type distribution is introduced. In particular, the class of exponential-phase type distributions is studied with some details. (C) 2016 Elsevier B.V. All rights reserved.
