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Article Citation - WoS: 30Citation - Scopus: 34Discrete Time Shock Models in a Markovian Environment(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, SerkanThis paper deals with two different shock models in a Markovian environment. We study a system from a reliability point of view under these two shock models. According to the first model, the system fails if the cumulative shock magnitude exceeds a critical level, while in the second model the failure occurs when the cumulative effect of the shocks in consecutive periods is above a critical level. The shock occurrences over discrete time periods are assumed to be Markovian. We obtain expressions for the failure time distributions of the system under the two model. Illustrative computational results are presented for the survival probabilities and mean time to failure values of the system.Article Citation - WoS: 13Citation - Scopus: 14On Mean Residual Life of Discrete Time Multi-State Systems(Nctu-national Chiao Tung Univ Press, 2013) Eryilmaz, SerkanThe mean residual life function is an important characteristic in reliability and survival analysis. Although many papers have studied the mean residual life of binary systems, the study of this characteristic for multi-state systems is new. In this paper, we study mean residual life of discrete time multi-state systems that have M + 1 states of working efficiency. In particular, we consider two different definitions of mean residual life function and evaluate them assuming that the degradation in multi-state system follows a Markov process.Article Citation - WoS: 4Citation - Scopus: 6Statistical Inference for a Class of Startup Demonstration Tests(Taylor & Francis inc, 2019) Eryilmaz, SerkanIn this article, we develop a general statistical inference procedure for the probability of successful startup p in the case of startup demonstration tests when only the number of trials until termination of the experiment are observed. In particular, we define a class of startup demonstration tests and present expectation-maximization (EM) algorithm to get the maximum likelihood estimate of p for this class. Most of well-known startup testing procedures are involved in this class. Extension of the results to Markovian startups is also presented.Article Citation - WoS: 43Citation - Scopus: 50On the lifetime behavior of a discrete time shock model(Elsevier, 2013) Eryilmaz, SerkanIn this article, we study a shock model in which the shocks occur according to a binomial process, i.e. the interarrival times between successive shocks follow a geometric distribution with mean 1/p. According to the model, the system fails when the time between two consecutive shocks is less than a prespecified level. This is the discrete time version of the so-called delta-shock model which has been previously studied for the continuous case. We obtain the probability mass function and probability generating function of the system's lifetime. We also present an extension of the results to the case where the shock occurrences are dependent in a Markovian fashion. (C) 2012 Elsevier B.V. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 13Compound Markov Negative Binomial Distribution(Elsevier, 2016) Eryilmaz, SerkanLet {Y-i}(i >= 1) be a sequence of {0,1} variables which forms a Markov chain with a given initial probability distribution and one-step transition probability matrix. Define N-n to be the number of trials until the nth success ("1") in {Y-i}(i >= 1). In this paper, we study the distribution of the random variable T = Sigma(Nn)(i=1) X-i, where {X-i}(i >= 1) is a sequence of independent and identically distributed random variables having a common phase-type distribution. The distribution of T is obtained by means of phase-type distributions. (C) 2015 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 6On the Mean and Extreme Distances Between Failures in Markovian Binary Sequences(Elsevier Science Bv, 2011) Eryilmaz, Serkan; Yalcin, FeminThis paper is concerned with the mean, minimum and maximum distances between two successive failures in a binary sequence consisting of Markov dependent elements. These random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes. Exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented. (C) 2011 Elsevier B.V. All rights reserved.
