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Citation - WoS: 22
Citation - Scopus: 24
Computing reliability indices of repairable systems via signature
(Elsevier Science Bv, 2014) Eryilmaz, Serkan
The purpose of this paper is to show the usefulness of system signature for computing some important reliability indices of repairable systems. In particular, we obtain signature-based expressions for stationary availability, rate of occurrence of failure, and mean time to the first failure of repairable systems. Using these expressions we compute corresponding reliability indices of all systems with three and four components. Computational results are also presented for consecutive-k-within-m-out-of-n:F and m-consecutive-k-out-of-n:F systems. (C) 2013 Elsevier B.V. All rights reserved.
Citation - WoS: 11
Citation - Scopus: 13
Compound Markov Negative Binomial Distribution
(Elsevier, 2016) Eryilmaz, Serkan
Let {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.
Citation - WoS: 44
Citation - Scopus: 51
On the lifetime behavior of a discrete time shock model
(Elsevier, 2013) Eryilmaz, Serkan
In 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.
Citation - WoS: 5
Citation - Scopus: 5
On the Sums of Distributions of Order Statistics From Exchangeable Random Variables
(Elsevier Science Bv, 2013) Eryilmaz, Serkan
In this paper, we obtain an expression between the sums of the marginal distributions of the order statistics and the common marginal distribution of an exchangeable random sequence. We also derive an expression between the sums of the joint distribution of two order statistics and the two dimensional joint distribution of an exchangeable random sequence. (C) 2013 Elsevier B.V. All rights reserved.
Citation - Scopus: 5
Component 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.
Citation - Scopus: 28
On stress-strength reliability with a time-dependent strength
(John Wiley and Sons Ltd, 2013) Eryilmaz,S.
The study of stress-strength reliability in a time-dependent context needs to model at least one of the stress or strength quantities as dynamic. We study the stress-strength reliability for the case in which the strength of the system is decreasing in time and the stress remains fixed over time; that is, the strength of the system is modeled as a stochastic process and the stress is considered to be a usual random variable. We present stochastic ordering results among the lifetimes of the systems which have the same strength but are subjected to different stresses. Multicomponent form of the aforementioned stress-strength interference is also considered. We illustrate the results for the special case when the strength is modeled by a Weibull process. © 2013 Serkan Eryilmaz.
Citation - WoS: 5
Citation - Scopus: 8
Discrete Scan Statistics Generated by Exchangeable Binary Trials
(Cambridge Univ Press, 2010) Eryilmaz, Serkan
Let {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.
Citation - WoS: 3
Citation - Scopus: 8
Consecutive k-within-m< System With Nonidentical Components
(Hindawi Ltd, 2012) Eryilmaz, Serkan
As a generalisation of consecutive k-out-of-n:F and k-out-of-n:F system models, a consecutive k-within-m-out-of-n: F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. In this paper, we study the survival function of a consecutive k-within-m-out-of-n:F system consisting of independent but nonidentical components. We obtain exact expressions for the survival function when 2m >= n. A detailed analysis for consecutive 2-within-m-out-of-n:F systems is presented and the asymptotic behaviour of hazard rate of these systems is investigated using mixture representations.
Citation - WoS: 20
Citation - Scopus: 20
(k_{1< k_{2< k_m< System and Its Reliability}}
(Elsevier Science Bv, 2019) Eryilmaz, Serkan
This paper is concerned with a system consisting of multiple types of components and having (k(1), k(2),..., k(m))-out-of-n structure. The (k(1), k(2),.., k(m))-out-of-n system is a system consisting of n components of type i, i = 1, 2,..., m, and functions if at least k(1) components of type 1, k(2) components of type 2,..., k(m) components of type m work, n = Sigma(n)(i=1) n(i). The exact and approximate expressions are obtained for the survival function of the system under concern. The weighted-(k(1), k(2),..., k(m))-out-of-n system is also defined and studied. This weighted model is applied to evaluate the wind power system that consists of two wind plants. (C) 2018 Elsevier B.V. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 9
Life Behavior of a System Under Discrete Shock Model
(Hindawi Ltd, 2012) Eryilmaz, Serkan
We study the life behavior of a system which is subjected to shocks of random magnitudes over discrete time periods. We obtain the survival function and mean time to failure of the system assuming that the sizes of the shocks follow a discrete probability distribution under cumulative and mixed shock models.

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