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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 - 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: 46
Citation - Scopus: 56
Marginal and Joint Reliability Importance Based on Survival Signature
(Elsevier Sci Ltd, 2018) Eryilmaz, Serkan; Coolen, Frank P. A.; Coolen-Maturi, Tahani
Marginal and joint reliability importance measures have been found to be useful in optimal system design. Various importance measures have been defined and studied for a variety of system models. The results in the literature are mostly based on the assumption that the components within the system are independent or identical. The present paper is concerned with computation of marginal and joint reliability importance for a coherent system that consists of multiple types of dependent components. In particular, by utilizing the concept of survival signature, expressions for marginal and joint reliability importance measures are presented. We also introduce reliability importance for a system of which only the survival signature is known, which therefore can be regarded to be a black box system. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 1
Citation - Scopus: 2
On the Lifetime of a Random Binary Sequence
(Elsevier Science Bv, 2011) Eryilmaz, Serkan
Consider a system with m elements which is used to fulfill tasks. Each task is sent to one element which fulfills a task and the outcome is either fulfillment of the task ("1") or the failure of the element ("0"). Initially, m tasks are sent to the system. At the second step, a complex of length m(1) is formed and sent to the system, where m(1) is the number of tasks fulfilled at the first step, and so on. The process continues until all elements fail and the corresponding waiting time defines the lifetime of the binary sequence which consists of "1" or "0". We obtain a recursive equation for the expected value of this waiting time random variable. (C) 2011 Elsevier B.V. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 28
Mean residual life of coherent systems consisting of multiple types of dependent components
(Wiley, 2018) Eryilmaz, Serkan; Coolen, Frank P. A.; Coolen-Maturi, Tahani
Mean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components' lifetimes are also defined and studied.
Citation - WoS: 7
Citation - Scopus: 7
A Generalized Class of Correlated Run Shock Models
(de Gruyter Poland Sp Zoo, 2018) Yalcin, Femin; Eryilmaz, Serkan; Bozbulut, Ali Riza
In this paper, a generalized class of run shock models associated with a bivariate sequence {(X-i, Y-i)}(i >= 1) of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X-1, X-2, ... over time, let the random variables Y-1, Y-2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = Sigma(N)(t=1) Y-t, where N is a stopping time for the sequence {Xi}(i >= 1) and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {X-i, 1 <= i <= N}Distributions of T and M are investigated when N has a phase-type distribution.
Citation - WoS: 1
Citation - Scopus: 2
On Bivariate Compound Sums
(Elsevier, 2020) Tank, Fatih; Eryilmaz, Serkan
The study of compound sums have always been very popular in the literature. Many models in insurance and engineering have been represented and solved by compound sums. In this paper, two different bivariate compound sums are proposed and studied. The phase-type distribution is applied to obtain the probability generating function of the bivariate sum. (C) 2019 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: 11
Citation - Scopus: 12
A New Mixed Δ-Shock Model With a Change in Shock Distribution
(Springer, 2023) Chadjiconstantinidis, Stathis; Tuncel, Altan; Eryilmaz, Serkan
In this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.
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.

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