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Citation - WoS: 14
Citation - Scopus: 15
Dynamic Modeling of General Three-State k-out-of-n< Systems: Permanent-Based Computational Results
(Elsevier Science Bv, 2014) Eryilmaz, Serkan; Xie, Min
This paper is concerned with dynamic reliability analysis of three-state k-out-of-n:G systems. It is assumed that the components and the systems can be in three states: perfect functioning, partial performance and complete failure. Using the concept of permanent, we study marginal and joint survival functions for the lifetime of two different three-state k-out-of-n:G systems that consist of independent and nonidentical components. Illustrative examples are also provided for the components which follow the Markov degradation process. (C) 2014 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 - 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: 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: 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: 19
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: 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: 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: 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: 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.

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