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Article Citation - WoS: 9Citation - Scopus: 9Mixture Representations for Three-State Systems With Three-State Components(Ieee-inst Electrical Electronics Engineers inc, 2015) Eryilmaz, SerkanThis paper is concerned with dynamic reliability modeling of three-state systems consisting of three-state s-independent components. The components and the systems are assumed to be in three states: perfect functioning, partial performance, and complete failure. Survival functions of such systems are studied in different state subsets. It is shown that the survival function of a three-state system with a general structure can be represented as a mixture of the survival functions of the three-state k-out-of-n:G systems. The results are illustrated for the three-state consecutive-k-out-of-n:G systems whose components degrade according to a Markov process.Article Citation - WoS: 14Citation - Scopus: 15Discrete Time Series-Parallel System and Its Optimal Configuration(Elsevier Sci Ltd, 2021) Dembinska, Anna; Eryilmaz, SerkanThis paper is concerned with properties of series-parallel systems when the component lifetimes have discrete failure time distribution. For a series-parallel system consisting of a specified number of subsystems, we particularly focus on the number of failed components in each subsystem at the time when the system fails. Each subsystem is assumed to have identical components while different subsystems have different types of components. Assuming all components within the system are independent, we obtain exact distributions of the number of failed components at the time when the system fails. For the special case when the components have phase-type failure time distributions, matrix-based expressions are derived for the quantities under concern. The results are used to obtain optimal configuration of the series-parallel system which is replaced at failure.Article Citation - WoS: 14Citation - Scopus: 16Joint Reliability Importance in Coherent Systems With Exchangeable Dependent Components(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, Serkan; Oruc, Ozlem Ege; Oger, VolkanIn this paper, a general formula for computing the joint reliability importance of two components is obtained for a binary coherent system that consists of exchangeable dependent components. Using the new formula, the joint reliability importance can be easily calculated if the path sets of the system are known. As a special case, an expression for the joint reliability importance of two components is also obtained for a system consisting of independent and identical components. Illustrative numerical results are presented to compare the joint reliability importance of two components in the bridge system for the two cases when the components are exchangeable dependent and when the components are independent and identical.Article Citation - WoS: 77Citation - Scopus: 80Reliability and Optimal Replacement Policy for an Extreme Shock Model With a Change Point(Elsevier Sci Ltd, 2019) Eryilmaz, Serkan; Kan, CihangirAn extreme shock model when there is a change in the distribution of the magnitudes of shocks is defined and studied. Such a model is useful in practice since a sudden change in environmental conditions may cause a larger shock. In particular, the reliability and mean time to failure of the system is obtained by assuming that the times between arrivals of shocks follow phase-type distribution. The optimal replacement policy that is based on a control limit is also proposed. The results are illustrated when the number of shocks until the change point follows geometric distribution.Article Citation - WoS: 11Citation - Scopus: 11Reliability and Performance Evaluation of Weighted K-out-of- N :g System Consisting of Components With Discrete Lifetimes(Elsevier Sci Ltd, 2024) Eryilmaz, SerkanFor the k-out-of-n n system consisting of components that have different weights, the system is in a good state if the total weight of working components is at least k . Such a system is known to be weighted k-out-of- n :G system. Although the weighted k-out-of-n n system that has continuously distributed components' lifetimes has been extensively studied, the discrete weighted k-out-of- n :G system has not been considered yet. The present paper fills this gap by modeling and analyzing the weighted k-out-of-n:G n :G system that consists of discretely distributed components' lifetimes. In particular, the behavior of the total capacity/weight of the system with respect to the component failures is evaluated. An optimization problem that is concerned with the determination of optimal number of spare components is also formulated by utilizing the mean lost capacity of the system.Article Citation - WoS: 2Citation - Scopus: 1Age replacement policies for discrete and continuous heterogeneous k-out-of-n systems(Springer, 2024) Eryilmaz, Serkan; Bulanik, IremThis paper studies age replacement policy for the k-out-of-n system that consists of independent but nonidentical components. Both continuously and discretely distributed components' lifetimes are considered. The failed components are replaced by new components and non-failed components are rejuvenated. Because the components are non-identical, the acquisition and rejuvenation costs of the components are chosen differently. The policy and the associated optimization problem are presented for general k and n, and 2-out-of-3 systems are studied in detail. The findings of the present paper extend the results in the literature from parallel systems to k-out-of-n systems.Article Citation - WoS: 46Citation - Scopus: 56Marginal and Joint Reliability Importance Based on Survival Signature(Elsevier Sci Ltd, 2018) Eryilmaz, Serkan; Coolen, Frank P. A.; Coolen-Maturi, TahaniMarginal 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.Article Citation - WoS: 21Citation - Scopus: 24A New Generalized Δ-Shock Model and Its Application To 1-out-of-(m+1):g Cold Standby System(Elsevier Sci Ltd, 2023) Eryilmaz, Serkan; Unlu, Kamil DemirberkAccording to the classical delta-shock model, the system failure occurs upon the occurrence of a new shock that arrives in a time length less than delta, a given positive value. In this paper, a new generalized version of the delta-shock model is introduced. Under the proposed model, the system fails if there are m shocks that arrive in a time length less than delta after a previous shock, m >= 1. The mean time to failure of the system is approximated for both discretely and continuously distributed intershock time distributions. The usefulness of the model is also shown to study 1-out-of-(m + 1):G cold standby system. Illustrative numerical results are presented for geometric, exponential, discrete and continuous phase-type intershock time distributions.Article Citation - WoS: 44Citation - Scopus: 52The Number of Failed Components in a Coherent System With Exchangeable Components(Ieee-inst Electrical Electronics Engineers inc, 2012) Eryilmaz, SerkanThis paper is concerned with the number of components that are failed at the time of system failure. We study the corresponding quantity for a coherent structure via the system signature. Furthermore, we study the distribution of the number of failures after a specified time until the system failure. We illustrate the results for well-known general classes of coherent systems such as linear consecutive k-within-m-out-of- n:F, and m-consecutive-k-out-of-: n:F.Article Citation - WoS: 24Citation - Scopus: 30Dynamic Assessment of Multi-State Systems Using Phase-Type Modeling(Elsevier Sci Ltd, 2015) Eryilmaz, SerkanMulti-state systems have attracted great attention due to their wide applications in engineering. They have been effectively used in modeling various systems such as power supply systems and transportation systems. In this paper, phase type modeling is proposed for dynamic assessment of nonrepairable multi-state systems when the system degrades According to a Markov process. The utility of phase type modeling is demonstrated in the computation of mean lifetimes, mean residual lifetimes, and derivation of survival functions of series and parallel systems. A stochastic comparison result between two systems is also obtained using phase representations of survival functions. Extensive numerical results are presented to illustrate the applicability of the approach. (C) 2015 Elsevier Ltd. All rights reserved.
