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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: 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: 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: 18Citation - Scopus: 21Modeling Dependence Between Two Multi-State Components Via Copulas(Ieee-inst Electrical Electronics Engineers inc, 2014) Eryilmaz, SerkanModeling statistical dependence between two systems or components is an important problem in reliability theory. Such a problem has been well studied for binary systems and components. In the present paper, we provide a way for modeling s-dependence between two multi-state components. Our method is based on the use of copulas which are very popular for modeling s-dependence. We obtain expressions for the joint state probabilities of the two components, and illustrate the results for the case when the degradation in both components follows a Markov process.Article Citation - WoS: 43Citation - Scopus: 51The 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: 17Citation - Scopus: 21Computing the Signature of a Generalized k-out-of-n< System(Ieee-inst Electrical Electronics Engineers inc, 2015) Eryilmaz, Serkan; Tuncel, AltanA generalized k-out-of-n system which is denoted by ((n(1), ... , n(N)), f, k) consists N of modules ordered in a line or a circle, and the ith module is composed of n(i) components in parallel. (n(i) >= 1, i = 1, ... , N). The system fails iff there exist at least failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n(1) = ... = n(N) = n, and present illustrative examples to demonstrate its application. Simulation based computation of the signature is provided when the modules have different numbers of components.Article Citation - WoS: 16Citation - Scopus: 18Start-Up Demonstration Test Based on Total Successes and Total Failures With Dependent Start-Ups(Ieee-inst Electrical Electronics Engineers inc, 2012) Yalcin, Femin; Eryilmaz, SerkanStart-up demonstration testing is an effective method for illustrating the reliability of a unit before purchasing it. The test consists of starting-up the unit, and observing the outcomes, either success or failure. According to the total successes total failures (TSTF) test procedure, a unit under test is accepted when a specified number of successes is observed before a specified number of failures; otherwise, the unit is rejected. We study the TSTF procedure for dependent start-ups where the outcome of the present start-up depends on the total number of successful start-ups so far. The main characteristics of the TSTF test are obtained under this previous-sum dependent model, and numerical illustrations are presented.Article Citation - WoS: 11Citation - Scopus: 11Reliability of Systems With Multiple Types of Dependent Components(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, SerkanMost practical systems consist of multiple types of components although the components perform the same task within the system. The analysis of such systems is more challenging than the systems with single type of components. In this paper, we present expressions for the survival function of the failure time, and mean time to failure of the system under the general case when the random failure times of components of the same type are exchangeable dependent and the random failure times of components of different type are dependent. As a case study, we apply our results to linear consecutive-k-out-of-n: F systems consisting of three different types of dependent components.Article Citation - WoS: 59Citation - Scopus: 68Reliability of a k-out-of-n< System Equipped With a Single Warm Standby Component(Ieee-inst Electrical Electronics Engineers inc, 2013) Eryilmaz, SerkanAk - out - of - n : system consists of components, and operates if at least of its components operate. Its reliability properties have been widely studied in the literature from different perspectives. This paper is concerned with the reliability analysis of a k - out - of - n : G system equipped with a single warm standby unit. We obtain an explicit expression for the reliability function of the system for arbitrary lifetime distributions. Two different mean residual life functions are also studied for the system.Article Citation - WoS: 6Citation - Scopus: 6Computing Barlow-Proschan Importance in Combined Systems(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, SerkanThis paper is concerned with the computation of the Barlow-Proschan importance measure for systems involving two common failure criteria, and consisting of statistically independent and identical components. The failure or survival of these systems generally depends on the number of consecutively failed or working components, or the total number of failed or working components in the whole system. The results are applied to (n, f, k) : F and < n, f, k >: F systems.
