Browsing by Author "Eryilmaz, Serkan"

Now showing 1 - 20 of 163

Citation - WoS: 13
Citation - Scopus: 13
Age Based Preventive Replacement Policy for Discrete Time Coherent Systems With Independent and Identical Components
(Elsevier Sci Ltd, 2023) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
The paper is concerned with an age based preventive replacement policy for an arbitrary coherent system that consists of components that are independent and have common discrete lifetime distribution. The system having an arbitrary structure is replaced preventively after a specific number of cycles or correctively at its failure time. The necessary conditions for the unique and finite replacement cycle that minimize the expected cost per unit of time are obtained. The policy is studied for some particular system models including the well-known k-out-of -n structure. The findings of the paper extend the results in the literature from single unit and parallel systems to an arbitrary coherent system. Numerical results are presented for particular discrete component lifetime distributions.
Age replacement policies for discrete and continuous heterogeneous k-out-of-n systems
(Springer, 2024) Eryilmaz, Serkan; Bulanik, Irem; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
This 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.
Citation - WoS: 5
Citation - Scopus: 5
Age Replacement Policy for Heterogeneous Parallel Systems
(Elsevier, 2024) Ozdemir, Irem Bulanik; Kilicoglu, Sevval; Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
The optimization policy on age replacement mostly focuses on systems comprised of identical components. In this paper, both discrete and continuous time age replacement policies are considered by relaxing the assumption of identical components and working with heterogeneous parallel system, i.e. system with not necessarily identical components. In particular, necessary conditions are obtained for the existence and uniqueness of optimal replacement cycle/time for the parallel system with two nonidentical components under the proposed policy. The extension of the results to a system with more than two components is also presented.(c) 2023 Elsevier B.V. All rights reserved.
Citation - WoS: 43
Citation - Scopus: 46
Age-Based Preventive Maintenance for Coherent Systems With Applications To Consecutive-k-out-of-n< and Related Systems
(Elsevier Sci Ltd, 2020) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
This article presents a signature-based representation for the expected cost rate of age-based preventive maintenance policy for a binary coherent system consisting of independent exponential components, and then specializes the method to consecutive k-out-of-n system and its generalizations. According to the age-based preventive maintenance policy, the system is replaced at failure or before failure. For an arbitrary coherent system, the number of failed components at replacement time is a random variable. Thus, the expected cost per unit of time involves the mean number of failed components at replacement time. This mean is represented in terms of signature. Extensive numerical and graphical examples are presented for m-consecutive k-out-of-n:F and consecuthre-k-within-m-out-of-n:F systems.
Citation - WoS: 35
Citation - Scopus: 42
An Algorithmic Approach for the Dynamic Reliability Analysis of Non-Repairable Multi-State Weighted k-out-of-n< System
(Elsevier Sci Ltd, 2014) Eryilmaz, Serkan; Bozbulut, Ali Riza; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
In this paper, we study a multi-state weighted k-out-of-n:G system model in a dynamic setup. In particular, we study the random time spent by the system with a minimum performance level of k. Our method is based on ordering the lifetimes of the system's components in different state subsets. Using this ordering along with the Monte-Carlo simulation algorithm, we obtain estimates of the mean and survival function of the time spent by the system in state k or above. We present illustrative computational results when the degradation in the components follows a Markov process. (C) 2014 Elsevier Ltd. All rights reserved.
Citation - WoS: 7
Citation - Scopus: 8
Analysis of the Two-Unit Cold Standby Repairable System With Damage and Repair Time Dependency Via Matrix-Exponential Distributions
(Taylor & Francis Ltd, 2021) Kus, Coskun; Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
In this paper, two-unit standby repairable system is studied via matrix-exponential distributions. The system under concern consists of one active and one standby components, and fails if either a damage size upon the failure of the active component is larger than a repair limit or the repair time of the failed unit exceeds the lifetime of the active unit, whichever happens first. Under the assumption that the damage size and repair time are statistically dependent, the Laplace transform of the system's lifetime is obtained. The Laplace transform is shown to be rational under particular cases, and the reliability evaluation of the system is performed via well-known distributional properties of the matrix-exponential distributions. The problem of estimating the unknown parameters of the operation time and repair time distributions is also discussed based on system's lifetime data.
Citation - WoS: 54
Citation - Scopus: 58
Assessment of a Multi-State System Under a Shock Model
(Elsevier Science inc, 2015) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
A system is subject to random shocks over time. Let c(1) and c(2) be two critical levels such that c(1) < c(2). A shock with a magnitude between c(1) and c(2) has a partial damage on the system, and the system transits into a lower partially working state upon the occurrence of each shock in (c(1), c(2)). A shock with a magnitude above c(2) has a catastrophic affect on the system and it causes a complete failure. Such a shock model creates a multi-state system having random number of states. The lifetime, the time spent by the system in a perfect functioning state, and the total time spent by the system in partially working states are defined and their survival functions are derived when the interarrival times between successive shocks follow phasetype distribution. (C) 2015 Elsevier Inc. All rights reserved.
Citation - WoS: 18
Citation - Scopus: 14
Assessment of Shock Models for a Particular Class of Intershock Time Distributions
(Springer, 2022) Kus, Coskun; Tuncel, Altan; Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
In this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems' lifetimes are obtained in a matrix form. Survival functions of the systems are approximated based on the Laplace-Stieltjes transforms. The results are applied for the reliability evaluation of a certain repairable system consisting of two components.
Citation - WoS: 9
Citation - Scopus: 12
The Behavior of Warm Standby Components With Respect To a Coherent System
(Elsevier Science Bv, 2011) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
This paper is concerned with a coherent system consisting of active components and equipped with warm standby components. In particular, we study the random quantity which denotes the number of surviving warm standby components at the time of system failure. We represent the distribution of the corresponding random variable in terms of system signature and discuss its potential utilization with a certain optimization problem. (C) 2011 Elsevier B.V. All rights reserved.
Citation - WoS: 28
Citation - Scopus: 29
Capacity Loss and Residual Capacity in Weighted k-out-of-n< Systems
(Elsevier Sci Ltd, 2015) Eryilmaz, Serkan; Eryılmaz, Serkan; Eryılmaz, Serkan; Industrial Engineering; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
A binary weighted-k-out-of-n:G system is a system that consists of n binary components, and functions if and only if the total weight of working components is at least k. The performance of such a system is characterized by its total weight/capacity. Therefore, the evaluation of the capacity of the system is of special importance for understanding the behavior of the system over time. This paper is concerned with capacity loss and residual capacity in binary weighted-k-out-of-n:G systems. These measures are potentially useful for the purposes of preventive action. In particular, recursive and non-recursive equations are obtained for the mean capacity loss and mean residual capacity of the binary weighted-k-out-of-n:G system while it is working at a specific time. The mean residual capacity after the failure of the system is also studied. (C) 2014 Elsevier Ltd. All rights reserved.
Citation - WoS: 9
Citation - Scopus: 10
Coherent System With Standby Components
(Wiley, 2018) Eryilmaz, Serkan; Erkan, T. Erman; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
A coherent system that consists of n independent components and equipped with r cold standby components is considered. A generalized mixture representation for the survival function of such a system is obtained, and it is used to examine reliability properties of the system. In particular, the effect of adding r standby components to a given set of original components is measured by computing mean time to failure of the system. The limiting behavior of the failure rate of the system is also examined using the mixture representation. The results are illustrated for a bridge system. A case study that is concerned with an oil pipeline system is also presented.
Citation - WoS: 18
Citation - Scopus: 21
Component importance for linear consecutive-k-Out-of-n and m-Consecutive-k-Out-of-n systems with exchangeable components
(Wiley-blackwell, 2013) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
Measuring the relative importance of components in a mechanical system is useful for various purposes. In this article, we study Birnbaum and Barlow-Proschan importance measures for two frequently studied system designs: linear consecutive k -out-of- n and m -consecutive- k -out-of- n systems. We obtain explicit expressions for the component importance measures for systems consisting of exchangeable components. We illustrate the results for a system whose components have a Lomax type lifetime distribution. (c) 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013
Citation - WoS: 5
Component Importance in Coherent Systems With Exchangeable Components
(Cambridge Univ Press, 2015) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
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.
Citation - WoS: 14
Citation - Scopus: 17
Compound Geometric Distribution of Order k
(Springer, 2017) Koutras, Markos V.; Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
The distribution of the number of trials until the first k consecutive successes in a sequence of Bernoulli trials with success probability p is known as geometric distribution of order k. Let T (k) be a random variable that follows a geometric distribution of order k, and Y (1),Y (2),aEuro broken vertical bar a sequence of independent and identically distributed discrete random variables which are independent of T (k) . In the present article we develop some results on the distribution of the compound random variable Y-t.
Citation - WoS: 11
Citation - Scopus: 13
Compound Markov Negative Binomial Distribution
(Elsevier, 2016) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
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: 6
Citation - Scopus: 6
Computing Barlow-Proschan Importance in Combined Systems
(Ieee-inst Electrical Electronics Engineers inc, 2016) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
This 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.
Citation - WoS: 5
Citation - Scopus: 6
Computing Finite Time Non-Ruin Probability and Some Joint Distributions in Discrete Time Risk Model With Exchangeable Claim Occurrences
(Elsevier, 2017) Eryilmaz, Serkan; Gebizlioglu, Omer L.; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
In this paper, we study a discrete time risk model based on exchangeable dependent claim occurrences. In particular, we obtain expressions for the finite time non-ruin probability, and the joint distribution of the time to ruin, the surplus immediately before ruin, and the deficit at ruin. An illustration of the results is given and some implications of the results are provided. Comparisons are made with the corresponding results for the classical compound binomial model of independent and identically distributed claim occurrences. (C) 2016 Elsevier E.V. All rights reserved.
Citation - WoS: 29
Citation - Scopus: 31
Computing Marginal and Joint Birnbaum, and Barlow-Proschan Importances in Weighted-k-out-of-n< Systems
(Pergamon-elsevier Science Ltd, 2014) Eryilmaz, Serkan; Bozbulut, Ali Riza; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
A weighted-k-out-of-n:G system is a system that consists of n binary components, each with its own positive weight, and operates only when the total weight of working components is at least k. Such a structure is useful when the components have different contributions to the performance of the entire system. This paper is concerned with both marginal and joint Birnbaum, and Barlow-Proschan (BP) importances of the components in weighted- k-out-of-n:G systems. The method of universal generating function is used for computing marginal and joint Birnbaum importances. The method for computing BP-importance is based on a direct probabilistic approach. Extensive numerical calculations are presented. By the help of these calculations and illustrations, it is possible to observe how the marginal and joint importances change with respect to the weights of components. (C) 2014 Elsevier Ltd. All rights reserved.
Citation - WoS: 1
Citation - Scopus: 2
Computing Minimal Signature of Coherent Systems Through Matrix-Geometric Distributions
(Cambridge Univ Press, 2021) Eryilmaz, Serkan; Eryılmaz, Serkan; Tank, Fatih; Eryılmaz, Serkan; Industrial Engineering; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
Signatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging problem, especially for complex coherent structures. In most cases the reliability of a binary coherent system can be linked to a tail probability associated with a properly defined waiting time random variable in a sequence of binary trials. In this paper we present a method for computing the minimal signature of a binary coherent system. Our method is based on matrix-geometric distributions. First, a proper matrix-geometric random variable corresponding to the system structure is found. Second, its probability generating function is obtained. Finally, the companion representation for the distribution of matrix-geometric distribution is used to obtain a matrix-based expression for the minimal signature of the coherent system. The results are also extended to a system with two types of components.
Citation - WoS: 59
Citation - Scopus: 63
Computing Optimal Replacement Time and Mean Residual Life in Reliability Shock Models
(Pergamon-elsevier Science Ltd, 2017) Eryilmaz, Serkan; Industrial Engineering; 06. School Of Engineering; 01. Atılım University
In this paper, matrix-based methods are presented to compute the optimal replacement time and mean residual lifetime of a system under particular class of reliability shock models. The times between successive shocks are assumed to have a common continuous phase-type distribution. The system's lifetime is represented as a compound random variable and some properties of phase-type distributions are utilized. Extreme shock model, run shock model, and generalized extreme shock model are shown to be the members of this class. Graphical illustrations and numerical examples are presented for the run shock model when the interarrival times between shocks follow Erlang distribution. (C) 2016 Elsevier Ltd. All rights reserved.