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Article Citation - WoS: 12Citation - Scopus: 18Phase Type Stress-Strength Models With Reliability Applications(Taylor & Francis inc, 2018) Eryilmaz, SerkanThe stress-strength model has attracted a great deal of attention in reliability analysis, and it has been studied under various modeling assumptions. In this article, the stress-strength reliability is studied for both single unit and multicomponent systems when stress and strength distributions are of phase type. Phase-type distributions, besides their analytical tractability, are a versatile tool for modeling a wide range of real life systems/processes. In particular, matrix-based expressions are obtained for the stress-strength reliability, and mean residual strength for an operating system. The results are illustrated for Erlang-type stress-strength distributions for a single unit system and a system having a general coherent structure. An example on the comparison of two multi-state units in stress-strength ordering is also presented.Article Citation - WoS: 22Citation - Scopus: 23On Residual Lifetime of Coherent Systems After the rth Failure(Springer, 2013) Eryilmaz, SerkanIn this article we study the residual lifetime of a coherent system after the rth failure, i.e. the time elapsed from the rth failure until the system failure given that the system operates at the time of the rth failure. We provide a mixture representation for the corresponding residual lifetime distribution in terms of signature. We also obtain some stochastic ordering results for the residual lifetimes.Article Citation - WoS: 7Citation - Scopus: 8A new look at dynamic behavior of binary coherent system from a state-level perspective(Springer, 2014) Eryilmaz, SerkanIn this paper we study lifetime properties of binary coherent systems from a state-level perspective. We define and study a system whose performance levels are determined by its total number of working components and structure. That is, the more working components the better performance level for the system. This enables us to make a more detailed analysis of a binary system. We obtain the distributions of the time that is spent by the system in a specific state subset and a specific state. Our analysis is based on the use of system signature. We also define an optimization problem concerned with the determination of the number of warm standby components.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: 20Citation - Scopus: 20On Optimal Age Replacement Policy for a Class of Coherent Systems(Elsevier, 2020) Eryilmaz, Serkan; Eryılmaz, Serkan; Pekalp, Mustafa Hilmi; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringAccording to the well-known age replacement policy, the system is replaced preventively at time t or correctively at system failure, whichever occurs first. For a coherent system consisting of components having common failure time distribution which has increasing failure rate, we present necessary conditions for the existence of the unique optimal value which minimizes the mean cost rate. The conditions are mainly based on the signature which only depends on the system's structure. The results are illustrated for linear and circular consecutive type systems. (C) 2020 Elsevier B.V. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 12The Behavior of Warm Standby Components With Respect To a Coherent System(Elsevier Science Bv, 2011) Eryilmaz, SerkanThis 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.Article Citation - WoS: 8Citation - Scopus: 9The Number of Failed Components Upon System Failure When the Lifetimes Are Discretely Distributed(Elsevier Sci Ltd, 2022) Eryilmaz, Serkan; Yalcin, FeminThe number of failed components at the time when the system fails is an important quantity which can be effectively used in the determination of the optimal number of spares. This paper is concerned with the distribution and expected value of this quantity when the lifetimes of a given coherent system are discretely distributed. In particular, the distribution of the corresponding random quantity is derived for all coherent systems of order three and four. The mean number of the failed components upon system failure is exactly derived for a linear consecutive-2-out-of-n:F structure. The mean of the quantity under concern is also computed for series and parallel systems consisting of disjoint modules. The latter computation provides an efficient way to obtain the corresponding mean for a larger system via the modules which have smaller number of components.Article Citation - WoS: 32Citation - Scopus: 44The Number of Failed Components in a k-out-of-n< System Consisting of Multiple Types of Components(Elsevier Sci Ltd, 2018) Eryilmaz, SerkanThe number of failed components in a failed or operating system is a very useful quantity in terms of replacement and maintenance strategies. These quantities have been studied in several papers for a system consisting of identical components. In this paper, the number of failed components at the time when the system fails and the number of failed components when the system is working are considered for a well-known and widely applicable k-out-of-n structure. The system is assumed to have multiple types of components. That is, the system consists of components having nonidentical failure time distributions. Optimization problems are also formulated to find optimal values of the number of components of each type, and the optimal replacement time.Article Citation - WoS: 45Citation - Scopus: 48Age-Based Preventive Maintenance for Coherent Systems With Applications To Consecutive-k-out-of-n< and Related Systems(Elsevier Sci Ltd, 2020) Eryilmaz, SerkanThis 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.Article Citation - WoS: 14Citation - Scopus: 15Age Based Preventive Replacement Policy for Discrete Time Coherent Systems With Independent and Identical Components(Elsevier Sci Ltd, 2023) Eryilmaz, SerkanThe 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.
