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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.Article Citation - WoS: 32Citation - Scopus: 37The Effectiveness of Adding Cold Standby Redundancy To a Coherent System at System and Component Levels(Elsevier Sci Ltd, 2017) Eryilmaz, SerkanThe effect of adding cold standby redundancy to a system at system and component levels provides a useful information in reliability design. For a series (parallel) system adding cold standby redundancy at the component (system) level yields longer system lifetime. In this paper, the effect of adding cold standby redundancy to a general coherent structure at system and component levels is studied. In particular, signature based expressions for the survival function of the system after standby redundancy at system and component levels are obtained. Thus for a given coherent structure with known signature, the survival functions and mean time to failure of new systems can be easily calculated and comparisons can be done in terms of stochastic ordering, and mean time to failure ordering. As a case study, circular consecutive-k-out-of-n:G system which can be used to analyze activities in a nuclear accelerator is considered.
