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Article Citation - WoS: 29Citation - Scopus: 31Computing Marginal and Joint Birnbaum, and Barlow-Proschan Importances in Weighted-k-out-of-n< Systems(Pergamon-elsevier Science Ltd, 2014) Eryilmaz, Serkan; Bozbulut, Ali RizaA 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.Article Citation - WoS: 13Citation - Scopus: 17Reliability of Weighted k-out-of-n< g Systems Consisting of Two Types of Components and a Cold Standby Component(Taylor & Francis inc, 2017) Franko, C.; Eryılmaz, Serkan; Tutuncu, G. Y.; Eryilmaz, S.; Eryılmaz, Serkan; Industrial Engineering; Industrial EngineeringIn this article, the influence of a cold standby component to the reliability of weighted k-out-of-n: G systems consisting of two different types of components is studied. Weighted k-out-of-n: G systems are generalization of k-out-of-n systems that has attracted substantial interest in reliability theory because of their various applications in engineering. A method based on residual lifetimes of mixed components is presented for computing reliability of weighted k-out-of-n: G systems with two types of components and a cold standby component. Reliability and mean time to failure of different structured systems have been computed. Moreover, obtained results are used for defining optimal system configurations that can minimize the overall system costs.
