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Article Citation - WoS: 8Citation - Scopus: 12On the Mean Residual Lifetime of Consecutive K-Out Systems(Springer, 2012) Salehi, E. T.; Asadi, M.; Eryilmaz, S.In recent years, consecutive systems were shown to have many applications in various branches of science such as engineering. This paper is a study on the stochastic and aging properties of residual lifetime of consecutive k-out-of-n systems under the condition that n-r+1, ra parts per thousand currency signn, components of the system are working at time t. We consider the linear and circular consecutive k-out-of-n systems and propose a mean residual lifetime (MRL) for such systems. Several properties of the proposed MRL is investigated. The mixture representation of the MRL of the systems with respect to the vector of signatures of the system is also studied.Article Citation - WoS: 18Citation - Scopus: 22Mean Time To Failure of Weighted k-out-of-n< G Systems(Taylor & Francis inc, 2015) Eryilmaz, SerkanThe purpose of this article is to develop a Monte-Carlo simulation algorithm for computing mean time to failure (MTTF) of weighted-k-out-of-n:G and linear consecutive-weighted-k-out-of-n:G systems. Our algorithm is based on the use of appropriately defined stochastic process which represents the total weight of the system at time t. These stochastic processes are explicitly defined and used along with the ordered component lifetimes to simulate MTTF of the systems with weighted components.Article Citation - WoS: 9Citation - Scopus: 13The Concept of Weak Exchangeability and Its Applications(Springer Heidelberg, 2017) Eryilmaz, SerkanA finite sequence of binary random variables is called a weak exchangeable sequence of order m if the sequence consists of m random vectors such that the elements within each random vector are exchangeable in the usual sense and the different random vectors are dependent. The exact and asymptotic joint distributions of the m-dimensional random vector whose elements include the number of successes in each exchangeable sequence are derived. Potential applications of the concept of weak exchangeability are discussed with illustrative examples.
