Aerospace Research Institute, Ministry of Science, Research and Technology, IRANInternational Journal of Reliability, Risk and Safety: Theory and Application2676-33461120181201A Study on the Multi-state (r, s)-out-of- n Systems with Dependent Components11167332310.30699/ijrrs.1.11ENAtefe GheisaryDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan, IranSareh GoliDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan, IranJournal Article20180701In the study of technical systems in reliability engineering, multi-state systems play a useful role. A multi-state system is a system consisting n components that system and its components may have several level performance. In the present paper, we introduce the multi-state (r, s)-out-of-n system consisting n elements having the property that each element consists two dependent components and each component of the elements and the system can be in one of m+1 possible states: 0, 1, 2,..., m. We investigate an efficient method to compute the exact reliability by using the distribution of bivariate order statistics. Depending on the number of active components of the multi-state (r, s)-out-of-n systems at time t, the mean residual lifetime function of the system is studied. Also, an example and illustrative graph is provided.http://www.ijrrs.com/article_73323_ef43d51acf3070f4cd22135ed8b2c7ad.pdf