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.1.11ENAtefeGheisaryDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan, IranSarehGoliDepartment 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