a study on the multi-state (r, s)-out-of- n systems with dependent components

In 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.