Reliability analysis of a multi-state system with identical units having two dependent components

The performance evaluation of a system having n identical units, each of which consists of two components has been successfully discussed in binary-state reliability analysis. in this paper, we study the performance evaluation of a multi-state system based on bivariate order statistics. the multi-state system consists of n independent and identical units, each having two components. the components of each unit are assumed to be s-dependent. However, the units work s-independently with each other. the system and each component of each unit having three performance levels "0 (failure), 1 (partially working) and 2 (completely working)" are considered. the degradation of the components follows Markov Process and also Farlie-Gumbel-Morgenstern distribution is used to model the s-dependence of the components. the reliability analysis of a multi-state k-out-of-n system are evaluated under the assumptions. Some dynamic performance measures for the system such as the mean residual and mean past lifetime functions based on bivariate order statistics are also evaluated. the performance of the system is especially examined for different values of s-dependence parameter, the degradation rates and different number of units for the system. the results are supported with some numerical examples and graphical representations.