Multi-State Vector-k-Out-of-n Systems

Multi-state generalizations of binary k-out-of-n systems yielded two generic types of models. The first type, component-based systems, accounts for the number of system components being in certain states. The second type, weight-based systems, assigns specific weights (or performance levels) to each system component in each state, and accounts for the cumulative weight of the components. The two types of systems cannot be mapped to each other. This paper introduces a new general model, named the multi-state vector-k-out-of-n system, which is motivated by transmission, transportation, manufacturing, and service applications. It shows that both existing component-based and weight-based k-out-of-n models are special cases of the suggested model. An algorithm for evaluating the state probabilities of the multi-state vector-k-out-of-n system is suggested. A numerical example is presented.