Multi-State Consecutive- k -out-of- n Systems

In the binary context, a consecutive- k -out-of- n system is failed if and only if at least k consecutive components are failed. In this paper we propose definitions of the multi-state consecutive- k -out-of- n :F and G systems. In the proposed definition, both the system and its components may be in one of M + 1 possible states: 0, 1,..., and M . The dual relationship between the proposed systems is identified. The concept of dominance is used to characterize the properties of multi-state systems. The concepts of duality, equivalence, and dominance are used in evaluation of system state distribution of multi-state consecutive- k -out-of- n systems. An algorithm is provided for evaluating system state distribution of decreasing multi-state consecutive- k -out-of- n :F systems. Another algorithm is provided to bound system state distribution of multi-state consecutive- k -out-of- n :F and G systems. Several examples are included to illustrate the proposed definitions, concepts, and algorithms.