Reliability estimation of a multi-state system

Multi-state consecutive-k-out-of-n system is the model that is generalized form two-state consecutive-k-out-of-n system. The reliability estimation of multi-state consecutive-k-out-of-n system is a hot and difficult spot in the reliability engineering field. When both the system and its components have different states: from complete failure up to perfect functioning and performance rate is associated with each component state, the reliability of the system was analyzed based on the reliability of components. The multi-state consecutive-k-out-of-n:F system may have different structures at different system levels. A new recursive algorithm for obtaining the system state distribution of multi-state consecutive-k-out-of-n:F system including the decreasing multi-state F system, the increasing multi-state F system, and other F systems was proposed. An instance was provided to illustrate the accuracy and availability of the method in the reliability estimation through comparison with the enumerating method. This algorithm is more effective for systems with many components. Moreover, it establishes foundation to the research on the complex multi-state system.