Reliability of circular consecutively-connected systems with multistate components

A circular consecutively-connected system with multistate components (CCCSMC) consists of a set of a components e_i, i∈[1,n] arranged in a circle. The e_i is followed by e _i+1, i∈[1,n-1]; e_n is followed by e₁ . The e_i can be in 1 of the states 0,…,k_i . If e_i is in state k∈[0,k_i], then its range is k (the k components following e_i are within its range). The system is functioning if and only if, for every component e _j, j∈[1,n] there is an e_i such that e_j is within the range of e_i. The paper gives a recursive algorithm for determining the CCCSMC reliability