Reliability evaluation for acyclic consecutively connected networks with multistate elements

In this paper, an algorithm for acyclic consecutively connected networks (ACCN) reliability evaluation is suggested. The ACCNs consist of a number of positions in which multistate elements (MEs) capable of receiving and/or sending a signal are allocated. Each network has a root position where the signal source is located, a number of leaf positions that can only receive a signal, and a number of intermediate positions containing MEs capable of transmitting the received signal to some other nodes. Each ME that is located in a nonleaf node can have different states determined by a set of nodes receiving the signal directly from this ME. The probability of each state is assumed to be known for each ME. The ACCN reliability is defined as the probability that a signal from the root node is transmitted to each leaf node. The suggested algorithm is based on a universal generating function technique.