Linear Multistate Consecutively-Connected Systems With Gap Constraints

This paper generalizes the linear multistate consecutively-connected system model by introducing allowable gaps. The new model consists of N +1 linearly ordered nodes. Some of these nodes contain statistically independent multistate elements with different characteristics. Each element j can provide a connection between the node to which it belongs and X_j next nodes, where X_j is a discrete random variable with known probability mass function. The system fails if it contains at least m consecutive nodes not connected with any previous node (m consecutive gaps). An algorithm based on the universal generating function method is suggested for the system reliability evaluation. Illustrative examples are presented.