Directed network reliability: Domination and computing coefficients of the success‐marginal expansion

The reliability for communication in a directed network can be expressed as a summation of terms, each of which involves a success‐marginal probability, that is, the probability of an event of the form {the arcs in set S are working}. Satyanarayana and Prabhakar introduced the concept of domination in order to characterize the coefficients of one such expression. This paper observes that domination can be interpreted as a partial derivative of the reliability multinomial and extends results derived for domination to the general class of expressions involving success‐marginal probabilities.