Abstract
The purpose of this paper is to introduce a fuzzy random delayed renewal process in which the interarrival times between two events are characterized as fuzzy random variables. The general properties of the process are discussed. In addition, the definition of a fuzzy random equilibrium renewal process, as a special case of the fuzzy random delayed renewal process, is also given. Finally, concerned with the fuzzy random equilibrium renewal process, the expected value of a fuzzy random equilibrium renewal variable and the mean chance of the remaining life are studied.