Delayed renewal process with uncertain interarrival times

Delayed renewal process and delayed renewal reward process are introduced in the framework of uncertainty theory and their uncertainty distributions are provided. Furthermore, delayed renewal theorem on the limit value of the expected renewal rate of the process and delayed renewal reward theorem on the limit value of the long-run expected reward per unit time are presented. At last, some examples are given. The results obtained in this paper coincide with uncertain renewal process and uncertain renewal reward process.