Uncertain renewal process is an important uncertain process. This paper discusses some sample properties of uncertain renewal process. Besides, it gives some theorems on first hitting time of renewal process.

It is well known that various characteristics in risk and queuing process can be formulated as Markov Renewal function. We study the max-position of finitely many Markov Renewal Reward process with countable state space. We define Markov Renewal equation associated with max-posed process. The solutions of the Markov Renewal Reward equation are derived and the asymptotic behaviors of the equatio...

The most commonly used models for the failure process of a repairable system are nonhomogeneous Poisson processes, corresponding to minimal repairs, and renewal processes, corresponding to perfect repairs. This paper studies a more general model for recurrent events, called the Trend-Renewal Process (TRP). This is a time transformed renewal process, having both the ordinary renewal process and ...

objective: nowadays, cord blood hematopoietic stem cells (hscs) are known as a valuable source for bone marrow transplantation but unfortunately their insufficient number is a limiting factor for using them in adult bone marrow transplantation. cord blood hcss expansion is an approach to overcome this problem, by inducing their self-renewal. tgf-b signaling pathway is a key inhibitory agent for...

Uncertain process is a sequence of uncertain variables indexed by time. This paper aims to introduce a kind of uncertain process named uncertain delayed renewal reward process whose interarrival times and rewards (or costs) are regarded as uncertain variables with the first interarrival ( i.e., renewal) time and reward different from the others, respectively. The main results include the uncert...