Renewal and Renewal-Intensity Functions with Minimal Repair

Some Blackwell-type Renewal Theorems for Weighted Renewal Functions

In this paper, a new approach is proposed to investigate Blackwell-type renewal theorems for weighted renewal functions systematically according to which of the tails of weighted renewal constants or the underlying distribution is asymptotically heavier. Some classical results are improved considerably.

Extended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy

Lam (2007) introduces a generalization of renewal processes named Geometric processes, where inter-arrival times are independent and identically distributed up to a multiplicative scale parameter, in a geometric fashion. We here envision a more general scaling, not necessar- ily geometric. The corresponding counting process is named Extended Geometric Process (EGP). Semiparametric estimates are...

Note on Fuzzy Random Renewal Process and Renewal Rewards Process

Recently, Zhao et al. [Fuzzy Optimization and Decision Making (2007) 6, 279-295] characterized the interarrival times as fuzzy random variables and presented a fuzzy random elementary renewal theorem on the limit value of the expected renewal rate of the process in the fuzzy random renewal process. They also depicted both the interarrival times and rewards are depicted as fuzzy random variables...

Renewal Theory

(1) Sn = S0 + n ∑ i=1 Xi When S0 = 0 the renewal process is an ordinary renewal process; when S0 is a nonnegative random variable the renewal process is a delayed renewal process. In either case, the individual terms Sn of this sequence are called renewals, or sometimes occurrences. With each renewal process is associated a renewal counting process N (t ) that tracks the total number of renewal...

Information Transmission with Renewal Neurons