Some bounds for the renewal function and the variance of the renewal process

作者：

Highlights：

• A new improved general lower bound for the renewal function.

• Improved upper and lower bounds for the renewal function based on reliability classifications (IMRL, DMRL, NWUE, NBUE, bounded failure rate, (n + 1)-NBU, (n + 1)-NWU, 2-NBUCX) of the distribution of the inter-arrival times.

• Improved bounds for the variance of the renewal process.

摘要

•A new improved general lower bound for the renewal function.•Improved upper and lower bounds for the renewal function based on reliability classifications (IMRL, DMRL, NWUE, NBUE, bounded failure rate, (n + 1)-NBU, (n + 1)-NWU, 2-NBUCX) of the distribution of the inter-arrival times.•Improved bounds for the variance of the renewal process.

论文关键词：Renewal process,Renewal function,IMRL(DMRL) class,NBUE (NWUE) class,NBU (NWU) class,Failure rate,Equilibrium distributions,Bounds,Variance

论文评审过程：Received 16 March 2022, Revised 17 June 2022, Accepted 17 August 2022, Available online 6 September 2022, Version of Record 6 September 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127497