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Simple Bounds on Cumulative Intensity Functions of Renewal and G-Renewal Processes with Increasing Failure Rate Underlying Distributions

机译：失效率不断增加的更新和G更新过程累积强度函数的简单界

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摘要

The article considers point processes most commonly used in reliability and risk analysis. Short-term and long-term behavior for the point processes used as models for repairable systems are introduced. As opposed to the long term, the term short term implies that a process is observed during an interval limited by a time close to the mean (or the median) of the respective underlying distribution. A new simple upper bound is proposed on the cumulative intensity function of the renewal process and G-renewal process with an increasing failure rate underlying distribution. The new bound is compared with some known bounds for the renewal process. Finally, a formal definition of "a boundary point" between the short-term repairable system behavior and long-term behavior is introduced. This point can also be used as a lower time limit beyond which the "long-term" Barlow and Proschan bound for the renewal process with NBUE underlying distribution could be effectively applied.
机译：本文考虑了可靠性和风险分析中最常用的点过程。介绍了用作可修复系统模型的点过程的短期和长期行为。与长期相反，短期是指在某个时间间隔内观察到某个过程，该时间间隔受时间间隔接近相应基础分布的平均值（或中位数）。针对更新过程和G更新过程的累积强度函数，提出了一个新的简单上限，其潜在故障率随着分布的增加而增加。将新范围与一些已知范围进行续订过程进行比较。最后，介绍了短期可修复系统行为和长期行为之间的“边界点”的正式定义。这一点也可以用作下限，在该下限之后，可以有效地应用具有NBUE基础分布的续签过程的“长期” Barlow和Proschan界限。

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