Abstract

Renewal reward processes measure the cumulative rewards up to a given time, and sometimes uncertainty and randomness exist at the same time due to the complexity of real world. This article considers the first hitting time for the renewal process with uncertain interarrival times and random rewards. Analytic representations and numerical algorithms for the chance distribution and expected value of first hitting time are derived. Numerical examples illustrate our methods in detail. Finally, the first hitting time is applied to modeling the shortage index for an uncertain random production risk process.

中文翻译：

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更新过程的第一次命中时间不确定的到达时间和随机奖励

摘要

更新奖励过程测量到给定时间的累积奖励，由于现实世界的复杂性，有时不确定性和随机性同时存在。本文考虑了更新过程的第一次命中时间，具有不确定的到达时间和随机奖励。推导了首发时间概率分布和期望值的解析表示和数值算法。数值示例详细说明了我们的方法。最后，将第一次命中时间应用于不确定随机生产风险过程的短缺指数建模。