发表机构
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在块替换策略下维护机器的问题，提出基于霍夫丁和伯恩斯坦的算法及卡普兰-迈耶更新算法，通过随机多臂老虎机方法实现低遗憾值，分析平均成本MDP，数值实验验证理论并揭示不同替换策略的成本差距。
AI 中文摘要
我们开发了数据驱动算法，用于在块替换策略下维护N个独立同分布的机器，即每台机器故障时替换，所有机器每隔k个时间间隔联合替换。目标是在寿命分布未知时从运行数据中学习成本最小化的间隔k*。在每个决策阶段，操作员选择k并观察故障历史，产生由更新函数控制的单位时间成本。我们将此问题表述为随机多臂老虎机问题，并提出基于霍夫丁和伯恩斯坦的下置信界算法，实现O(K log T)的遗憾值，与赖-罗宾斯下界匹配。利用块替换特有的嵌套观察属性，相关变体实现O((K - k*)log T)的遗憾值，并且仅需要O(1)次对次优臂k < k*的直接拉动。一种互补的卡普兰-迈耶更新算法从删失数据中对寿命分布进行非参数估计，在长期实现几乎确定的策略一致性和经验上接近零的增量遗憾值。我们还分析了两个平均成本MDP：一个时间流逝公式表明块替换在其策略类中对于任何寿命分布都是最优的，以及一个年龄向量公式证明在故障率增加的分布下具有单调阈值结构，并提供了一个黄金标准成本基准。数值实验证实了理论排序，并揭示了最优块替换和年龄依赖替换之间的结构成本差距。
英文摘要
We develop data-driven algorithms for maintaining $N$ independent identical machines under a \textit{block replacement policy}, in which each machine is replaced upon failure and all machines are jointly replaced at regular intervals of length $k$. The goal is to learn the cost-minimizing interval $k^*$ from operational data when the lifetime distribution is unknown. At each decision epoch, the operator selects $k \in \{1, 2, \ldots, K\}$, observes the resulting failure history (a mixture of complete and right-censored lifetimes) and incurs a per-unit-time cost governed by the renewal function. We formulate this as a stochastic multi-armed bandit and propose Hoeffding- and Bernstein-based lower-confidence-bound algorithms achieving $O(K \log T)$ regret, matching the Lai--Robbins lower bound. Exploiting a nested observation property unique to block replacement, correlated variants attain $O((K-k^*)\log T)$ regret and require only $O(1)$ direct pulls of suboptimal arms $k < k^*$. A complementary Kaplan--Meier renewal algorithm estimates the lifetime distribution nonparametrically from censored data, achieving almost-sure policy consistency and empirically near-zero incremental regret at long horizons. We additionally analyze two average-cost MDPs: a time-elapsed formulation establishing that block replacement is optimal within its policy class for any lifetime distribution, and an age-vector formulation proving a monotone threshold structure under increasing failure rate distributions and providing a gold-standard cost benchmark. Numerical experiments confirm the theoretical ordering and reveal structural cost gaps between optimal block and age-dependent replacement.
Comments36 pages, 4 figures
