We study optimal data pooling for shared learning in two common maintenance operations: condition-based maintenance and spare parts management. We consider a set of systems subject to Poisson input -- the degradation or demand process -- that are coupled through an a-priori unknown rate. Decision problems involving these systems are high-dimensional Markov decision processes (MDPs) and hence notoriously difficult to solve. We present a decomposition result that reduces such an MDP to two-dimensional MDPs, enabling structural analyses and computations. Leveraging this decomposition, we (i) demonstrate that pooling data can lead to significant cost reductions compared to not pooling, and (ii) show that the optimal policy for the condition-based maintenance problem is a control limit policy, while for the spare parts management problem, it is an order-up-to level policy, both dependent on the pooled data.

翻译：我们研究了两种常见维护运营——基于状态的维护与备件管理——中共享学习的最优数据池化策略。考虑一组受泊松输入（退化或需求过程）影响的系统，这些系统通过先验未知的速率相互耦合。涉及这些系统的决策问题是高维马尔可夫决策过程（MDP），因此求解极其困难。本文提出一种分解结果，可将此类MDP简化为二维MDP，从而支持结构性分析与计算。利用该分解方法，我们：(i) 证明与不进行数据池化相比，数据池化可显著降低成本；(ii) 表明基于状态的维护问题的最优策略为控制极限策略，而备件管理问题的最优策略为订货至库存水平策略，且两者均依赖于池化数据。