Data Driven Block Replacement Scheduling

• URL: http://arxiv.org/abs/2607.15229v1
• Date: Thu, 16 Jul 2026 17:31:15 GMT
• Title: Data Driven Block Replacement Scheduling
• Abstract summary: We develop data-driven algorithms for maintaining $N$ independent identical machines under a textitblock replacement policy<n>The goal is to learn the cost-minimizing interval $k*$ from operational data when the lifetime distribution is unknown.<n>A complementary Kaplan--Meier renewal algorithm estimates the lifetime distribution noncensorally from censored data, achieving almost-sure policy consistency and empirically near-zero incremental regret at long horizons.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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