通过约束、无约束、复合和极小极大优化对广义渐进混合删失数据进行最优设计
Optimal Design for Generalized Progressive Hybrid Censored Data via Constrained, Unconstrained, Compound, and Minimax Optimization
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中文总结 AI 辅助
研究寿命测试实验中广义渐进混合删失方案的最优设计问题，通过成本约束优化框架及多目标优化模型，结合可变邻域搜索算法确定最优方案，同时用香农微分熵评估，该方法为最优寿命测试设计提供计算框架并奠定多目标优化基础。
中文摘要 AI 辅助
本文研究了寿命测试实验中I型广义渐进混合删失方案的最优设计问题。该设计问题涉及同时确定检查时间、保证的失效数和渐进删失方案。首先，我们开发了一个成本约束优化框架来确定最优删失方案，建立了A最优性准则和实验成本关于检查时间和保证失效数的结构性质，揭示了它们之间的冲突行为，从而开发了一种有效搜索算法以减轻计算负担。在此基础上，提出了一个多目标优化模型，同时最小化A最优性准则和实验成本，并提出了可变邻域搜索算法来有效确定最优渐进移除向量。数值研究表明，熵最优设计通常与A最优设计不同，这表明香农熵表征了观测数据中的不确定性而非估计精度。该方法为最优寿命测试设计提供了一个有效的计算框架，并为未来结合统计效率、实验成本和信息理论不确定性的多目标优化奠定了基础。
英文摘要
This paper studies the optimal design of Type-I generalized progressive hybrid censoring schemes for life-testing experiments. The design problem involves simultaneously determining the inspection time, the guaranteed number of failures, and the progressive censoring scheme. First we develop a cost-constrained optimization framework for determining the optimal censoring scheme. Structural properties of the A-optimality criterion and the experimental cost with respect to the inspection time and the guaranteed number of failures are established. It reveals that they are conflicting behaviors which enables to develop an efficient search algorithm that substantially reduces the computational burden. Building on these theoretical results, a multi-objective optimization model is proposed to simultaneously minimize A-optimality criterion and the experimental cost. A Variable Neighborhood Search (VNS) algorithm is proposed to efficiently determine the optimal progressive removal vector by exploring the feasible design space while avoiding exhaustive enumeration. The resulting compromise designs simultaneously improve estimation precision and reduce experimental cost. In addition, the Shannon differential entropy of the observed lifetime distribution is derived and employed as a complementary information-theoretic measure for evaluating the selected censoring schemes. Numerical studies show that entropy-optimal designs generally differ from A-optimal designs, indicating that Shannon entropy characterizes uncertainty in the observed data rather than estimation precision. The proposed methodology provides an efficient computational framework for optimal life-test design and offers a foundation for future multi-objective optimization incorporating statistical efficiency, experimental cost, and information-theoretic uncertainty.
