提出多规则下单位分类新方法,提升制造决策因果推断准确性
Effect Identification and Unit Categorization in the Multi-Score Regression Discontinuity Design with Application to LED Manufacturing
- 定义多维阈值下的单位行为类型,扩展传统分类体系
- 证明在排除特定类型单位后仍可识别合规者因果效应
- 通过分解布尔规则提高非合规单位识别精度,降低估计方差
RDD(回归不连续设计)是识别和估计单个运行变量阈值处因果效应的常用框架。然而,实践中决策常涉及多个阈值与标准,尤其在生产系统中。标准多评分RDD(MRD)方法将问题简化为一维设计,虽可沿用现有方法,但可能导致因误分类而产生非合规性。本文发展理论工具以检测并减少对符合子规则单位的估计模糊性。特别地,提出多维阈值规则下单位行为类型的正式定义与分类,扩展了传统的遵从者、始终参与者、从不参与者分类,并引入违抗者与犹豫者。进一步识别出在多维下可估计遵从者因果效应的条件,并确立排除从不参与者与始终参与者后识别依然有效的前提。此外,研究了将复杂布尔规则(如AND型、OR型)分解为简单组件如何影响单位行为分类,从而更准确识别并剔除非合规单位,改善估计效果。通过基于生产数据校准的半合成模拟与光电半导体制造的真实数据验证,结果表明该框架在优化生产政策方面具有实际价值,且可降低估计方差,凸显了MRD在制造场景中的适用性。
原文摘要 · Abstract (English)
RDD (Regression discontinuity design) is a widely used framework for identifying and estimating causal effects at the cutoff of a single running variable. In practice, however, decision-making often involves multiple thresholds and criteria, especially in production systems. Standard MRD (multi-score RDD) methods address this complexity by reducing the problem to a one-dimensional design. This simplification allows existing approaches to be used to identify and estimate causal effects, but it can introduce non-compliance by misclassifying units relative to the original cutoff rules. We develop theoretical tools to detect and reduce "fuzziness" when estimating the cutoff effect for units that comply with individual subrules of a multi-rule system. In particular, we propose a formal definition and categorization of unit behavior types under multi-dimensional cutoff rules, extending standard classifications of compliers, alwaystakers, and nevertakers, and incorporating defiers and indecisive units. We further identify conditions under which cutoff effects for compliers can be estimated in multiple dimensions, and establish when identification remains valid after excluding nevertakers and alwaystakers. In addition, we examine how decomposing complex Boolean cutoff rules (such as AND- and OR-type rules) into simpler components affects the classification of units into behavioral types and improves estimation by making it possible to identify and remove non-compliant units more accurately. We validate our framework using both semi-synthetic simulations calibrated to production data and real-world data from opto-electronic semiconductor manufacturing. The empirical results demonstrate that our approach has practical value in refining production policies and reduces estimation variance. This underscores the usefulness of the MRD framework in manufacturing contexts.
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