基于高斯混合模型的非参数控制图

Nonparametric Control Chart Based on Gaussian Mixture Model

摘要: 在工业生产过程中，由于设备参数、原料特性以及工艺条件的异质性，过程数据往往呈现出复杂的多模态分布特征。这类数据结构超出传统统计过程控制方法所依赖的单模态或同分布假设的适用范围。多模态数据复杂的多峰特性，使得基于参数化分布假设的传统建模方法难以准确刻画数据的真实分布，进而影响过程监控。针对这种情况，本文提出了一种数据驱动的监控方法。首先，引入高斯混合模型对多模态过程数据进行概率密度建模，克服了传统方法在分布形式上的先验假设局限；其次，基于该模型构建负对数似然统计量，并结合指数加权移动平均策略，实现对过程异常的检测。数值仿真与实例验证了本文所提控制图的可行性和实用价值，为多模态过程的质量监控提供了一种有效的新思路。

Abstract: In industrial production processes, process data often exhibit complex multimodal distribution characteristics due to heterogeneity in equipment parameters, raw material properties, and process conditions. Such data structures exceed the applicability of traditional statistical process control methods, which typically rely on unimodal or identically distributed assumptions. The intrinsic multi-peak nature of multimodal data makes it difficult for conventional parametric modeling approaches to accurately capture the true data distribution, thereby compromising process monitoring performance. To address this issue, this paper proposes a data-driven monitoring method. First, a Gaussian mixture model is introduced to model the probability density of multimodal process data, overcoming the limitations of prior distributional assumptions inherent in traditional methods. Based on this model, a negative log-likelihood statistic is constructed and integrated with an exponentially weighted moving average strategy to detect process anomalies. Numerical simulations and real-world case studies demonstrate the feasibility and practical value of the proposed control chart, offering an effective new approach for quality monitoring in multimodal processes.