基于经验似然比检验对多数据流的在线监控

Online Monitoring of Multiple Data Streams Based on Empirical Likelihood Ratio Test

摘要: 随着人工智能与大数据的飞速发展，对多数据流的实时在线监控已成为智能制造与质量管理的核心需求。从统计过程控制的角度，提出了监控复杂结构的多数据流均值是否发生漂移的变点模型。鉴于部分数据流的偏态或长尾等特点，将单个数据流的经验似然比检验统计量转化为Q统计量。为了同时监控多数据流的中小漂移，通过Q统计量建立Max-EWMA控制图进行在线监控。以威布尔分布、指数分布、对数正态分布和t分布为例，通过蒙特卡洛模拟研究所给出的在线监控方法的性能。模拟结果表明，该控制图对监控中小漂移具有较理想的性能。

Abstract: With the rapid development of artificial intelligence and big data, real-time online monitoring of multiple data streams has become a core requirement for intelligent manufacturing and quality management. From the perspective of statistical process control, a change-point model is proposed to monitor whether the mean of complex-structured multi-data streams experiences drift. Considering characteristics such as skewness or long-tailed distributions in certain data streams, the empirical likelihood ratio test statistic for individual data streams is transformed into a Q-statistic. To simultaneously monitor small and medium drifts across multiple data streams, a Max-EWMA control chart is established using the Q-statistic for online monitoring. Taking the Weibull distribution, exponential distribution, log-normal distribution, and t-distribution as examples, the performance of the proposed online monitoring method is investigated through Monte Carlo simulations. The simulation results demonstrate that this control chart exhibits ideal performance in monitoring small and medium drifts.