监控广义线性Profile数据的变样本容量动态控制图

Dynamic Control Charts with Variable Sample Size for Monitoring Generalized Linear Profile Data

摘要: 对于离散响应变量的profile数据，比如二元的、多项的、次序的和Poisson响应的profile，进行有效的监控越来越受到统计过程控制领域研究人员的关注。这些profile都可看作广义线性模型的特殊情况。本文提出了一种基于加权似然比检验的第二阶段的变样本容量动态控制图用来监控广义线性profile数据。不仅能增强对中小漂移的检测敏感度，还可以提高检测的速度, 降低抽样成本，提高企业统计决策的精确度和可靠度。通过平均运行长度来衡量控制图的性能表现，模拟结果表明，与静态控制图相比，所提出的控制图对于模型参数的变化有很好的监控能力。

Abstract: In recent years, effective profile monitoring for discrete response variables, such as binary, multinomial, ordinal or Poisson variables, has increasingly attracted interest of researchers in the area of statistical process control. Such quality characteristics are often modeled as special cases of generalized linear models. A new control chart is developed based on the weighted likelihood ratio test with adaptive sample sizes, which is used to monitoring generalized linear profile data. It can not only enhance the sensitivity of detecting small and medium-sized shift, but it can also improve the speed of detection, reduce sampling costs, and improve the accuracy and reliability of enterprise statistical decision-making. The performance of the control chart is measured by the average running length, and the simulation results show that compared with the static control chart, the proposed control chart has good monitoring ability for changes in model parameters.