基于多元泊松模型的累积和控制图设计
CUSUM Control Chart Design for Multivariate Poisson Distribution
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摘要: 多元离散数据在现代制造业中非常普遍,多元泊松控制图常被用来监控此类数据, 如MP, MP-CUSUM和MP-EWMA图等.然而, 这些控制图都假设数据服从等协方差的多元泊松模型,因为等协方差的多元泊松模型对各个变量之间的相关性有严格的约束,因此应用范围狭窄. 本文基于异协方差多元泊松模型,提出GMP-CUSUM累积和控制图. 在考虑不同模型, 变量偏移个数和偏移大小的情况下,通过蒙特卡洛模拟比较了传统控制图和新控制图GMP-CUSUM的平均运行链长(ARL),证明异协方差多元泊松模型更加适应对多元离散数据的建模, 应用范围广,并且新控制图能更快速地检测到异常过程偏移, 灵敏度高.Abstract: Multiple discrete data are very common in the manufacturing industry. Most control charts are built based on the assumption of the multivariate Poisson model with a single common covariance term, which allows only equal covariance. However, this assumption may not be realistic, for the cases observed in different regions sometimes are dependent with different covariance. Besides, these control charts cannot provide fault diagnosis information. This article presents GMP-CUSUM chart based on the multivariate Poisson model with two-way covariance structure. Using Monte Carlo simulation, we compare the average running chain length (ARL) of traditional MP control chart and the new control chart considering various factors. The results show that the latter model is more suitable for modeling multivariate discrete data and the new control chart increases sensitivity to process shifts. When applied to raw data directly, the proposed method is powerful yet simple to use in practice.