A multivariate control chart for monitoring trivariate Poisson processes with spatial correlation

一种面向三元空间相关Poisson过程的控制图设计

¹ School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China
² School of Mechanical Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received: 19 June 2021

Abstract

The multivariate and discrete data are commonly used to monitor product defects and epidemic diseases. It is difficult to model their complex structure and design a suitable control chart to monitor them in the area of statistical process control. To monitor the tri-variate Poisson process, this paper establishes a one-parameter copula function to describe the spatial correlation and designs a control chart based on the log-likelihood ratio test. The Markov chain is employed to approximate the average run length and to measure the performance of the control chart. Simulation results show that the proposed chart is efficient for detecting upward shifts and can achieve better monitoring performances when the target mean shift in control chart design is equal to a true mean shift. Compared with D chart, the proposed chart achieves a better performance when the correlation level is high.

摘要

多元离散数据常见于产品缺陷监测和流行疾病监控等环节。传统的多元控制图假设变量服从正态分布或假设各维度的变量相互独立，难以满足监控需求，因此针对多元离散数据的控制图设计一直是统计过程控制领域的热点问题。以三元Poisson过程为研究对象，引入单一参数的copula函数描述其空间相关性，基于对数似然比方法构建一种相匹配的多元CUSUM控制图。采用马尔科夫链法近似计算平均运行链长，验证控制图分别在不同的相关强度和均值变化水平下的性能，并与D控制图进行比较。仿真结果表明，该控制图能有效监控三元Poisson过程中的均值漂移，并且目标偏移量与实际偏移量接近时会获得更好的监控效果。当数据间相关性较强时，该控制图的监控性能优于D控制图。