基于多元泊松时间序列的累积和控制图设计

CUSUM Control Chart Design for Multivariate Poisson Time Series

多元离散自相关数据在现代制造业中非常普遍,时间序列控制图常被用来监控此类数据,如P-CUSUM和P-EWMA图等。然而,这些控制图都建立在一维的泊松时间序列模型基础上,忽视多个维度之间的相关性,因此应用范围有限。基于多元泊松一阶自回归时间序列模型,建立多元累积和控制图。之后利用蒙特卡洛模拟,研究了模型参数和偏移距离对该控制图性能的影响。与传统的一维离散自相关数据的控制图相比,在某些参数组合的情形下,新控制图对过程偏移具有较高的灵敏度。

Multiple discrete autocorrelation data are very common in the manufacturing industry.The most commonly used control charts for monitoring such data include P-CUSUM and P-EWMA charts.However,these control charts are based on one-dimensional Poisson integer time series model,ignoring the correlation between multiple dimensions.In this paper,a multivariate control chart is established on the generalized Poisson-integer first-order autoregressive time series model.Monte Carlo simulation is used to compare the average running chain length(ARL) of multivariate control charts with traditional one-dimensional control charts.The results show that the new control chart improves the sensitivity to process shifts in the case of certain parameters.