监视过程均值变化的残差控制图检测能力分析

Detectability Analysis of Residual Control Charts for Monitoring Change in Mean Deviation

对过程实施统计质量控制的基本假设前提是观测值彼此独立,但实际工作中经常出现过程的观测值存在自相关的现象.若自相关过程的残差满足独立同分布条件,对残差实施控制图监视是解决自相关过程控制的方法之一.应用检测能力指数和平均运行长度两种衡量指标,分析了自相关过程由时间序列模型AR(1)描述时,残差控制图对过程均值变化的检测能力.结果表明,残差EWMA(φ≤1-λ)控制图对过程均值小偏移较灵敏,当φ<0时,残差EWMA控制图对过程均值大偏移的检测能力略差于残差Shewhart控制图.

When using control charts to monitor a process, a necessary assumption is that any two of the observations in the process are independent with each other. However, such observations are frequently autocorrelation in practice. If the residuals in the autocorrelation process satisfy the conditions that they are independent random variables and in the same distribution, applying control charts to residual monitoring is one of the effective ways to control the autocorrelation process. Taking the detectability index and average run length as evaluation indices, the detectability of residual control chart to the change in mean deviation is analyzed when the correlation process is expressed by the time series model AR （1）. The results show that the EWMA residual control chart （ φ≤1 - λ） is highly sensitive to small mean deviation but lower to great mean deviation than Shewhart control chart when the process parameter φ 〈 0.