带参数估计的EWMA方差控制图稳健性分析

Robustness Study on EWMA Variance Control Chart with Estimated Parameters

EWMA方差控制图是一种有效用于检验过程方差漂移的统计工具．实践中，过程参数多数是未知的，需要对过程的均值与方差等参数在过程阶段Ⅰ通过历史的受控数据进行估计．文章主要研究带参数估计的EWMA方差控制图．首先梳理了常用的7种标准差的估计，考虑阶段Ⅰ常见的4类干扰项，使用均方误差作为估计量有效性评价准则．对7种参数估计的EWMA方差控制图，在4类干扰项情况下，设计控制图的控制上限参考表，并比较失控平均运行长度和运行长度的标准差在阶段Ⅱ监控方差不同漂移幅度的表现．发现在均值干扰项的情况下，7种标准差的估计中经过样本筛选后的中位数绝对偏差均值估计ADM’的表现较优；而在方差干扰项的情况下，7种标准差的估计中中位数绝对偏差中位数估计MDM的表现较优．

Exponentially weighted moving average （EWMA） variance control chart is regarded as one of the most useful statistical tools in detecting process variance shifts. In practice, the process parameters are unknown, which should be estimated from subgroups （Phase Ⅰ） taken when the process is assumed to be in control. This paper mainly studies the EWMA variance control chart with estimated parameters. We summarize seven kinds of standard deviation estimators and compare their effectiveness under four types of disturbances using the mean of square error as a criterion.We build the upper control limit tables of EWMA variance control chart with seven kinds of estimators under four types of disturbances and compare the robustness of EWMA variance control charts in detecting the variance shifts in PhaseⅡ , in terms of the out of control average run length （ARL1） and standard deviation of run length （SDRL1）. We find that sampled mean of the sample-average absolute deviation from the median ADM＇ performs better turbance of mean exits, while the from the median MDM is the best than another six kinds of estimator when the dismedian of the sample-average absolute deviation in the case of variance disturbance.