Abstract: Due to inaccuracy estimation of statistic distribution,the false alarm probability of bivariate double sampling generalized variance control chart was higher than its real value.To avoid this drawback and then make the control chart be fit for any distribution,Cornish-Fisher expansion algorithm was used to correct the control limits of chart.In comparison with the original bivariate double sampling generalized variance control chart presented by Grigoryan and He,the improved control chart offered better performances.Furthermore,the advantage of proposed control chart was illustrated with an example.Because Grigoryan and He did not take the false alarm probability as one of the main performances and also did not calculate the probability,the calculation approaches of false alarm probability for both original and improved control charts were established.

Key words: Cornish-Fisher expansion algorithm, bivariate double sampling generalized variance control chart, false alarm probability, chi square distribution

摘要： 为解决二元双抽样广义方差控制图存在虚发报警概率偏高的问题,采用Cornish-Fisher展开算法对控制图进行修正,以使控制图适用于任意分布总体。通过与Grigoryan和He所研究的二元双抽样广义方差控制图的性能进行对比,验证了改进后控制图的性能优势,并通过实例研究进一步说明了该优势。针对Grigoryan和He未以虚发报警概率作为主要研究指标,且未给出二元双抽样广义方差控制图的虚发报警概率计算方法的缺陷,在进行控制图性能对比之前还构建了二元双抽样广义方差控制图及其改进控制图虚发报警概率的计算方法。

关键词: Cornish-Fisher展开算法, 二元双抽样广义方差控制图, 虚发报警概率, 卡方分布