控制过程方差的CUSUMQ图及其性质

崔恒建．控制过程方差的ＣＵＳＵＭＱ图及其性质．数理统计与管理，１９９８，１７（４），３３～３８．Ｑｕｓｅｎｂｅｒｒｙ（１９９５）基于样本方差的标准化变换Φ－１［Ｈｎ－１（（ｎ－１）Ｓ２／σ２０）］提出了控制过程方差的累积和（ＣＵＳＵＭ）Ｑ控制图。本文我们描述了在控制过程方差变化中这种ＣＵＳＵＭＱ控制图的性质，并将控制图的设计方法用到单边及双边的ＣＵＳＵＭＱ图，说明它几乎是最优的。而且我们发现在控制过程方差的微小变化时，设计的ＣＵＳＵＭＱ图的性能要优于基于ｌｏｇ（Ｓ２）的ＣＵＳＵＭ和ＥＷＭＡ图

The CUSUM Q Charts and Its Properties forMonitoring Process Variance

Abstract Quesenberry (1995) has proposed a standardized cumulative sum (CUSUM) Q control chart for monitoring process variance based on the standardized transformation of the sample variance Φ-1Hn-1((n-1)S2/σ20).The properties of this kind of CUSUM Q control chart for detecting changes in the process variance are described,and design procedures are developed for one sided and two sided CUSUM Q charts that are nearly optimal in this paper.It is found that the performance of the designed CUSUM Q is superior to that of the CUSUM and EWMA charts based on log(S2)for monitoring small changes of variance.