Statistical Papers 42, 207-223 (2001) Statistical Papers 9 Springer-Verlag 2001 The EWMA-X-S-control chart and its performance in the case of precise and imprecise data Dietmar Stemann I and Claus Weihs 2 1 Department of Economics, University of Hagen, FeitstraBe 140, 58084 Hagen, Germany 2Department of Statistics, University of Dortmund, 44221 Dortmund, Germany Received: February 25, 1999; revised version: December 22, 1999 1 Introduction T h e dominating instrument of online quality assurance is the control chart. W h e n monitoring a stochastic quality characteristic by means of a controlchart three cases are distinguished, control of location, control of variation,and simultaneous control of location and variation. Moreover, control charts without and with m e m o r y are distinguished. Control charts without memory were introduced in 1931 by W.A.Shewhart and dominate until today in industrial practice. Using such charts,the qualitystatusof the actualproduction isjudged only by means of the information in the actual sample. The quality history of the production process is totallyignored. O n the contrary,controlcharts with m e m o r y also use the information in the samples since the last process correction. This use of older process information facilitates earlierreaction to small and m e d i u m process changes in relationto controlwithout m e m o r y . The most important control charts with memory are CUSUM- and EWMA-charts. The most important differencebetween CUSUM- and EWMA-charts is the fact that the CUSUM-chart uses older sample information equally weighted, whereas by the EWMA-chart oldersample information is downgraded. Moreover, EWMA-charts allow the controlof the strength of the influence of past information. This demonstrates the enormous flexibility of the E W M A principle. Although it is well-known that EWMA-charts are more sensitive to small process disturbances than Shewhart-charts, only two E W M A type control charts for the simultaneous control of loca- tion and variationcan be found in the literature.G a n (1995) introduces an E W M A - c h ~ r t which combines the EWMA-X~-chart and the EWMA-InS2-chart by Crowder and Hamilton (1992). The EWMA-InS2-chart uses the logarithm of the empirical variance S 2 as a measure for variation.