On Properties of<i>Q</i>Charts for Variables

Abstract

The sensitivity of four tests on Shewhart type Q charts and of specially designed EWMA and CUSUM Q charts to detect one-step permanent shifts of either a normal mean or standard deviation has been studied. The usual test that signals for one point beyond three standard deviations on a Shewhart chart is found to have poor sensitivity, generally. The test that signals when four out of five consecutive points are beyond one standard deviation in the same direction is found to be a good omnibus test. The EWMA and CUSUM Q charts are the most sensitive and are about comparable in overall performance.