On Properties of Binomial Q Charts for Attributes

Abstract

The sensitivity of four tests on Shewhart Q charts and of specially designed exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) Q charts to detect one-step permanent shifts of a binomial probability parameter p 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 most sensitive and are about comparable in overall performance.

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