X¯ chart with adaptive sample sizes

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Abstract
Standard Shewhart control charts employ fixed sample sizes at equal sampling intervals. By varying the sample size depending on the current location of the process mean, the mean time to detect an off-target condition can be reduced. The adaptive-sample-size control chart is compared with the fixed-sample-size control chart in terms of average run length under shifts in the process mean of variable magnitude. Significant improvements have been obtained with the adaptive-sample-size charts, particularly for small shifts. These improvements are achieved without increasing the in-control average sample size beyond that of the fixed-sample-size approach. A fast initial response is suggested and advantages of the procedure over fixed-sample-size control are illustrated with two examples from discrete manufacturing processes.

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