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Statistics for Six Sigma Green Belts with Minitab and JMP by David M. Levine

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11.8. Control Charts for The Mean and The Standard Deviation

As the sample size n increases, the range becomes increasingly less efficient as a measure of variability. This is the case because the range ignores all information between the two most extreme values; as the sample size increases, the range will use a smaller proportion of the information available in a sample. In addition, the probability of observing an extreme value in a sample increases as n gets larger. A single extreme value will result in an unduly large value for the sample range and will inflate the estimate of process variability. Thus, as the subgroup size increases, the individual subgroup standard deviations provide a better estimate of the process standard deviation ...

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