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The results of this study indicate that X̄ charts with subgroups of size n require about 400/(n-1) samples, and X charts require about 300 values to estimate control limits that perform like known limits. The results also indicate that using estimated control limits results in charts for which the events that individual points exceed the control limits are dependent. One result of this dependence in a charting program is to increase the rate of false alarms after short runs, even though the ARL is increased. The implications of this to the use of Q charts are discussed.
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Charles P. Quesenberry (1993) studied this question.
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