Calculate the control limits for averages and ranges for the following: number of samples = 7; x = 50; R = 7. From Table 4.3, we find that for a sample size of 7, we have A2 = 0.419, D4 = 1.924 and D3 = 0.078. Equations (4.11) and (4.12) give the upper and lower control limits for the averages as UCLx = x + A2R = 50 + (0.419)(7) = 52.933 LCLx = x _ A2R = 50 _ (0.419)(7) = 47.067 For the ranges, Eqs. (4.13) and (4.14) yield UCLR = D4R = (1.924)(7) = 13.468 LCRR = D3R = (0.078)(7) = 0.546
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