The control limits are set to three times standard deviation of the sample distribution (s). s can be calculated from a the population standard deviation using the factor d2 according to the central limit theorem:
σ= R/d2 = 4.44/2.059 = 2.156
S = a/V^ = 2.156/2 = 1.078
± 3 s = 1.078.3 = 3.23, which is close to the A2 •R value of 3.24, which corresponds to the distance from the centerline to one of the control limits in the variable control charts.
It is interesting to note that of the total population of l〇〇 numbers (Table 3.2), then the standard deviation is a = 2.156, which is exactly the one predicted by the R estimator. If the specifications limits are given, then the Cp, Cpk, and reject rates can be calculated as in the example in the previous chapter.