The x and R values for 20 samples of size 5 are shown in Table 10E.6. Specifications on this product have been established as 0.550 ± 0.02.

(a) Construct a modified control chart with three-sigma limits, assuming that if the true process fraction nonconforming is as large as 1%, the process is unacceptable.
(b) Suppose that if the true process fraction nonconforming is as large as 1%, we would like an acceptance control chart to detect this out-of-control condition with probability 0.90. Construct this acceptance control chart, and compare it to the chart obtained in part (a).

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TABLE 10E.6 Data for Exercise 10.8 Sample Number 0.549 0.0025 0.0021 0.0023 0.0029 0.0018 0.0017 0.551 1 0.550 0551 0553 0.0024 0.0022 0.0028 0.0020 0.0030 0,0031 0.0022 0.0023 0.0021 0.0019 0.0018 0.0021 0.0022 10 0.547 0.549 14 15 16 17 18 19 0.550 0556 0.550 0.551