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).

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