# The x-bar and R values for 20 samples of size five are shown in the following table. Specifications on this product have been established as 0.550 ± 0.02. Sample Number Xbar R 1 0.549 0.0025 2 0.548 0.0021 3 0.548 0.0023 4 0.551 0.0029 5 0.553 0.0018 6 0.552 0.0017 7 0.55 0.002 8 0.551 0.0024 9 0.553 0.0022 10 0.556 0.0028 11 0.547 0.002 12 0.545 0.003 13 0.549 0.0031 14 0.552 0.0022 15 0.55 0.0023 16 0.548 0.0021 17 0.556 0.0019 18 0.546 0.0018 19 0.55 0.0021 20 0.551 0.0022 Construct a modified control chart with three sigma limits, assuming that if the true process fraction non conforming is as large as 1%, the process is unacceptable. 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).

The x-bar  and R values for 20 samples of size five are shown in the following table. Specifications on this product have been established as 0.550 ± 0.02.

 Sample Number Xbar R 1 0.549 0.0025 2 0.548 0.0021 3 0.548 0.0023 4 0.551 0.0029 5 0.553 0.0018 6 0.552 0.0017 7 0.55 0.002 8 0.551 0.0024 9 0.553 0.0022 10 0.556 0.0028 11 0.547 0.002 12 0.545 0.003 13 0.549 0.0031 14 0.552 0.0022 15 0.55 0.0023 16 0.548 0.0021 17 0.556 0.0019 18 0.546 0.0018 19 0.55 0.0021 20 0.551 0.0022

1. Construct a modified control chart with three sigma limits, assuming that if the true process fraction non conforming is as large as 1%, the process is unacceptable.

1. 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).