A machining operation requires close tolerances on a certain part for automobile engines. The current specification for this measurement is 3.0 cm ± .001. The quality control procedure is to take a sample of size 4 and measure each of the parts. On the basis of past samples of size 4, x-bar = 3.0 and R-bar = .0020.
a. Construct an average and range chart for this part.
b. On the basis of the following data, is the process in control?

c. Is the process running outside of its specifications?

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Sample 12 3 4 X 3.0005 2.9904 3.0010 3.0015 3.0008 R 0.0024 0.0031 0.0010 0.0040 0.0010