An extrusion die is used to produce aluminum rods. The diameter of the rods is a critical quality characteristic. The following table shows xÌ… and r values for 20 samples of five rods each. Specifications on the rods are 0.5035 ± 0.0010 inch. The values given are the last three digits of the measurement; that is, 34.2 is read as 0.50342.

(a) Using all the data, find trial control limits for XÌ… and R charts, construct the chart, and plot the data.

(b) Use the trial control limits from part (a) to identify out-of- control points. If necessary, revise your control limits, assuming that any samples that plot outside the control limits can be eliminated. Estimate σ.

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Sample 34.2 1 3 2 31.6 3 31.8 33.4 5 35.0 6. 32.1 2 32.6