The specifications require that the height of shock shafts have \(\mu=1.6\) meters and \(\sigma=0.03\) meters.

(a) Use the specifications to calculate a central line and three-sigma control limits for an \(\bar{x}\) chart with \(n=5\).

(b) Use the specifications to calculate a central line and three-sigma control limits for an \(R\) chart with \(n=5\).

(c) Plot the following means and ranges, obtained in 20 successive random samples of size 5 , on charts based on the control-chart constants obtained in part (a) and (b), and discuss the process.

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Sample R Sample R 1 1.65 0.05 11 1.66 0.19 1234567890 1.63 0.08 12 1.64 0.26 1.58 0.19 13 1.68 0.21 1.46 0.04 14 1.69 0.18 1.69 0.02 15 1.49 0.12 1.55 0.01 16 1.53 0.34 7 1.58 0.03 17 1.56 0.32 1.60 0.06 18 1.59 0.36 1.59 0.01 19 1.59 0.29 1.63 0.12 20 1.61 0.15