Car Giant manufactures seats for Mazda and Lexus cars. One of the components of a front seat cushion is a wire spring, produced from 4mm steel wire. A machine is used to bend the wire so that the spring’s length is 500mm. If the springs are longer than 500mm they will loosen and eventually fall out. If they are too short, they won’t easily fit into position. To determine whether the process is under control, random samples of four springs are taken every hour. The last 25 samples are shown in the table below.

(a) Calculate the values of x and R. (b) Determine the values of the center, LCL, and UCL for x and R charts. (c) Construct the control charts and plot the sample data on the charts.
 

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Sample Spring 1 Spring 2 Spring 3 Spring 4 501.65 1 501.02 504.34 501.10 499.80 498.89 499.47 497.90 499.33 500.41 3 497.12 498.35 500.34 4 500.68 501.39 499.74 500.92 499.22 495.87 498.00 499.44 497.89 502.10 500.03 7 497.24 501.04 498.74 503.51 499.06 497.96 8 501.22 504.53 505.37 9. 499.15 501.11 502.39 10 498.90 505.99 500.05 499.33 11 497.38 497.80 497.57 500.72 12 499.70 500.99 501.35 496.48 13 501.44 500.46 502.07 500.50 495.21 500.32 501.27 501.22 14 498.26 495.54 15 497.57 497.00 16 500.95 502.07 500.60 500.44 17 499.70 500.56 501.18 502.36 501.18 500.02 504.98 501.71 18 501.57 502.09 19 504.20 500.92 20 498.61 499.63 498.68 501.84 21 499.05 501.82 500.67 497.36 22 497.85 494.08 501.79 501.95 23 501.08 500.75 503.12 503.06 503.56 24 501.18 501.09 502.88 25 502.03 501.44 498.76 499.39 Sample Spring 1 Spring 2 Spring 3 Spring 4 501.65 1 501.02 504.34 501.10 499.80 498.89 499.47 497.90 499.33 500.41 3 497.12 498.35 500.34 4 500.68 501.39 499.74 500.92 499.22 495.87 498.00 499.44 497.89 502.10 500.03 7 497.24 501.04 498.74 503.51 499.06 497.96 8 501.22 504.53 505.37 9. 499.15 501.11 502.39 10 498.90 505.99 500.05 499.33 11 497.38 497.80 497.57 500.72 12 499.70 500.99 501.35 496.48 13 501.44 500.46 502.07 500.50 495.21 500.32 501.27 501.22 14 498.26 495.54 15 497.57 497.00 16 500.95 502.07 500.60 500.44 17 499.70 500.56 501.18 502.36 501.18 500.02 504.98 501.71 18 501.57 502.09 19 504.20 500.92 20 498.61 499.63 498.68 501.84 21 499.05 501.82 500.67 497.36 22 497.85 494.08 501.79 501.95 23 501.08 500.75 503.12 503.06 503.56 24 501.18 501.09 502.88 25 502.03 501.44 498.76 499.39