In an injection molding process, the die wears out gradually. To account for this wear, it is suggested that a trend chart be constructed for the outside diameter of the component produced. Samples of size 5 are selected and the sample average X and range R are found. The results of 20 such samples are shown in Table 7-24. Construct the centerline and control limits of a trend chart for the sample average. Is the process in control? If the process is out of control, assume special causes, and revise the limits. Suppose that the specification limits are 110 ± 8 mm. At what point should the die be changed?
TABLE 7-24

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Sample Sample Sample Sample Sample Average, x (mm) Range, R (mm) Sample Average, X (mm) Range, R (mm) 107.6 104.3 103.5 05.7 104.8 08.5 109.7 05.3 12.6 110.5 3.1 2.6 2.8 2.4 3.2 2.5 2.8 1.7 2.4 2.0 2.3 2.5 2.4 12 13 14 15 16 13.3 109.8 110.3 108.6 112.7 114.2 115.5 112.8 116.2 2.6 1.8 2.8 18 19 20 2.7 2.2 10