The fill volume of soft-drink beverage bottles is an important quality characteristic. The colume is measured (approximately) by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle against a coded scale. On this scale a reading fo zero corresponds to the correct fill height. Fifteen samples of size n = 10 have been analyzed, and the fill heights are shown in Table 6E.6.

(a) Set up x and S control charts on this process. Does the process exhibit statistical control? If necessary construct revised control limits.
(b) Set up an R chart, and compare it with the s chart in part (a).

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TABLE 6E.6 Fill Height Data for Exercise 6.11 Sample 1 2.5 05 20-10 10-10 05 5 05-1.5 2 00 00 05 10 15 1.0-10 1.0 15-1.0 3 15 10 10-10 00-1.5 -10 -1.0 1.0-1.0 4 0.0 0.5一2.000-1.01.5-1.50.0-20-1.5 500 00 0.0-05 05 10-05-0.5 0.0 00 6 1.0 -03 00 00 00 05-10 10 20 L0 7 1.0-10-1.0-1.0 0.0 1.5 00 0 0.0 0.0 800 -15-05 15 00 00 0-10 0.5-0.5 9 -20 -15 15 15 00 00 05 10 0.0 L0 10 -05 35 00-10-15-15-10-1.0 10 0.5 00 15 00 002.0 -1.5 0.5-05 20-10 12 00-2.0-05 00-05 20 15 00 05-1.0 3 -L0-05-0.5 -1.0 00 05 0.5-15-1,0-1.0 14 05 10-1.0-05 -20-1.0 -15 00 15 1.5 0 00 15 15 10-1.0 00 1.0-20-1.5