Consider the piston ring data shown in Table 6.3. Assume that the specifications on this component are 74.000 0.05 mm.

(a) Set up x and R control charts on this process. Is the process in statistical control?
(b) The control limits on the x chart in part (a) are identical to the control limits on the x chart in Example 6.3, where the limits were based on s. Will this always happen?
(c) Estimate process capability for the piston-ring process. Estimate the percentage of piston rings produced that will be outside of the specification.

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TABLE 6.3 Inside Diameter Measurements (mm) for Automobile Engine Piston Rings Sample Number Observations 4.030 74002 74.019 73.992 74.008 73.995 73.992 74.001 74.011 74.004 3 73.988 74.024 74.02 7405 74.002 74.002 73996 73.993 7401574.009 3.992 74.007 74.05 73989 74.014 74.009 73994 73997 73985 73.993 73995 74.006 7399474.000 74.005 73.985 74.003 73993 74.015 73.988 4.008 73995 7.009 74.005 74.004 73.998 74.000 73990 74007 73.995 3.994 73.998 73994 73,995 7390 4.004 74,000 74007 74.000 73.996 3.983 74.002 73.998 73.997 74.012 74.006 73.967 73994 74.000 73984 15 74012 74014 73.998 73999 74.007 4.00073.984 74.005 73998 7396 3.994 74.012 73.986 74.005 74.007 4.006 74.010 74.018 74.003 74.000 3.984 74.002 74.3 74.00S 7397 4.000 74.010 74,013 74.020 74.003 21 73.982 74.00 74.015 74.005 73996 4.00473.999 73.990 74.006 74.009 23 74.010 73.989 73.990 74.009 74.014 24 74.015 74.008 73.993 74,000 74.010 3.982 73.984 3995 74.017 74.013 74.010 74.001 0.0148 0,0147 0.0091 00122 74.003 4.003 73.996 74.000 73.997 74.004 73,998 3.994 74.001 73.998 73.990 0.0055 0.0123 0.0029 0.0042 0.0105 0.0153 0.0073 73.997 4,001 74.007 3.998 74.009 4.000 74.002 74.002 74.005 73.998 Σ " I ,850.028 00106 0.0085 0.0074 0.0119 0.0162 0.2351 74.001 -0.0094