Refer to the production of molded-rubber expansion joints used in heating and air conditioning systems, Exercise 16.6. To monitor the mean of the manufacturing process, eight joints (rather than one joint) were randomly selected from the production line and their diameters (in inches) measured each hour, for a period of 12 hours, as shown in the table. The data for the 12 samples will be used to construct an x̅-chart.

a. Locate the center line for the x̅-chart.

b. Locate upper and lower control limits.

c. Calculate and plot the 12 sample means to produce an x̅-chart for the joint diameters. Does the process appear to be in control?

Data from Exercise 16.6

Molded-rubber expansion joints, used in heating and air-conditioning systems, are designed to have internal diameters of 5 inches. To monitor the manufacturing process, one joint was randomly selected each hour from the production line and its diameter (in inches) measured, for a period of 12 hours, as shown in the table. The data will be used to construct a variable control chart.

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RUBBERJNT2 Hour Molded-Rubber Expansion Joint Diameters 1 5.08 5.01 4.99 4.93 4.98 5.00 5.04 4.97 2 4.88 5.10 4.93 5.02 5.06 4.99 4.92 4.91 3 4.99 5.00 5.02 5.01 5.03 4.92 4.97 5.01 4 5.04 4.96 5.01 5.00 5.00 4.98 4.91 4.96 5.00 4.93 4.94 5.02 5.01 4.97 5.08 5.11 6 4.83 4.92 4.96 4.91 5.01 5.03 4.93 5.000 7 5.02 5.01 4.96 4.98 5.00 5.07 4.94 5.01 8 4.91 5.00 4.97 5.03 5.02 4.99 4.98 4.99 5.06 5.04 4.99 5.02 4.97 5.000 5.01 5.01 10 4.92 4.98 5.01 5.01 4.97 5.00 5.02 4.93 11 5.01 5.00 5.02 4.98 4.99 5.00 5.01 5.01 12 4.92 5.12 5.06 4.93 4.98 5.02 5.04 4.97 9,