A pizza restaurant monitors the size (measured by the diameter) of the 10-inch pizzas that it prepares. Pizza crusts are made from doughs that are prepared and prepackaged in boxes of 15 by a supplier. Doughs are thawed and pressed in a pressing machine. The toppings are added, and the pizzas are baked. The wetness of the doughs varies from box to box, and if the dough is too wet or greasy, it is difficult to press, resulting in a crust that is too small. The first shift of workers begins work at 4 P.M., and a new shift takes over at 9 P.M. and works until closing. The pressing machine is readjusted at the beginning of each shift. The restaurant takes live consecutive pizzas prepared at the beginning of each hour from opening to closing on a particular day. The diameter of each baked pizza in the subgroups is measured, and the pizza crust diameters obtained are given in Table 17.7. Use the pizza crust diameter data to do the following:

a. Show that x̅̅ = 10.032 and  = .84.

b. Find the center lines and control limits for the x̅ and R charts for the pizza crust data.

c. Set up the x̅ and R charts for the pizza crust data. 

d. Is the R chart for the pizza crust data in statistical control? Explain.

e. Is the x chart for the pizza crust data in statistical control? If not, use the x chart and the information given with the data to try to identify any assignable causes that might exist.

f. Suppose that, based on the x̅ chart, the manager of the restaurant decides that the employees do not know how to properly adjust the dough pressing machine. Because of this, the manager thoroughly trains the employees in the use of this equipment. Because an assignable cause (incorrect adjustment of the pressing machine) has been found and eliminated, we can remove the subgroups affected by this unusual process variation from the data set. We therefore drop subgroups 1 and 6 from the data. Use the remaining eight subgroups to show that we obtain revised center lines of x̅̅ = 10.2225 and R̅ = .825.

g. Use the revised values of x and R to compute revised x and R chart control limits for the pizza crust diameter data. Set up x̅  and R charts using these revised limits. Be sure to omit subgroup means and ranges for subgroups 1 and 6 when setting up these charts. 

h. Has removing the assignable cause brought the process into statistical control? Explain.