Question

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 five 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 here: Subgroup 1 2 3 4 5 6 7 8 9 10 Time 4 p.m. 5 p.m. 6 p.m. 7 p.m. 8 p.m. 9 p.m. 10 p.m. 11 p.m. 12 p.m. 1 a.m. Pizza Crust Diameter (Inches) 1 2 3 4 5 9.3 9.1 9.3 9.2 9.2 9.5 10.3 10.2 10.0 10.0 10.5 10.3 9.B 10.0 10.3 10.7 9.5 9.B 10.0 10.0 10.0 10.5 10.0 10.5 10.5 9.4 9.5 9.0 9.2 9.3 11.0 10.0 10.3 10.3 10.0 10.0 10.2 10.1 10.3 11.0 10.0 10.4 10.4 10.5 10.0 11.0 10.5 10.1 10.2 10.2 Mean, I Range, R 9.22 0.2 10.00 0.8 10.18 0.7 10.00 1.2 10.30 0.5 9.28 0.5 10.32 1.0 10.32 1.0 10.26 0.5 10.40 0.9 Use the pizza crust diameter data to do the following: (a) Calculate 7 and R. (Round your X to 3 decimal places and R to 2 decimal places.) x-bar R-bar (b) Find the center lines and control limits for the and R charts for the pizza crust data. (Round intermediate calculations and final answers to 3 decimal places.) CL (X-bar) UCL(x-bar) LCL(x-bar) CL(R-bar) UCL(R) No LCL(R)

Answer 1

Page LCL (50) = - 3 R dain 10.028 0.421 10.007 0.73 CL (Ř ) = UCLCR) = DGO Du © 2 - 114X0.73 LCL (R = 1.543 D3 R 100-28 - 9.22- 9.28 8 こ 10.223 R = 7.3 0.2-0.5 0-825 ot CL (5) = UCL (x) = 10.223 x + 3 da un 10.223 + 3x0.825 2-326853 10.223 to.476 10.699 Je - 3 dan LCL (0) = 9.747 CLCR) = 0.825 UCLLŔ) = DUR 2-114 x 0.25 = 1.744