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The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the box-fil

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Answer #1

Solution:
UCL and LCL for Range chart can be calculated as
UCLRbar = D4*Rbar
LCLRbar = D3*Rbar
Given in the question
Range average(Rbar) = 7 grams
Number of packets in a box = 8
So from table 3 sigma limits for Xbar and R chart is D3 = 0.136 and D4 = 1.864
So UCL and LCL for Range chart is
UCL = D4*Rbar = 1.864*7 = 13.048 or 13.05
LCL = D3*Rbar = 0.136*7 = 0.952 or 0.95
So UCLRbar = 13.05 grams and LCLRbar = 0.95 grams

UCL and LCL for Xbar chart can be calculated as
UCLXbar = Xdoublebar + A2*Rbar
LCLXbar = Xdoublebar - A2*Rbar
Given in the question
Xdoublebar = 47
Range average = 7 grams
Number of packets in a box = 8
So from table 3 sigma limits for Xbar and R chart is A2 = 0.373
So UCL and LCL for Range chart is
UCLXbar = Xdoublebar + A2*Rbar = 47 + 0.373 * 7 = 49.611 or 49.61
LCLXbar = Xdoublebar - A2*Rbar = 47 - 0.373*7 = 44.389 or 44.39
So UCLXbar = 49.61 grams and LCLXbar = 44.39 grams

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