The Oceanside Apparel Company manufactures men\'s knit shirts. The production pr

Question

The Oceanside Apparel Company manufactures men's knit shirts. The production process requires material to be cut into large patterned squares, which are then sewn together. If the squares are not the correct length, the final shirt will be either too large or too small. The target length is 45 inches. In order to monitor the cutting process, Oceanside managers took2 samples of four squares each and measured the lengths. For each sample, they then calculated the sample mean and range. Finally, they calculated the average sample mean (45.0 inches) and average range value (4.0 inches) for the 22 samples. Managers felt that these values were acceptable; that is, the process was in control Click the icon to view the values of the A2. D3, and D4 constants More Info a. Upper Control Limit (UCL?- Enter your response rounded to two decimal places) Lower Control Limit (LCL)(Enter your response rounded to two decimal places) Upper Control Limit (UCLEter your response rounded to two decimal places,) Lower Control Limit (LCLR) 0.00. (Enter your response rounded to two decimal places.) Sample Size N 2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31 0.29 0.27 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 b. Using the control charts you developed in part a, plot the following samples. Circle any that appea ?Click the icon to view the sample data Choose the correct X chart below 0.08 0.14 0.18 0.22 0.26 0.28 9 10 12 O R

Explanation / Answer

Following details are provided :

Average sample mean = Xbar = 45 inches

Average range value = Rbar = 4 inches

Sample size = n = 4 ( the manager took samples of 4 squares each )

Following are the relevant data for n = 4 :

A2 = 0.73

D4 = 2.28

D3 = 0

On basis of above data:

Control limits for Xbar chart :

Upper Control Limit , UCLx = Xbar + A2xRbar = 45 + 0.73 x 4 inches = 45 + 2.92 inches = 47.92 inches

Lower Control Limit , LCLx = Xbar – A2 x Rbar = 45 – 0.73 x 4 inches = 45 – 2.92 inches= 42.08 inches

Control Limits for Range chart :

Upper control limit ( UCLr ) = D4.Rbar = 2.28 x 4 inches = 9.12 inches

Lower Control Limit ( LCLr ) = D3.Rbar = 0 x $ inches = 0

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