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 36 inches. In order to monitor the cutting process, Oceanside managers took 22 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 (36.0 inches) and average range value (1.8 inches) for the 22 samples. Managers felt that these values were acceptable; that is, the process was in control.
a. (**) Develop the appropriate control chart(s) to monitor the fabric length.
b. (**) Using the control chart(s) you developed in part a, plot the following samples. Circle any that appear to be out of control.

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SAMPLE (n = 4) MEASUREMENTS (IN INCHES) 1 37.3 36.5 38.2 36.2 2 33.4 35.8 37.9 36.2 32.1 34.8 39.1 35.3 4 36.1 37.2 36.7 34.2 32.1 34.0 35.6 36.1 -N 3 5