The Southern Mills Company produces denim cloth. During the weaving process, dyed yarn on large, round beams is fed into looms where it is woven into cloth. During this weaving process the yarns are stretched beyond their natural length. As a result, the woven fabric can shrink as much as 15%; however, shrinkage of only as much as 3% is the acceptable limit for Southern’s customers. To prevent shrinkage, the fabric is put through a chemical process, but beams of fabric can still exceed the shrinkage limit. The Southern quality-management team has taken a sample of 100 finished fabric beams each day for one month (i.e., 30 days) and tested them for shrinkage. The results of this inspection process showing the number of fabric beams that exceed the 3% shrinkage limit are as follows:
Develop a p-chart for fabric shrinkage using control limits and indicate if the process is out of control.