Automatic machines that fill packages of all-purpose flour to a desired standard weight need to be monitored closely. A random sample of four packages is selected and weighed. The average weight is then computed. Observations from 15 such samples are shown in Table. The desired weight of packages is 80 oz.
Historical information on the machine reveals that the standard deviation of the weights of individual packages is 0.2 oz.
Assume an acceptable type I error rate of 0.05. Also assume that it is desired to detect shifts in the process mean of 0.15 oz. Construct a cumulative sum chart and determine whether the machine needs to be adjusted to meet the target weight.
