=+54. Instead of constructing x and R charts for 30 subgroups of size 4, a friend suggests the simpler alternative of calculating the standard deviation s of the 30 means to establish 3-sigma limits for a control chart. That is, it is suggested that the 30 means be plotted on a chart with control limits x 6 3s .

Sample means that fall outside these control limits would indicate process problems. Explain what is wrong with this procedure.