When a certain manufacturing process is in control, it produces items whose values are normally distributed with mean 10 and standard deviation 2. The following simulated data represent the values of 25 subgroup averages of size 5 from a normal population with mean 11 and standard deviation 2. That is, these data represent the subgroup averages after the process has gone out of control with its mean value increasing from 10 to 11. Table 13.3 presents these 25 values along with the moving averages based on span size k = 8 as well as the upper and lower control limits. The lower and upper control limits for t > 8 are 9.051318 and 10.94868.

As the reader can see, the first moving average to fall outside its control limits occurred at time 11, with other such occurrences at times 12, 13, 14, 16, and 25. (It is interesting to note that the usual control chart — that is, the moving average with k = 1 — would have declared the process out of control at time 7 since X 7 was so large. However, this is the only point where this chart would have indicated a lack of control (see Figure 13.3).