Let a be a number between 0 and 1, and define a sequence 
for t = 1, 2,.... Substituting for Wt-1 its representation in terms of Xt-1 and Wt-2, then substituting for Wt-2, and so on, results in
The fact that Wt depends not only on Xt but also on averages for past time points, albeit with (exponentially) decreasing weights, suggests that changes in the process mean will be more quickly reflected in the Wt 's than in the individual Xt '
c. An exponentially weighted moving-average control chart plots the Wt 's and uses cntrol limits µ0 
3σt (or x in place of µ0). Construct such a chart for the data of Example 16.9, using µ0 = 40.
Example 16.9 Reconsider the charcoal briquette data displayed in Table 16.4 of Example 16.8. The target value is µ0 = 40, and the size of a shift to be quickly detected is ? = .3. Thus
