The fact that wtnbspdepends not only on xtnbspbut also on

Question

Let a be a number between 0 and 1, and define a sequence  for t = 1, 2,.... Substituting for W_t-1 its representation in terms of X_t-1 and W_t-2, then substituting for W_t-2, and so on, results in

The fact that W_t depends not only on X_t 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 X_t '

c. An exponentially weighted moving-average control chart plots the Wt 's and uses cntrol limits µ₀  3σ_t (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