Let a be a number between 0 and 1, and define a sequenceby andfor . Substituting for its

Chapter 16, Problem 46

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Let a be a number between 0 and 1, and define a sequenceby andfor . Substituting for its representation interms of and , then substituting for , and soon, results inThe fact that Wt depends not only on but also on averagesfor past time points, albeit with (exponentially) decreasingweights, suggests that changes in the process mean will bemore quickly reflected in the Wts than in the individual s.a. Show that .b. Let , and show thatc. An exponentially weighted moving-average control chartplots the Wts and uses control limits (orin place of m0). Construct such a chart for the data ofExample 16.9, using m0 5 40.

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