Let a be a number between 0 and 1, and define a sequence W1, W2, W3,... by
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Wt = aXÌ t + a(1 - a)XÌ t-1 + . . . + α(1 - α)t-1XÌ 1+ (1 - α)tµ
The fact that Wt depends not only on XÌ 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 XÌ t's.
a. Show that E(Wt) = µ.
b. Let Ït2 = V(Wt), and show that
c. An exponentially weighted moving-average control chart plots the Wt's and uses control limits µ0 ± 3Ït (or xÌ¿ in place of µ0). Construct such a chart for the data of Example 16.9, using µ0 = 40.
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Related Book For
Probability And Statistics For Engineering And The Sciences
ISBN: 9781305251809
9th Edition
Authors: Jay L. Devore
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