00245 Üf7c8f2fa9aad4150428b54cab4aa7e

247

Statistical Process Monitoring

IMA x«o	IMA with step X-0	Forecast Errors X-0 hłMi
X«0.1		\ = 0.1 L
		X*0.5 __________I_____
1 I ^1 Ä„m ' w		X * 1 _1_

10

5

o H

-5 --10-

10 -5 -0

-5 -) -10-

10 -5 -0 --5 --10-

10

5

O

-5 -Å‚ -10

FigurÄ™ 3. Simulated IMAs (left column), IMAs with a 5o shift at period 150 (center column) and residuals (right column). IMAs (left) wander morÄ™ as X increases. The wandering makes step shifts in the level (center) morÄ™ difficult to see as X increases. Step shifts in the IMAs cause a pattemed change in the residuals (right). The mean of the residuals (shifted down for clarity) is plotted in the lower portion of each residual plot. It jumps by an amount equal to the size of the shift in the IMA and then decays back to zero at a geometrie ratÄ™ of 1 -X.