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Applications of the EWMA

process to target shown in Figurę 5a. The latter case involves adjustments which are too large coupled with mis-interpreting white noise as a true process signal. This results in frequent adjustments in altemating direction, or the over-control shown in Figurę 5b. (Although not shown here, contour plots for L = 0 and L = 3 are similar in shape to Figurę 4.) While these controller performance deficiencies are noticeable, they are not extreme even for large errors in tuning. Therefore, this EWMA controller is seen to be robust to errors in tuning for 0 <

L<, 3.

Comparison Of EWMA and Modified Shewhart Algorithms

Use of the modified Shewhart chart with rules of runs for making process adjustments has been common in the Monsanto Fibers Division. An example of such a chart is shown in Figurę 6, where the following rules are noted along the left-hand vertical axis:

Rule 1: Rule violation if 10 of 11 points are on the same side of target.

Rule 2: Rule violation if 4 of 5 points are in Zonę B or beyond on the same side of target.

Rule 3: Rule violation if 2 of 3 points are in Zonę C or beyond on the same side of target.

Rule 4 : Rule violation if one point is in Zonę D.

-4

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LEGEND

Time Order Y t-T a r 9 e 1    — - Zt

A-.4 |-I0 o.-IO S.-0, IsislOO W Ł-5

EWMA Umili - 1 Lo _z - ± 1Ji J33 - * JO

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Time Ordę

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Figurę 5a. Simulation of the EWMA Algorithm with Sluggish Control.