GainSeeker 10.2.0

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Calculating Control Limits

GainSeeker calculates control limits in several user-definable methods. You can calculate control limits for Range and charts using the Factors or Sample Standard Deviation (SSD) methods. When the subgroup size is one, the calculations are slightly different.

Factors method of calculating control limits for Range charts:Factors method of calculating control limits for Range charts:

For a chart with a subgroup size greater than one:

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If the subgroup size is one, the upper and lower control limits are calculated using a different constant:

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Sample Standard Deviation method of calculating control limits:Sample Standard Deviation method of calculating control limits:

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Factors method of calculating control limits for S charts:Factors method of calculating control limits for S charts:

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Short Run limits:Short Run limits:

Target/Nominal method:

Short Run limits for Target/Nominal are calculated using the Factors or SSD method shown at the beginning of this topic.

Range/Short Run method:

For R charts:

Control Limit	Value:
	A2
	-A2
	D4
	D3

For S Charts:

Control Limit	Value:
	A3
	-A3
	B4
	B3

Standardized method:

Control Limit	Value:
	3
	-3
	3
	-3

Non-symmetrical control limits:Non-symmetrical control limits:

When the subgroup size is one, the data set is non-normal and modeled, and GainSeeker is configured to calculate non-symmetrical control limits, GainSeeker reports non-symmetrical control limits as follows:

UCLx = Mean + 3SD = point above mean where 0.135% of the data falls above this point

LCLx = Mean - 3SD = point below mean where 0.135% of the data falls below this point

For a more detailed explanation of how Mean +/- 3SD is calculated, see Flow Chart Analysis of Non-Normal Data.

Assumptions when calculating control limits:

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Subgroup size	A2	A3	B3	B4	E2	D3	D4
2	1.880	2.659	-----	3.267	2.66	-----	3.267
3	1.023	1.954	-----	2.568	1.772	-----	2.574
4	0.729	1.628	-----	2.266	1.457	-----	2.282
5	0.577	1.427	-----	2.089	1.290	-----	2.114
6	0.483	1.287	0.030	1.970	1.184	-----	2.004
7	0.419	1.182	0.118	1.882	1.109	0.076	1.924
8	0.373	1.099	0.185	1.815	1.054	0.136	1.864

References:

Boyd, D.F. "Applying the Group Chart for and R." Industrial Quality Control.
Ford Motor Company, Product Quality Office. Continuing Process Control and Process Capability Improvement. 1984. Pages 14, 33.
General Motors Corporation. General Motors Statistical Process Control Manual. August, 1984. Page 4-4.
Grant, Eugene L. and Richard S. Leavenworth. Statistical Quality Control, Fifth Edition. McGraw-Hill Book Company, 1980. Pages 79 - 81.