# Table of Constants for Control Charts

D

#### D.Scott

Table of constants n=25

A - 0.600
A2 - 0.153
A3 - 0.606
c4 - 0.9896
B3 - 0.565
B4 - 1.435
B5 - 0.559
B6 - 1.420
d2 - 3.931
1/d2 - 0.2544
d3 - 0.709
D1 - 1.804
D2 - 6.058
D3 - 0.459
D4 - 1.541

>25 - use 3/sqrt for A & A2
use 1-(3/sqrt) for B3
use 1+(3/sqrt) for B4

Source"Quality Control and Industrial Statistics" (Acheson J Duncan)

Hope this is what you need

Dave

[This message has been edited by D.Scott (edited 17 August 2001).]

D

#### D.Scott

Sorry, but the source I have states "the fourth significant figures for (D) are in doubt for n greater than 5". It does not even show a calculation for sample size greater than 25. Maybe someone else can help shed some light.

Dave

R

#### Rick Goodson

yii,

Why do you want to take sample sizes greater than 25?

Rick

Y

#### yii

One of the engineers requested to increase the sample size from 20 to 30 and he was asking for constants for n = 30. Now that pose an interesting question. Why the cutoff of n = 25? What's the explanation behind it?

R

#### Rick Goodson

yii,

Without getting into the statistical proofs the reason involves the central limit theorm. If you recall Shewhart's experiments we find that if many samples of any sample size n are taken from a unoiverse, the averages (X-bar values) of the samples will form a frequency distribution and the average of the averages (X-Double Bar) of that frequency distribution will tend to be near the average of the universe (u, mu). The spread of the X-bar values of the frequency distribution will depend on the spread of the universe and the sample size with the spread of the X-bar values being smaller as n gets larger. In the long run the standard deviation of the X-bar values will be the standard deviation of the population divided by the square root of the sample size. This holds regardless of the shape of the universe.

Now with that in mind, the subgroup size for a control chart is basically an economical decision. We chose a 'rational subgroup' so that the variation within the units is small. If the variation with in a subgroup represents the piece-to-piece variability over a short period of time, then unusual variation between subgroups would reflect changes in the process that should be investigated. The practical problem we face is whether to take large samples less frequently or smaller samples more frequently. The longer we wait between samples the longer the process may run in an out of control condition if an assignable cause enters the picture. Keep in mind also that as the sample size increases the control limits get smaller moving toward the central line of the chart.

If you want more information on the statistics involved try these texts:

Quality Control and Industrial Statistics by Acheson Duncan
Statistical Process Control by The Autimotive Industry Action Group (AIAG)
Statistical Quality Control by Grant and Leavenworth
Hope this helps.

Regards,

Rick

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