Table 8A - Variable Data

ref : AIAG manual for SPC

X bar and R Charts

Chart for

Averages

Control

Limits

Factor

Subgroup size

(n)

2

3

4

5

6

7

8

9

10

15

25

A2

1.880

1.023

0.729

0.577

0.483

0.419

0.373

0.337

0.308

0.223

0.153

Chart for

Averages Chart for Standard Deviation (s)

Chart for Ranges (R)

Divisors

Divisors

to

to

Control

Estimate Factors for Control

estimate Factors for Control

Limits

Factor

Limits

Limits

σx

σx

d2

1.128

1.693

2.059

2.326

2.534

2.704

2.847

2.970

3.078

3.472

3.931

D3

0.076

0.136

0.184

0.223

0.347

0.459

Centerline

X bar and R Charts

CL X = X

CLR = R

X bar and s Charts

X bar and s charts

CLX = X

CL s = s

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D4

3.267

2.574

2.282

2.114

2.004

1.924

1.864

1.816

1.777

1.653

1.541

A3

2.659

1.954

1.628

1.427

1.287

1.182

1.099

1.032

0.975

0.789

0.606

c4

0.7979

0.8862

0.9213

0.9400

0.9515

0.9594

0.9650

0.9693

0.9727

0.9823

0.9896

B3

0.030

0.118

0.185

0.239

0.284

0.428

0.565

Control Limits

UCLX = X + A2 R

LCL

UCLR = D4 R

LCL R = D3 R

UCLX = X + A3 S

LCL X = X − A3 S

UCL s = B4 s

LCL s = B 3 s

Control Chart Factors

X

= X − A2 R

B4

3.267

2.568

2.266

2.089

1.970

1.882

1.815

1.761

1.716

1.572

1.435

σx

R

d2

s

c4

Page 1 of 3

Tables of Constants for Control charts

Table 8B Variable Data

ref : AIAG manual for SPC

Median Charts

Chart for

Medians

Charts for Individuals

Chart for

Individuals

Chart for Ranges (R)

Control Divisors to

Limits

Estimate Factors for Control

Factor

Limits

σx

Subgroup

size

2

3

4

5

6

7

8

9

10

~

A2

1.880

1.187

0.796

0.691

0.548

0.508

0.433

0.412

0.362

d2

1.128

1.693

2.059

2.326

2.534

2.704

2.847

2.970

3.078

D3

0.076

0.136

0.184

0.223

D4

3.267

2.574

2.282

2.114

2.004

1.924

1.864

1.816

1.777

Centerline

CL

Median Charts

~

X

~

=X

CLR = R

Charts for

Individuals

CL

X

=X

CLR = R

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Control

Limits

Factor

E2

2.660

1.772

1.457

1.290

1.184

1.109

1.054

1.010

0.975

Chart for Moving Range (R)

Divisors

to

Estimate Factors for Control

σx

Limits

d2

1.128

1.693

2.059

2.326

2.534

2.704

2.847

2.970

3.078

D3

0.076

0.136

0.184

0.223

D4

3.267

2.574

2.282

2.114

2.004

1.924

1.864

1.816

1.777

Control Limits

UCL

~

X

~

~

= X + A2 R

UCLR = D4 R

UCL X = X + E 2 R

UCLR = D4 R