Tables of Constants for Control charts
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
X bar and s Charts
X bar and s charts
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
CL X = X
UCLX = X + A2 R
LCL X = X − A 2 R
CLR = R
UCLR = D4 R
LCL R = D3 R
CLX = X
UCLX = X + A3 S
LCL X = X − A3 S
CL s = s
UCL s = B4 s
LCL s = B 3 s
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Control Chart Factors
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 Ranges (R)
Control Divisors to
Limits
Estimate Factors for Control
Factor
σx
Limits
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
Centerline
Median Charts
Charts for
Individuals
D4
3.267
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
Chart for
Individuals
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
Control Limits
~
~
UCL X~ = X + A 2 R
~
LCL X~ = X − A 2 R
CLR = R
UCLR = D4 R
LCL R = D3 R
CL X = X
UCL X = X + E 2 R
LCL X = X − E 2 R
CLR = R
UCLR = D4 R
LCL R = D3 R
CL X~
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~
= X
D4
3.267
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
Control Chart Factors
Page 2 of 3
Tables of Formulas for Control charts
Table 8 C Attribute Data
ref : AIAG manual for SPC
Centerline
Control Limits
Samples not necessarily of constant size
UCL p i = p + 3
p chart for
CL p = p
proportions of
units in a category
c chart for
number of
incidences in one
or more
categories
CL c = c
ni
LCL p i = p − 3
p (1 − p )
ni
If the Sample size is constant (n)
UCL p = p + 3
np chart for
number / rate of CLnp = np
units in a category
p (1 − p )
p (1 − p )
n
LCL p = p − 3
p (1 − p )
n
UCLnp = np + 3 np(1 − p)
LCLnp = np − 3 np(1 − p)
UCLc = c + 3 c
LCLc = c − 3 c
Samples not necessarily of constant size
CLu = u
u chart for
number of
incidences per
unit in one or
more categories
UCLu = u + 3
LCLu = u − 3
u
ni
UCL u = u − 3
u
n
UCL u = u − 3
u
n
using average sample size
UCL u = u + 3
u
n
If the sample size is constant (n)
UCL u = u + 3
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u
ni
u
n
Control Chart Factors
Page 3 of 3