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Tables of Constants for Control charts
Table 8A - Variable Data
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
ref : AIAG manual for SPC
X bar and s charts
Chart for
Averages
Chart for Standard Deviation (s)Chart for Ranges (R)
Divisors Divisors
to to
Control
Estimate
Factors for Control
Limits
estimate
Factors for Control
Factor
LimitsLimits
σ
x
σ
x
A
2
1.880
1.023
0.729
0.577
0.483
0.419
0.373
0.337
0.308
0.223
0.153
d
2
1.128
1.693
2.059
2.326
2.534
2.704
2.847
2.970
3.078
3.472
3.931
D
3
-
-
-
-
-
0.076
0.136
0.184
0.223
0.347
0.459
D
4
3.267
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
1.653
1.541
A
3
2.659
1.954
1.628
1.427
1.287
1.182
1.099
1.032
0.975
0.789
0.606
c
4
0.7979
0.8862
0.9213
0.9400
0.9515
0.9594
0.9650
0.9693
0.9727
0.9823
0.9896
B
3
-
-
-
-
0.030
0.118
0.185
0.239
0.284
0.428
0.565
B
4
3.267
2.568
2.266
2.089
1.970
1.882
1.815
1.761
1.716
1.572
1.435
Centerline
X bar and R Charts
Control Limits
UCL
X
=X+A
2
R
LCL
X
σ
x
R
d
2
CL
X
=X
CL
R
=R
=X−A
2
R
UCL
R
=D
4
R
UCL
X
=X+A
3
S
LCL
R
=D
3
R
X bar and s Charts
CL
X
=X
LCL
X
=X−A
3
S
CL
s
=s
UCL
s
=B
4
s
LCL
s
=B
3
s
s
c
4
Institute of Quality and Reliability
Control Chart FactorsPage 1 of 3
Tables of Constants for Control charts
Table 8B Variable Data
Median Charts
Chart for
Medians
Chart for Ranges (R)
Chart for
Individuals
Control
Limits
Factor
E
2
2.660
1.772
1.457
1.290
1.184
1.109
1.054
1.010
0.975
ref : AIAG manual for SPC
Charts for Individuals
Chart for Moving Range (R)
Divisors
to
Estimate
Factors for Control
σ
x
Limits
d
2
1.128
1.693
2.059
2.326
2.534
2.704
2.847
2.970
3.078
D
3
-
-
-
-
-
0.076
0.136
0.184
0.223
D
4
3.267
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
Subgroup
size
2
3
4
5
6
7
8
9
10
Control
Divisors to
Limits
Estimate
Factors for Control
Factor
σ
x
Limits
~
A
2
1.880
1.187
0.796
0.691
0.548
0.508
0.433
0.412
0.362
d
2
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
Median Charts
Charts for
Individuals
CL
~
X
Control Limits
UCL
~
X
~
=X
~
~
=X+A
2
R
LCL
~
X
~
=X−A
2
R
CL
R
=R
UCL
R
=D
4
R
LCL
R
=D
3
R
CL
X
=X
UCL
X
=X+E
2
R
LCL
X
=X−E
2
R
CL
R
=R
UCL
R
=D
4
R
LCL
R
=D
3
R
Institute of Quality and Reliability
Control Chart FactorsPage 2 of 3
Tables of Formulas for Control charts
Table 8 C Attribute Data
Centerline
ref : AIAG manual for SPC
Control Limits
Samples not necessarily of constant size
UCL
p chart for
CL
p
=p
proportions of
units in a category
p
i
=p+3
p(1−p)
n
i
LCL
p
i
=p−3
p(1−p)
n
i
p(1−p)
n
If the Sample size is constant (n)
UCL
p
=p+3
p(1−p)
n
LCL
p
=p−3
np chart for
number / rate of
units in a category
c chart for
number of
incidences in one
or more
categories
CL
np
=np
UCL
np
=np+3np(1−p)
UCL
c
=c+3c
LCL
np
=np−3np(1−p)
LCL
c
=c−3c
CL
c
=c
Samples not necessarily of constant size
u chart for
number of
incidences per
unit in one or
more categories
CL
u
=u
UCL
u
=u+3
u
n
i
u
n
LCL
u
=u−3
u
n
i
u
n
using average sample size
UCL
u
=u+3UCL
u
=u−3
If the sample size is constant (n)
UCL
u
=u+3
u
n
UCL
u
=u−3
u
n
Institute of Quality and Reliability
Control Chart Factors Page 3 of 3
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