Tables of Constants for Control charts - MIT
Tables of Constants for Control charts
Table 8A - Variable Data
ref : AIAG manual for SPC
X bar and R Charts
X bar and s charts
Chart for
Chart for
Averages
Chart for Ranges (R)
Divisors
Averages Chart for Standard Deviation (s) Divisors
Control
to
Control
to
Limits Estimate Factors for Control Limits estimate Factors for Control
Factor
x
Subgroup size
Limits
Factor
x
Limits
(n)
A2
d2
D3
D4
A3
c4
B3
B4
2
1.880 1.128 -
3.267 2.659 0.7979 -
3.267
3
1.023 1.693 -
2.574 1.954 0.8862 -
2.568
4
0.729 2.059 -
2.282 1.628 0.9213 -
2.266
5
0.577 2.326 -
2.114 1.427 0.9400 -
2.089
6
0.483 2.534 -
2.004 1.287 0.9515 0.030 1.970
7
0.419 2.704 0.076 1.924 1.182 0.9594 0.118 1.882
8
0.373 2.847 0.136 1.864 1.099 0.9650 0.185 1.815
9
0.337 2.970 0.184 1.816 1.032 0.9693 0.239 1.761
10
0.308 3.078 0.223 1.777 0.975 0.9727 0.284 1.716
15
0.223 3.472 0.347 1.653 0.789 0.9823 0.428 1.572
25
0.153 3.931 0.459 1.541 0.606 0.9896 0.565 1.435
X bar and R Charts X bar and s Charts
Centerline
CLX = X
CLR = R
CLX = X CL s = s
Control Limits
x
UCL X
=
X
+ A2R
LCL X = X - A 2 R
R
UCLR = D4R
LCLR = D3R
d2
UCL X
=
X
+ A3S
LCL X
=
X
-
A3S
s
UCL s = B4 s
LCL s = B3 s
c4
Institute of Quality and Reliability world-class-
Control Chart Factors
Page 1 of 3
Subgroup size
2 3 4 5 6 7 8 9 10
Tables of Constants for Control charts
Table 8B Variable Data
ref : AIAG manual for SPC
Median Charts
Charts for Individuals
Chart for Medians
Chart for Ranges (R)
Chart for Individuals
Control Limits Factor
~ A2
1.880 1.187 0.796 0.691 0.548 0.508 0.433 0.412 0.362
Divisors to Estimate
x
d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078
Factors for Control Limits
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 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
x
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
Median Charts
Charts for Individuals
Centerline
~ CL ~ = X
X
CLR = R
CL X = X CLR = R
Control Limits
~~
~
UCL
~ X
=
X
+
A2 R
LCL
~ X
=
X
-
A2 R
UCLR = D4R
LCLR = D3R
UCLX = X + E2 R LCLX = X - E2 R
UCLR = D4R
LCLR = D3R
Institute of Quality and Reliability world-class-
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
p chart for proportions of
CL p = p
units in a category
p (1 - p )
UCL pi = p + 3
ni
If the Sample size is constant (n)
p(1 - p)
LCL pi = p - 3
ni
p(1 - p)
UCL p = p + 3
n
p(1 - p)
LCL p = p - 3
n
np chart for
number / rate of CLnp = np UCLnp = np +3 np(1- p) LCLnp = np -3 np(1- p)
units in a category
c chart for
number of CLc = c
incidences in one
or more
categories
u chart for number of incidences per unit in one or more categories
CLu = u
UCLc = c + 3 c LCLc = c - 3 c
Samples not necessarily of constant size
u UCLu = u + 3 ni using average sample size
u LCLu = u - 3 ni
u UCLu = u + 3 n
u UCLu = u - 3 n
If the sample size is constant (n)
u UCLu = u + 3 n
u UCLu = u - 3 n
Institute of Quality and Reliability world-class-
Control Chart Factors
Page 3 of 3
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