Formulas and Tables

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

Skewness formula

Formulas and Tables

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

Coefficient of variance formula

Where

sigma-individuals

Formulas and Tables

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

Sigma

sigma-individuals

Sigma of the individuals (actual sigma)

sigma-estimated

Estimated sigma

Subgroup Size
d2
Subgroup Size
d2
2
1.128
14
3.407
3
1.693
15
3.472
4
2.059
16
3.532
5
2.326
17
3.588
6
2.534
18
3.640
7
2.704
19
3.689
8
2.847
20
3.735
9
2.970
21
3.778
10
3.078
22
3.819
11
3.173
23
3.858
12
3.258
24
3.895
13
3.336
25
3.931

Formulas and Tables

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

Median and range chart formulas

X-bar control limits are based on either range or sigma, depending on which chart it is paired with. When the X-bar chart is paired with a range chart, the most common (and recommended) method of computing control limits based on 3 standard deviations is:

Median chart formulas

Upper control limit

Lower control limit:

Range

range-bar-formula

k is the number of subgroups

Upper control limit

Lower control limit

Tabular values for median and range charts
Subgroup Size
A2
D3
D4
2
1.880
—–
3.268
3
1.023
—–
2.574
4
0.729
—–
2.282
5
0.577
—–
2.114
6
0.483
—–
2.004
7
0.419
0.076
1.924
8
0.373
0.136
1.864
9
0.337
0.184
1.816
10
0.308
0.223
1.777
11
0.285
0.256
1.276
12
0.266
0.283
1.717
13
0.249
0.307
1.693
14
0.235
0.328
1.672
15
0.223
0.347
1.653
16
0.212
0.363
1.637
17
0.203
0.378
1.622
18
0.194
0.391
1.608
19
0.187
0.403
1.597
20
0.180
0.415
1.585
21
0.173
0.425
1.276
22
0.167
0.434
1.566
23
0.162
0.443
1.557
24
0.157
0.451
1.548
25
0.153
0.459
1.541

Formulas and Tables

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

Individuals and moving range chart formulas

The most common (and recommended) method of computing control limits for an individuals chart based on 3 standard deviations is:

Individuals (X)

Upper control limit

Lower control limit

Moving Range

Upper control limit

Lower control limit

Tabular values for X and range charts
Subgroup
Size
E2
D4
1
2.660
3.268
2
2.660
3.268
3
1.772
2.574
4
1.457
2.282
5
1.290
2.114
6
1.184
2.004
7
1.109
1.924
8
1.054
1.864
9
1.010
1.816
10
0.975
1.777

Formulas and Tables

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

X-bar and sigma chart formulas

X-bar control limits are based on either range or sigma, depending on which chart it is paired with. When the X-bar chart is paired with a sigma chart, the most common (and recommended) method of computing control limits based on 3 standard deviations is:

X-bar

x-bar-formula

n is the number of observations

x-double-bar-formula

k is the number of subgroups

f-x-bar-sigma-ucl

Upper control limit

f-x-bar-sigma-lcl

Lower control limit

Sigma

s-bar-formula

k is the number of subgroups

range-bar-formula

k is the number of subgroups

f-sigma-ucl

Upper control limit

f-sigma-lcl

Lower control limit

Subgroup Size
A3
B3
B4
2
2.659
—–
3.267
3
1.954
—–
2.568
4
1.628
—–
2.266
5
1.427
—–
2.089
6
1.287
0.030
1.970
7
1.182
0.118
1.882
8
1.099
0.185
1.815
9
1.032
0.239
1.761
10
0.975
0.284
1.716
11
0.927
0.321
1.679
12
0.886
0.354
1.646
13
0.850
0.382
1.618
14
0.817
0.406
1.594
15
0.789
0.428
1.572
16
0.763
0.448
1.552
17
0.739
0.466
1.534
18
0.718
0.482
1.518
19
0.698
0.497
1.503
20
0.680
0.510
1.490
21
0.663
0.523
1.477
22
0.647
0.534
1.466
23
0.638
0.545
1.455
24
0.619
0.555
1.445
25
0.606
0.565
1.435

Formulas and Tables

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

X-bar and range chart formulas

X-bar control limits are based on either range or sigma, depending on which chart it is paired with. When the X-bar chart is paired with a range chart, the most common (and recommended) method of computing control limits based on 3 standard deviations is:

X-bar

x-bar-formula

n is the number of observations

x-double-bar-formula

k is the number of subgroups

Upper control limit

Lower control limit

Range

range-bar-formula

k is the number of subgroups

Upper control limit

Lower control limit

Tabular values for X-bar and range charts
Subgroup Size
A2
d2
D3
D4
2
1.880
1.128
—–
3.268
3
1.023
1.693
—–
2.574
4
0.729
2.059
—–
2.282
5
0.577
2.326
—–
2.114
6
0.483
2.534
—–
2.004
7
0.419
2.704
0.076
1.924
8
0.373
2.847
0.136
1.864
9
0.337
2.970
0.184
1.816
10
0.308
3.078
0.223
1.777
11
0.285
3.173
0.256
1.744
12
0.266
3.258
0.283
1.717
13
0.249
3.336
0.307
1.693
14
0.235
3.407
0.328
1.672
15
0.223
3.472
0.347
1.653
16
0.212
3.532
0.363
1.637
17
0.203
3.588
0.378
1.622
18
0.194
3.640
0.391
1.608
19
0.187
3.689
0.403
1.597
20
0.180
3.735
0.415
1.585
21
0.173
3.778
0.425
1.575
22
0.167
3.819
0.434
1.566
23
0.162
3.858
0.443
1.557
24
0.157
3.895
0.451
1.548
25
0.153
3.931
0.459
1.541

Quality Advisor

A free online reference for statistical process control, process capability analysis, measurement systems analysis,
control chart interpretation, and other quality metrics.

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

Formulas and Tables

Variables control charts

Descriptive statistics

Tables

Attributes control charts

Rare event charts

Capability indices

Quality Advisor

A free online reference for statistical process control, process capability analysis, measurement systems analysis,
control chart interpretation, and other quality metrics.

Default White Guide

SPC DEMO

Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

Don’t miss out! Book a demo of our specialized SPC software and unlock immediate improvements in your processes.

Book a Demo

Additional Resources

Recommended websites

ASQ – American Society of Quality site offers quality resources and information. Also visit ASQ’s magazine Quality Progress online.

iSixSigma – Quality resources for achieving Six Sigma results, this site includes articles and discussion forums.

Quality Digest – The online edition of Quality Digest magazine offers articles, news, and resources.

Quality Magazine – Quality Magazine’s online edition offers articles and a reader forum.

SPC Press – SPC press and Statistical Process Controls, Inc. specialize in statistical tools for understanding and using data. They offer public and in-house seminars, consulting, implementation assistance, books, videos, training aids, and specialty items.

MicroRidge – Hardware and software solutions for RS232 and network data acquisition. Products include our line of gage interfaces and software keyboard wedges.

Institute for Healthcare Improvement (IHI) – The Institute for Healthcare Improvement offers resources and services to help healthcare organizations make dramatic and long-lasting improvements that enhance clinical outcomes and reduce costs.

National Association for Healthcare Quality (NAHQ) – NAHQ is dedicated to improving the quality of healthcare and to supporting the development of professionals in healthcare quality.