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2024年3月29日发(作者:respond读音)

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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