STANDARDS FOR SAMPLING PLANS

• Citation: 7 CFR Part 43
• Sections: 6

§ 43.101 Meaning of words.

Words used in this subpart in the singular form shall be considered to impart the plural, or vice versa, as the case may demand.

§ 43.102 Definitions.

Statistical and inspection or sampling terms and their respective definitions that are used in the sampling plans and operating characteristic curves of which are pertinent to the understanding of inspection by attributes follow:

Acceptable quality level ( AQL ). The AQL is expressed in terms of percent defective or defects per 100 units. Lots having a quality level equal to a specified AQL will be accepted approximately 95 percent of the time when using the sampling plans prescribed for that AQL.

Acceptance number ( Ac ). The number in a sampling plan that indicates the maximum number of defects or defectives permitted in a sample in order to consider a lot as meeting a specific requirement.

Acceptance sampling. The art or science that deals with procedures in which decisions to accept or reject lots or processes are based on the examination of samples.

Attributes. Refers to the measurement of a given factor noting and recording the presence or absence of some characteristic (attribute) in each of the units in the group under consideration.

Consumer's risk. The risk a consumer takes that a lot will be accepted by a sampling plan even though the lot does not conform to requirements. In the standards of this subpart this risk is nominally set at ten percent.

Consumer protection. The ability of a sampling plan to reject unacceptable supplies. This is measured as the complement of the probability of acceptance (Pa) for the Limited Quality (LQ) lots. The consumer protection is 90 percent in these standards.

Defect. A failure to meet a requirement imposed on a unit with respect to a single quality characteristic. A unit may contain more than one defect.

Defective. A defective unit; one containing one or more defects with respect to the quality characteristic(s) under consideration.

Inspection. The examination (including testing) of supplies (including, when appropriate, raw materials, components and intermediate assemblies).

(a) Acceptance inspection. An inspection to determine conformance of supplies to specified requirements in order to accept or reject the supplies.

(b) Estimation inspection. In dealing with attributes, an inspection to determine the amount of the supplies conforming to a specified requirement—usually expressed as a percentage.

Inspection by attributes. Inspection whereby either the sample unit is classified as defective or non-defective with respect to a requirement or set of requirements (when on a “defective” basis); or, inspection whereby the number of defects in each sample unit is counted with respect to a requirement or set of requirements (when on a “defect” basis).

Limiting quality ( LQ ). The LQ is expressed in terms of percent defective or defects per 100 units. Lots inspected under the standards of this subpart that have a ten percent probability of acceptance are referred to as a lot having a quality level equal to LQ.

Lot. A collection of units of the same size, type and style which has been manufactured or processed under essentially the same conditions. The term shall mean “inspection lot,” i.e., a collection of units of product from which a sample is to be drawn and inspected to determine conformance with the acceptability criteria. An inspection lot may differ from a collection of units designated as a lot for other purposes (e.g., production lot, shipping lot, etc.).

Lot size. The number of units in the lot.

Operating characteristic curve ( OC curve ). A curve that gives the probability of acceptance as a function of a specific lot quality level.

Probability of acceptance ( Pa ). For a given sampling plan and a given quality of inspection lots, is that percentage of inspection lots expected to be accepted.

Process capability. Performance of a process under normal operating conditions. The performance is measured with respect to specific characteristics.

Producer's risk. The risk that a producer takes that a lot will be rejected by a sampling plan even though the lot conforms to requirements. In the standards of this subpart this risk is nominally set at five percent.

Random sampling. A process of selecting a sample from a lot whereby each unit in the lot has an equal chance of being chosen. Ordinary haphazard choice is generally insufficient to guarantee randomness. Devices such as tables of random numbers are used to remove subjective biases inherent in personal choice.

Rejection number ( Re ). The number in a sampling plan that indicates the minimum number of defects or defectives permitted in a sample that will cause a lot to fail a specific requirement.

Sample. Any number of sample units which are to be used for inspection.

Sample size. The number of sample units which are to be included in the sample.

Sample unit. A container, the entire contents of a container, a portion of the contents of a container, a composite mixture of a product, or any other unit of container or commodity to be used for inspection.

Sampling. The act of drawing or selecting sample units from a given lot.

Sampling plan. A specific plan which states the sample size(s), acceptance number(s) and rejection number(s). In the standards of this subpart two types of sampling plans are provided:

(a) Single sampling plan. A sampling inspection scheme in which a decision to accept or reject an inspection lot is based on the inspection of a single sample. A single sampling plan consists of a single sample size with associated acceptance and rejection number(s).

(b) Double sampling plan. A sampling inspection scheme which involves use of two independently drawn but related samples, a first sample (n 1 ) and a second sample which is added to the first to form a total sample size (n t ). A double sampling plan consists of a first and total sample size with associated acceptance and rejection number(s). Inspection of the first sample leads to a decision to accept, to reject, or to take a second sample and the examination of a second sample, when required, always leads to a decision to accept or reject.

§ 43.103 Purpose and scope.

(a) This subpart contains selected single and double sampling plans for inspection by attributes. They are to serve as a source of plans for developing sound specifications, standards, or sampling and inspection procedures.

(b) The sampling plans of this subpart and corresponding operating characteristic curves are indexed by acceptable quality level, AQL. The AQL's expressed in percent defectives or defects per hundred units are:

0.065

0.40

2.5

8.5

0.10

0.65

4.0

10.0

0.15

1.0

5.0

12.5

0.25

1.5

6.5

15.0

§ 43.104 Master table of single and double sampling plans.

(a) In the master table, a sampling plan is selected by first determining the sample size or sizes and AQL to be used. Then find the applicable acceptance (Ac) and rejection (Re) numbers at the intersection of the sample size(s) row and AQL column. These numbers together with the sample size or sizes constitute a sampling plan.

(b) Single sampling plans having a sample size of 66 or greater and an acceptance number of 1 are not included in the Master Table. These plans are listed in the tables which supplement the Master Table and accompany the OC curves as indexes to the comparable double sampling plans. The use of these single sampling plans do not facilitate the practice of using two or more AQL's simultaneously with the same sample size.

§ 43.105 Operating characteristics (OC) curves.

The OC curves shows the ability of the various sampling plans, presented for each AQL, to distinguish between lots of different quality.

§ 43.106 Choosing AQL's and sampling plans.

(a) The selection of AQL's and sampling plans for given lot sizes depends on too many factors to permit the issuance of a “pre-selected” standard set of plans for specified lot sizes. Each user of the standards of this subpart should select AQL's and sampling plans that are tailored to best meet his needs.

(b) Some of the factors that must be considered prior to selecting the AQL's are:

(1) Class of defects such as major and minor: Major defects would generally require lower AQL's than those for minor defects;

(2) Process capabilities under good commercial practice with respect to the defects in question: For example, if under normal production processes, the defect level cannot be kept below 2.0 percent defective, the selection of an AQL of 0.15 percent defective, although desirable for the defects in question, may not be practical;

(3) Consumer preferences: These may require higher AQL's or permit lower AQL's than process capabilities would indicate; and

(4) Time and cost required to sample and inspect a lot under various AQL's: The smaller the AQL the more time and cost of inspection.

(c) Some of the factors that may be considered prior to selecting the sampling plans for given lot sizes are:

(1) The applicable AQL(s): The AQL dictates, among other things, the smallest sample size that can be used and the size of the “jumps” from one sample size to the next larger one;

(2) The relative ability of the plans to discriminate between “good” and “bad” lots: Although several plans in these standards have the same AQL, they differ in their ability to reject lots worse than the AQL's. The OC curve in the standards of this subpart provide the basis for determining the discriminating ability of each plan;

(3) The amount, time, and cost of sampling required;

(4) The size and value of the lots relative to the producer and consumer protection a sampling plan affords: One may be willing to take larger risks of passing “bad” lots that are small or of lesser value than they would for larger more valuable lots;

(5) The knowledge about the lot(s) to be submitted for inspection: Lots consisting of product produced under essentially the same conditions may require smaller sample sizes than those consisting of product produced by different shifts and different raw stock for example; and

(6) The record of the quality level of previously submitted lots: The sample size can be smaller for lots submitted from a supplier with a consistent record of quality levels significantly better than the specified AQL(s) than sample sizes for the supplier whose records show considerable variability in quality, “borderline” supplies or product worse than the AQL.

Master Table of Single and Double Sampling Plans 1

Sample size code letter

Sample size

Acceptable quality levels

0.065

0.10

0.15

0.25

0.40

0.65

1.0

1.5

2.5

4.0

5.0

6.5

8.5

10.0

12.5

15.0

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

Ac Re

AA

n 1 =1

0 1

A

n 1 =2

0 1

B

n 1 =3

0 1

0 3

1 2

n t =8

2 3

C

n 1 =4

0 1

1 2

D

n 1 =5

0 1

1 2

E

n 1 =6

1 2

2 3

EE

n 1 =7

2 3

F

n 1 =9

0 1

1 2

2 3

3 4

G

n 1 =11

1 2

2 3

3 4

H

n 1 =13

0 1

2 3

3 4

4 5

J

n 1 =21

0 1

0 2

0 2

2 3

1 4

3 4

3 5

4 5

5 6

6 7

n t =31

1 2

2 3

3 4

5 6

K

n 1 =29

0 1

0 2

1 2

2 3

1 4

3 4

4 5

3 7

5 6

6 7

7 8

n t =65

1 2

6 7

9 10

L

n 1 =48

0 1

0 2

1 2

2 3

3 4

4 5

5 6

6 7

7 8

8 9

10 11

11 12

n t =72

1 2

M

n 1 =84

0 1

0 2

0 3

2 3

3 4

4 5

6 7

7 8

9 10

11 12

13 14

15 16

18 19

n t =120

1 2

n t =132

2 3

N

n 1 =126

0 1

0 2

0 3

2 3

3 4

4 5

6 7

9 10

10 11

13 14

16 17

18 19

22 23

26 27

n t =180

1 2

n t =210

2 3

P

n 1 =200

0 1

0 2

0 3

2 3

3 4

4 5

6 7

9 10

13 14

15 16

19 20

24 25

27 28

33 34

39 40

n t =284

1 2

n t =326

2 3

Q

n 1 =315

0 1

0 2

0

2 3

3 4

4 5

6 7

8 9

13 14

19 20

22 23

28 29

35 36

41 42

50 51

59 60

n t =435

1 2

n t =519

2 3

R

n 1 =500

0 2

0 3

2 3

3 4

4 5

6 7

9 10

12 13

18 19

28 29

33 34

42 43

53 54

62 63

76 77

90 91

n t =644

1 2

n t =836

2 3

S

n 1 =800

0 3

2 3

3 4

4 5

6 7

9 10

13 14

18 19

27 28

42 43

50 510

64 65

82 83

95 96

117 118

140 141

n t =1304

2 3

T

n 1 =1250

2 3

3 4

4 5

6 7

9 10

13 14

19 20

26 27

41 42

63 64

76 77

U

n 1 =2000

3 4

4 5

6 7

9 10

13 14

19 20

28 29

39 40

62 63

96 97

1 Double plans are indicated by 2 sample sizes, n 1 (first) and n t (total). Ac=Acceptance number Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=0.065 Percent Defective (or AQL=0.065 Defects per Hundred Units)

[Sampling plans—AQL=0.065]

Comparable sampling plans

Identification letter of OC curve

Q

R

S, T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

315

0

1

624

1

2

1250

2

3

2,000

3

Double

500

0

2

800

0

3

644

1

2

1304

2

3

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=0.10 Percent Defective (or AQL=0.10 Defects per Hundred Units)

[Sampling plans—AQL=0.10]

Comparable sampling plans

Identification letter of OC curve

P

Q

R, S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

200

0

1

408

1

2

800

2

3

1,250

3

4

2,000

4

Double

315

0

2

500

0

3

435

1

2

836

2

3

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=0.15 Percent Defective (or AQL=0.15 Defects per Hundred Units)

[Sampling plans—AQL=0.15]

Comparable sampling plans

Identification letter of OC curve

N

P

Q

R, S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

126

0

1

264

1

2

500

2

3

800

3

4

1,250

4

5

2,000

6

7

Double

200

0

2

315

0

3

284

1

2

519

2

3

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=0.25 Defects per Hundred Units

[Sampling plans—AQL=0.25]

Comparable sampling plans

Identification letter of OC curve

M

N

P, Q

R

S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

84

0

1

168

1

2

315

2

3

500

3

4

800

4

5

1250

6

7

2000

9

10

Double

126

0

2

200

0

3

180

1

2

326

2

3

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=0.40 Percent Defective (or AQL=0.40 Defects per Hundred Units)

[Sampling plans—AQL=0.40]

Comparable sampling plans

Identification letter of OC curve

L

M

N, P

Q

R

S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

48

0

1

108

1

2

200

2

3

315

3

4

500

4

5

800

6

7

1250

9

10

2000

13

10

Double

84

0

2

126

0

3

120

1

2

210

2

3

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=0.65 Percent Defective (or AQL=0.65 Defects per Hundred Units)

[Sampling plans—AQL=0.65]

Comparable sampling plans

Identification letter of OC curve

K

L

M, N

P

Q

R

S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

29

0

1

66

1

2

126

2

3

200

3

4

315

4

5

500

6

7

800

9

10

1250

13

14

2000

19

20

Double

48

0

2

84

0

3

72

1

2

132

2

3

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=1.0 Percent Defective (or AQL=1.0 Defects per Hundred Units)

[Sampling plans—AQL=1.0]

Comparable sampling plans

Identification letter of OC curve

J

K, L

M

N

P

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

21

0

1

48

1

2

84

2

3

126

3

4

200

4

5

Double

29

0

2

65

1

2

Q

R

S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

315

6

7

500

9

10

800

13

14

1250

19

20

2000

28

29

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=1.5 Percent Defective (or AQL=1.5 Defects per Hundred Units)

[Sampling plans—AQL=1.5]

Comparable sampling plans

Identification letter of OC curve

H

J, K

L

M

N

P

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

13

0

1

29

1

2

48

2

3

84

3

4

126

4

5

200

6

7

Double

21

0

2

31

1

2

Q

R

S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

315

8

9

500

12

13

800

18

19

1,250

26

27

2,000

39

40

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=2.5 Percent Defective (or AQL=2.5 Defects per Hundred Units)

[Sampling plans—AQL=2.5]

Comparable sampling plans

Identification letter of OC curve

F

J, K

L

M

N

P

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

9

0

1

29

2

3

48

3

4

84

4

5

126

6

7

200

9

10

Double

21

0

2

31

2

3

Q

R

S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

315

13

14

500

18

19

800

27

28

1,250

41

42

2,000

62

63

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=4.0 Percent Defective (or AQL=4.0 Defects per Hundred Units)

[Sampling plans—AQL=4.0]

Comparable sampling plans

Identification letter of OC curve

D

G

J

K L

M

N

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

5

0

1

11

1

2

21

2

3

48

4

5

84

6

7

126

9

10

Double

29

1

4

65

6

7

P

Q

R

S

T

U

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

200

13

14

315

19

20

500

28

29

800

42

43

1250

63

64

2000

96

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=5.0 Percent Defective (or AQL=5.0 Defects per Hundred Units)

[Sampling plans—AQL=5.0]

Comparable sampling plans

Identification letter of OC curve

C

F

J, K

L

M

N

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

4

0

1

1

1

2

29

3

4

48

5

6

84

7

8

126

10

11

Double

21

1

4

31

3

4

P

Q

R

S

T

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

200

15

16

315

22

23

500

33

34

800

50

51

1250

76

77

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=6.5 Percent Defective (or AQL=6.5 Defects per Hundred Units)

[Sampling plans—AQL=6.5]

Comparable sampling plans

Identification letter of OC curve

B

E

H

J

K

L

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

3

0

1

6

1

2

13

2

3

21

3

4

29

4

5

48

6

7

M

N

P

Q

R

S

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

84

9

10

126

13

14

200

19

20

315

28

29

500

42

43

800

64

65

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=8.5 Percent Defective (or AQL=8.5 Defects per Hundred Units)

[Sampling plans—AQL=8.5]

Comparable sampling plans

Identification letter of OC curve

D

G

J

K, L

M

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

5

1

2

11

2

3

24

4

5

48

7

8

84

11

1

Double

21

3

5

29

3

7

31

5

6

65

9

10

N

P

Q

R

S

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

126

16

17

200

24

25

315

35

36

500

53

54

800

82

83

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=10.0 Percent Defective (or AQL=10.0 Defects per Hundred Units)

[Sampling plans—AQL=10.0]

Comparable sampling plans

Identification letter of OC curve

A

C

F

H

J

K

L

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

2

0

1

4

1

2

9

2

3

13

3

4

21

4

5

29

5

6

48

8

9

M

N

P

Q

R

S

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

84

13

14

126

18

19

200

27

28

315

41

42

500

62

63

800

95

96

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristics (OC) Curves for AQL=12.5 Percent Defective (or AQL=12.5 Defects per Hundred Units)

[Sampling plans—AQL=12.5]

Identification letter of OC curve

Comparable sampling plans

B, EE

G

J

K

L

M

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

7

2

3

11

3

4

21

5

6

29

6

7

48

10

11

84

15

16

Double

3

0

3

8

2

3

N

P

Q

R

S

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

126

22

23

200

33

34

315

50

51

500

76

77

800

117

118

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.

Sampling Plans and Operating Characteristic (OC) Curves for AQL=15.0 Percent Defective (or AQL=15.0 Defects per Hundred Units)

[Sampling plans—AQL=15.0]

Comparable sampling plans

Identification letter of OC curve

AA

B

E

F

H

J

K

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

1

0

1

3

1

2

6

2

3

9

3

4

13

4

5

21

6

7

29

7

8

L

M

N

P

Q

R

S

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

n c

Ac

Re

Single

48

11

12

84

18

19

126

26

27

200

39

40

315

59

60

500

90

91

800

140

141

n c =Cumulative sample size. Ac=Acceptance number. Re=Rejection number.