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Electronic Code of Federal Regulations

e-CFR data is current as of December 5, 2019

Title 7Subtitle BChapter ISubchapter A → Part 43


Title 7: Agriculture


PART 43—STANDARDS FOR SAMPLING PLANS


Contents

Definitions

§43.101   Meaning of words.
§43.102   Definitions.

Sampling Plans

§43.103   Purpose and scope.
§43.104   Master table of single and double sampling plans.
§43.105   Operating characteristics (OC) curves.
§43.106   Choosing AQL's and sampling plans.

Authority: Secs. 203, 205, 60 Stat. 1087, as amended, 1090, as amended; 7 U.S.C. 1622, 1624.

Source: 29 FR 5870, May 5, 1964, unless otherwise noted. Redesignated at 42 FR 32514, June 27, 1977, and further redesignated at 46 FR 63203, Dec. 31, 1981.

Definitions

§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 (n1) and a second sample which is added to the first to form a total sample size (nt). 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.

Sampling Plans

§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:

0.0650.402.58.5
0.100.654.010.0
0.151.05.012.5
0.251.56.515.0

§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 Plans1

Sample size code letterSample sizeAcceptable quality levels
0.0650.100.150.250.400.651.01.52.54.05.06.58.510.012.515.0
Ac  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  ReAc  Re
AAn1=1  0   1
An1=2  0   1
Bn1=3  0   1  0   3  1   2
   nt=8  2   3
Cn1=4  0   1  1   2
Dn1=5  0   1  1   2
En1=6  1   22   3
EEn1=7  2   3
Fn1=9  0   1  1   2  2   3  3   4
Gn1=11  1   2  2   3  3   4
Hn1=13  0   1  2   3  3   4  4   5
Jn1=21  0   1  0   2  0   2  2   3  1   4  3   4  3   5  4   5  5   6  6   7
   nt=31  1   2  2   3  3   4  5   6
Kn1=29  0   1  0   2  1   2  2   3  1   4  3   4  4   5  3   7  5   6  6   7  7   8
   nt=65  1   2  6   7  9  10
Ln1=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
   nt=72  1   2
Mn1=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
   nt=120  1   2
   nt=132  2   3
Nn1=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
   nt=180  1   2
   nt=210  2   3
Pn1=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
   nt=284  1   2
   nt=326  2   3
Qn1=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
   nt=435  1   2
   nt=519  2   3
Rn1=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
   nt=644  1   2
   nt=836  2   3
Sn1=800  0   3  2   3  3   4  4   5  6   7  9  10  13  14  18  19  27  28  42  4350  510  64  65  82  83  95  96117  118140  141
   nt=1304  2   3
Tn1=1250  2   3  3   4  4   5  6   7  9  10  13  14  19  20  26  27  41  42  63  64  76  77
Un1=2000  3   4  4   5  6   7  9  10  13  14  19  20  28  29  39  40  62  63  96  97

1Double plans are indicated by 2 sample sizes, n1 (first) and nt (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 plansIdentification letter of OC curve
QRS, TU
ncAcRencAcRencAcRencAcRe
Single31501624121250232,0003
Double5000280003
64412130423

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.023.gif

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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 plansIdentification letter of OC curve
PQR, STU
ncAcRencAcRencAcRencAcRencAcRe
Single2000140812800231,250342,0004
Double3150250003
   4351283623

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.024.gif

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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 plansIdentification letter of OC curve
NPQR, STU
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single126012641250023800341,250452,00067
Double2000231503
   2841251923

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.025.gif

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

[Sampling plans—AQL=0.25]

Comparable sampling plansIdentification letter of OC curve
MNP, QRSTU
ncAcRencAcRencAcRencAcRencAcRencAcRencAcRe
Single8401168123152350034800451250672000910
Double1260220003
   1801232623

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.026.gif

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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 plansIdentification letter of OC curve
LMN, PQRSTU
ncAcRencAcRencAcRencAcRencAcRencAcRencAcRencAcRe
Single48011081220023315345004580067125091020001310
Double840212603
   1201221023

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.027.gif

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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 plansIdentification letter of OC curve
KLM, NPQRSTU
ncAcRencAcRencAcRencAcRencAcRencAcRencAcRencAcRencAcRe
Single29016612126232003431545500678009101250131420001920
Double48028403
   721213223

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.028.gif

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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 plansIdentification letter of OC curve
JK, LMNP
ncAcRencAcRencAcRencAcRencAcRe
Single2101481284231263420045
Double2902
   6512
   QRSTU
ncAcRencAcRencAcRencAcRencAcRe
Single3156750091080013141250192020002829

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.029.gif

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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 plansIdentification letter of OC curve
HJ, KLMNP
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single13012912482384341264520067
Double2102
   3112
   QRSTU
ncAcRencAcRencAcRencAcRencAcRe
Single31589500121380018191,25026272,0003940

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.030.gif

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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 plansIdentification letter of OC curve
FJ, KLMNP
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single90129234834844512667200910
Double2102
   3123
   QRSTU
ncAcRencAcRencAcRencAcRencAcRe
Single3151314500181980027281,25041422,0006263

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.031.gif

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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 plansIdentification letter of OC curve
DGJK LMN
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single5011112212348458467126910
Double2914
   6567
   PQRSTU
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single200131431519205002829800424312506364200096

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.032.gif

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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 plansIdentification letter of OC curve
CFJ, KLMN
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single4011122934485684781261011
Double2114
   3134
   PQRST
ncAcRencAcRencAcRencAcRencAcRe
Single200151631522235003334800505112507677

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.033.gif

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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 plansIdentification letter of OC curve
BEHJKL
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single3016121323213429454867
   MNPQRS
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single8491012613142001920315282950042438006465

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.034.gif

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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 plansIdentification letter of OC curve
DGJK, LM
ncAcRencAcRencAcRencAcRencAcRe
Single51211232445487884111
Double21352937
   315665910
   NPQRS
ncAcRencAcRencAcRencAcRencAcRe
Single12616172002425315353650053548008283

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.035.gif

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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 plansIdentification letter of OC curve
ACFHJKL
ncAcRencAcRencAcRencAcRencAcRencAcRencAcRe
Single2014129231334214529564889
   MNPQRS
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single84131412618192002728315414250062638009596

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.036.gif

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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 curveComparable sampling plans
B, EEGJKLM
ncAcRencAcRencAcRencAcRencAcRencAcRe
Single723113421562967481011841516
Double303
   823
   NPQRS
ncAcRencAcRencAcRencAcRencAcRe
Single1262223200333431550515007677800117118

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.037.gif

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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 plansIdentification letter of OC curve
AABEFHJK
ncAcRencAcRencAcRencAcRencAcRencAcRencAcRe
Single101312623934134521672978
   LMNPQRS
ncAcRencAcRencAcRencAcRencAcRencAcRencAcRe
Single4811128418191262627200394031559605009091800140141

nc=Cumulative sample size.   Ac=Acceptance number.   Re=Rejection number.

eCFR graphic ec02se91.038.gif

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