Marketing and

Regulatory

Programs

Agricultural

Marketing 

Service

Specialty 

Crops

Program

Specialty

Crops

Inspection

Division

United States Standards

for Inspection by 

Variables

Effective May 29, 1973

Reprinted October 18, 2019
This is a reprint of the United States Standards for Inspection by Variables which 

have been in effect since May 29, 1973 and were updated to modify the format and 

update obsolete contact information.

Voluntary U.S. grade standards are issued under the authority of the Agricultural 

Marketing Act of 1946, which provides for the development of official U.S. grades to 

designate different levels of quality. These grade standards are available for use by 

producers, suppliers, buyers, and consumers. As in the case of other standards for 

grades of fresh and processed fruits, vegetables, and specialty crops these 

standards are designed to facilitate orderly marketing by providing a convenient 

basis for buying and selling, for establishing quality control programs, and for 

determining loan values. 

The U.S. grade standards and inspection instructions for all fresh and processed fruits,

vegetables, and specialty crops are available on the internet and upon request at the 

address below. These documents provide detailed interpretations of the grade standards 

and provide step-by-step procedures for grading the product. 

Grade standards are issued by the U.S. Department of Agriculture (USDA) after careful 

consideration of all data and views submitted during rulemaking. The Department 

welcomes suggestions for improving the standards in future revisions. Comments may be 

submitted to, and copies of standards and inspection instructions obtained from: 

Director, Specialty Crops Inspection Division

Specialty Crops Program, 

USDA, Agricultural Marketing Service

1400 Independence Avenue, SW, STOP 0240 

Washington, D.C. 20250

Authority: 7 U.S.C. 1621-1627. 

Note: Compliance with the provisions of these standards shall not excuse failure to 

comply with the provisions of the Federal Food, Drug, and Cosmetic Act, or 

with applicable State laws and regulations.

Non-Discrimination Policy: In accordance with Federal civil rights law and U.S. Department of Agriculture (USDA) civil rights regulations and 

policies, the USDA, its Agencies, offices, and employees, and institutions participating in or administering USDA programs are prohibited from 

discriminating based on race, color, national origin, religion, sex, gender identity (including gender expression), sexual orientation, disability, age, 

marital status, family/parental status, income derived from a public assistance program, political beliefs, or reprisal or retaliation for prior civil 

rights activity, in any program or activity conducted or funded by USDA (not all bases apply to all programs). Remedies and complaint filing 

deadlines vary by program or incident.

Persons with disabilities who require alternative means of communication for program information (e.g., Braille, large print, audiotape, American 

Sign Language, etc.) should contact the responsible Agency or USDA's TARGET Center at (202) 720-2600 (voice and TTY) or contact USDA 

through the Federal Relay Service at (800) 877-8339. Additionally, program information may be made available in languages other than English.

To file a program discrimination complaint, complete the USDA Program Discrimination Complaint Form, AD-3027, found online at How to File a 

Program Discrimination Complaint and at any USDA office or write a letter addressed to USDA and provide in the letter all of the information 

requested in the form. To request a copy of the complaint form, call (866) 632-9992. Submit your completed form or letter to USDA by: (1) mail:

U.S. Department of Agriculture, Office of the Assistant Secretary for Civil Rights, 1400 Independence Avenue, SW, Washington, D.C. 20250-

9410; (2) fax: (202) 690-7442; or (3) email: program.intake@usda.gov.

USDA is an equal opportunity provider, employer, and lender.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

1

United States Standards for Inspection by Variables

______________________________________________________________________

Section Page No.

Purpose, Options, Requirements................................................................................. 2

§52.201 Purpose........................................................................................................... 2

§52.202 Options............................................................................................................ 2

§52.203 Requirements for application........................................................................... 2

Definitions...................................................................................................................... 3

§52.204 Definitions. ...................................................................................................... 3

Records.......................................................................................................................... 6

§52.205 Records........................................................................................................... 6

Procedure ...................................................................................................................... 7

§52.206 Sampling. ........................................................................................................ 7

§52.207 Measurements, calculations, and recording data............................................ 7

§52.208 Application of sampling allowance. ................................................................. 9

§52.209 Acceptance and rejection criteria. ................................................................... 9

Sampling Allowance Chart......................................................................................... 11

§52.210 Sampling allowance chart ............................................................................. 11
United States Standards for Determination of Inspection by Variables (May 29, 1973)

2

Purpose, Options, Requirements

§52.201 Purpose.

The purpose of these standards is to:

(a) Designate and define symbols and terminology associated with statistical quality

control;

(b) Prescribe a procedure for collecting and recording data that is adaptable to use 

for statistical quality control; and

(c) Provide a statistical procedure for determining compliance of a variable, which 

may be any measurable product characteristic, with a specified requirement.

§52.202 Options.

These standards provide for three operations, any of which may be applied to determine

compliance of a variable. These options are based on procedures employing the use 

of:

(a) Conventional averages;

(b) The median; or

(c) Moving averages.

§52.203 Requirements for application.

These standards are written in general terms to be applied to any variable. Therefore, 

in order to use these standards it will be necessary to predetermine:

(a) The sampling allowance code;

(b) The sampling frequency;

(c) The values for:

(1) Specified averages;

(2) Warning limits;

(3) Reject limits; and

(4) Maximum range, when requested.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

3

Definitions

§52.204 Definitions.

Statistical and inspection symbols and terms and their respective definitions which are

pertinent to the understanding and application of these standards follow.

(a) Symbols defined.

LRL—The lower reject limit for individual measurements. The lowest value an

individual measurement may have without causing the production to be rejected

for failure to meet prescribed requirements for individual measurements. 

LRLxx—The lower reject limit for subgroup averages or medians. The lowest

value the average or median of a subgroup may have without causing the

production to be rejected for failure to meet prescribed requirements for 

subgroup averages.

LWL—The lower warning limit for individual measurements. This value serves

as a warning point that the production may have reached a level where the

chances of subsequently finding an individual measurement that will fall below

the LRL have increased to a degree that the production may be in danger of

rejection.

LWLxx—The lower warning limit for subgroup averages or medians. This value

serves as a warning point that the quality of the production may have reached a

level where the chances of subsequently finding a subgroup average or median

that will fall below the LRLxx have increased to a degree that the production may

be in danger of rejection.

m—The number of subgroups in a sample.

Mi—The median of all the individual measurements in a subgroup.

MMi—The median of all the individual measurements or subgroup medians (Mi) in

a sample.

n—The total number of sample units or measurements in a sample. n= (m)(ns).

ns—The number of sample units or measurements in a subgroup.

R—A range of measurements, the difference between the highest measurement 

and the lowest measurement within a subgroup.

RR—The average range of all the subgroup ranges.

RR’—A specified average range value.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

4

Rmax—A specified maximum range for a subgroup.

s—The standard deviation of the individual measurements.

sxx—The standard deviation of the averages.

URL—The upper reject limit for individual measurements. The highest value an 

individual measurement may have without causing the production to be rejected 

for failure to meet prescribed requirements for individual measurements.

URLxx—The upper reject limit for subgroup averages or medians. The highest 

value the average or median of a subgroup may have without causing the 

production to be rejected for failure to meet prescribed requirements for 

subgroup averages.

UWL—The upper warning limit for individual measurements. This value serves 

as a warning point that the quality of the production may have reached a level 

where the chances of subsequently finding an individual measurement that will 

exceed the URL have increased to a degree that the production may be in 

danger of rejection.

UWLxx—The upper warning limit for subgroup averages or medians. This value 

serves as a warning point that the quality of production may have reached a level 

where the chances of subsequently finding a subgroup average or median that 

will exceed the URLxx—have increased to a degree that the production may be in 

danger of rejection.

X—The value of an individual measurement for a variable.

XX—The average of all individual measurements in a subgroup.

XX’max—A specified maximum lot average value.

XX’max adjusted—XX’max plus a sampling allowance.

XX’min—A specified minimum lot average value.

XX’min adjusted—XX’min minus a sampling allowance.

XX—The arithmetic mean of all the individual measurements in a sample. When

the average is calculated for each subgroup in a sample for conventional 

averages, XX is also the average of the subgroup averages.

(b) Terms defined.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

5

Average.—The arithmetic mean of two or more values; the sum of all 

measurements divided by the number of measurements.

Median.—The median is the middle value with respect to magnitude of all the 

individual measurements when the number of individual measurements is odd. 

When the number of individual measurements is even and arranged according to 

magnitude, the median is the arithmetic mean of the two middle values.

Moving average.—A scheme under which a series of consecutive measurements 

are made until such number equals the subgroup size; the average is then 

determined and recorded; as new data is collected from continuing production, 

the first measurement of the subgroup is dropped, the next new value is added, 

and a new average is calculated; this process of adding new measurements, 

dropping the oldest measurement in the subgroup, and calculating the average 

on the new data is continued throughout the production. 

Example: 

XX 1 = 

5+7+3

3

= 5.00

XX2 = 7+3+4

3

= 4.67

XX3 = 

3+4+6

3

= 4.33

Moving range.—The difference between the highest measurement and lowest

measurement within a subgroup from which a moving average is obtained.

One-sided specification.—A specification with rejection limits applicable to only

one side of the specified lot average. When only lower reject limits apply, the

term “low—sided specification” may be used. When only upper reject limits

apply, the term “high—sided specification” may be used.

Two- sided specification.—A specification with both upper and lower rejection

limits applicable.

Sample.—Any number of sample units to be used for inspection of a lot.

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 allowance.—The amount that the sample quality may deviate from the

lot quality due solely to the fact that only a portion has been taken from the whole

lot.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

6

Subgroup.—Generally a small group of sample units representing a portion of a

sample. The term “subgroup” is synonymous with the term “sample” when the

sample contains only one subgroup.

Variable.—Any measurable product characteristic.

Records

§52.205 Records.

(a) General. Records required for use in the implementation of these standards 

consist of a data sheet, referred to as an “ XX and R data sheet,” on which 

numerical values are recorded, and/or a control chart on which certain numerical 

values are recorded in the form of plottings. It is desirable to use both forms. 

The control chart may be incorporated on the same sheet with the XX and R data 

sheet. However, one of these forms may be used in lieu of both as desired at the 

option of the packer.

(b) XX and R data sheets. A separate data sheet shall be maintained for each item. 

When a single item is simultaneously produced on more than one processing 

line, it is desirable to maintain one data sheet for the item. In such instances, the 

processing line designation shall be recorded with the corresponding data. 

The XX and R data sheets shall provide for recording the following information: 

(1) The time a sample unit or subgroup has been drawn;

(2) The X values;

(3) The total values of all the X values in the subgroups when conventional 

averages are used;

(4) The values for MM, R, RR, Mi, XX, and XX

(c) XX and R control charts. Control charts consist of an XX chart and may consist of 

an R chart. When both are used they are contained on the same sheet with the 

limits for the XX chart on the top portion and the limits for the R chart on the lower 

portion with a space separating the two such that plottings from one does not 

overlap those of the other. 

Separate control charts shall be maintained for each item. More than one day's 

production of an item may be plotted on a single control chart. 

(1) XX charts.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

7

(i) The XX charts for two-sided specifications shall consist of lines and 

values properly representing both the upper and lower reject and 

warning limit(s), and may require the use of minimum and 

maximum specification lot averages.

(2) R charts. When the R chart is used, it shall consist of lines and values 

properly representing RR', Rmax, and the lower limit for R. For subgroup 

sizes of 6 or less the value of the lower limit for R will always be zero. 

Procedure

§52.206 Sampling.

(a) General. In order to obtain the most reliable results, sampling should be 

performed at a point where no further change in the variable can occur.

Sample units or subgroups shall be drawn separately for each code, container 

size, and style. 

(b) Subgroup Sampling. Sampling by subgroups consists of drawing more than one 

sample unit at approximately the same time. This type of sampling is required in 

the use of the conventional XX and R determinations for variables.

When a single code is processed on more than one line simultaneously, it is 

desirable to obtain a subgroup representing a single line, alternating the lines 

each time a subgroup is drawn for that code. If the processing procedure 

prohibits obtaining a subgroup representing a single line, it shall be necessary to 

sample by code only, omitting line identity. Each subgroup thus obtained will 

generally represent more than one line and consequently reflect variations in the 

code as a whole but not variations for a single line.

(c) Sample unit sampling. This procedure consists of drawing a single sample unit 

at random at specified intervals from a production. This type of sampling may 

employ the use of a moving average and is applicable to a variable or a process 

when subgroup sampling is not feasible.

§52.207 Measurements, calculations, and recording data.

(a) General. Immediately after the sample unit or subgroup has been taken, 

measurements and calculations shall be made and recorded on the appropriate 

form as required.

(b) Recording data on the XX and R data sheet. The data to be recorded on the

XX and R data sheet is as follows: 

(1) The time the sample unit or subgroup is taken;

(2) The value for each individual measurement (X value);
United States Standards for Determination of Inspection by Variables (May 29, 1973)

8

(3) The total value for all the X values in the subgroup, when applicable;

(4) The average value (XX) for each subgroup, when applicable;

(5) The Mi value for each subgroup, when applicable;

(6) The range value (R) for each subgroup, when applicable;

(7) The sample median value (MMi) when the median is used;

(8) The sample average value (XX) when required; and

(9) The average range value (RR) when applicable.

(c) Recording data on the XX and R control chart. The data to be recorded on the XX

and R control chart is as follows:

(1) Individual measurements (X values). The values representing the 

individual measurements of each subgroup (X value) shall be plotted on 

the XX chart. The distance between the smallest and largest values of the 

individual measurements in the subgroup may be used for R in lieu of 

plotting the range on the R chart. It is desirable to plot all the values for a 

subgroup on the same linear segment of the chart. Identical values are 

plotted adjacently in such a manner as to associate such values with the 

subgroup in which they occur.

(2) The median. When the median option is used, the median for each 

subgroup shall be identified on the XX chart in such a manner as to make it 

readily distinguishable from the rest of the values in the subgroup. When 

a subgroup consists of an even number of individual measurements, the

median represented by the arithmetic mean of the two middle values shall 

also be plotted on the XX chart in such a manner as to associate it with the 

subgroup from which it was calculated. 

When the median option is used for a particular production, it is not 

permissible to change to the option for conventional averages during the 

same shift.

(3) Subgroup averages (XX values). When the option for conventional 

averages is used, the average of each subgroup is calculated and 

recorded on the XX and R data sheet. The subgroup average is then 

plotted on the XX chart in such a manner as to associate it with the 

subgroup from which it was calculated. When this option is used, it is not 

permissible to change to the median option during the same shift.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

9

(4) The range (R value). The range of each subgroup, when required, shall 

be plotted on the R chart.

(5) The average median (MMi value) and sample average (XX value). When the 

plotted values obviously indicate the acceptability of the lot, MMi or XX need

not be obtained. When the plotted values for Mi or XX or both indicate the

acceptability of a lot may be questionable, MMi in the case of the median

option, or XX in the case of the option for conventional averages must be

obtained and recorded. Acceptability of the lot with respect to the sample

median or sample average may then be determined in accordance with

acceptance criteria as prescribed under § 52.209(a) of these standards.

§52.208 Application of sampling allowance.

The amount of sampling allowance is obtained from the sampling allowance chart in 

these standards. The actual value for the sampling allowance is obtained from the point 

of intersection of a horizontal line drawn from a point on the vertical axis representing 

the sample size to the diagonal line for the item involved. The value on the horizontal 

axis corresponding to the vertical line nearest to this point of intersection is the sampling 

allowance. 

The sampling allowances are applied to the specified lot averages to allow for 

deviations from these averages that are inherent in any sampling procedure. These

allowances are applied to the specified lot averages only when the sample average (XX

or MMi) is less than XX’min or greater than XX’max. When this occurs; the specification 

average is adjusted by subtracting the allowance from XX’min or adding to XX’max whichever 

is applicable.

§52.209 Acceptance and rejection criteria.

(a) Conventional averages and the median.

(1) Acceptance. A lot shall be accepted as meeting specified requirements 

for a variable provided that:

(i) All X values are equal to or greater than LRL and equal to or less 

than URL;

(ii) All Mi or XX values are equal to or greater than LRLxx and equal to or 

less than URLxx;

(iii) MMi or XX is equal to or less than XX’max adjusted and equal to or 

greater than XX’min adjusted; and
United States Standards for Determination of Inspection by Variables (May 29, 1973)

10

(iv) The condition under paragraph (a) (2) (ii) of this section does not 

exist.

(2) Rejection. A lot shall be rejected for failure to meet specified requirements 

for a variable under the following conditions:

(i) Failure to meet any of the requirements under paragraph (a) (1), (i), 

(ii), or (iii) of this section; or

(ii) All Mi or XX values are less than XX’min or greater than XX’max.

(b) Moving averages. 

(1) Acceptance. A lot shall be accepted as meeting specified requirements 

for a variable provided that:

(i) All X values are equal to or greater than LRL and equal to or less 

than URL;

(ii) All XX values are equal to or greater than LRLxx and equal to or less 

than URLxx;

(iii) XX is equal to or less than XX’max adjusted and equal to or greater 

than XX’ adjusted; and

(iv) The condition under paragraph (b) (2) (ii) of this section does not 

exist.

(2) Rejection. A lot shall be rejected for failure to meet specified requirements 

for a variable under the following conditions:

(i) Failure to meet any of the conditions under paragraph (b) (1) (i), (ii), 

and (iii) of this section; or

(ii) All XX values are less than XX’min or greater than XX’max.
United States Standards for Determination of Inspection by Variables (May 29, 1973)

11

Sampling Allowance Chart

§52.210 Sampling allowance chart