ASTM E2762-10(2020)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E2762 − 10 (Reapproved 2020) An American National Standard
Standard Practice for
Sampling a Stream of Product by Variables Indexed by
AQL
This standard is issued under the fixed designation E2762; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2.2 Other Standards:
MIL-STD-414 Sampling Procedures and Tables for Inspec-
1.1 Purpose—This practice establishes lot or batch sam-
tion by Variables for Percent Defective
pling plans and procedures for inspection by variables using
MIL-STD-105E Sampling Procedures and Tables for In-
MIL-STD-414 as a basis for sampling a steady stream of lots
spection by Attributes
indexed by AQL.
1.2 This practice provides the sampling plans of MIL-STD-
3. Terminology
414 inASTM format for use byASTM committees and others.
3.1 Definitions:
It recognizes the continuing usage of MIL-STD-414 in indus-
3.1.1 For a more extensive list of terms in E11 standards,
tries supported by ASTM. Most of the original text in MIL-
see Terminology E456.
STD-414 is preserved in Sections6–9 of this practice.
3.1.2 acceptance quality limit (AQL), n—qualitylimitthatis
1.3 The values stated in inch-pound units are to be regarded
the worst tolerable process average when a continuing series of
as standard. No other units of measurement are included in this
lots is submitted for acceptance sampling. E2234
standard.
3.1.2.1 Discussion—This definition supersedes that given in
1.4 This standard does not purport to address all of the
MIL-STD-105E and MIL-STD-414.
safety concerns, if any, associated with its use. It is the
3.1.3 classification of defects, n—the enumeration of pos-
responsibility of the user of this standard to establish appro-
sible defects of the unit of product classified according to their
priate safety, health, and environmental practices and deter-
seriousness, that is, critical, major, or minor defect. E2234
mine the applicability of regulatory limitations prior to use.
1.5 This international standard was developed in accor-
3.1.4 critical defect, n—a defect that judgment and experi-
dance with internationally recognized principles on standard-
ence indicate would result in hazardous or unsafe conditions
ization established in the Decision on Principles for the
for individuals using, maintaining, or depending upon the
Development of International Standards, Guides and Recom-
product, or a defect that judgment and experience indicate is
mendations issued by the World Trade Organization Technical
likely to prevent performance of the function of a major end
Barriers to Trade (TBT) Committee.
item. E2234
3.1.5 defect, n—any nonconformance of the unit of product
2. Referenced Documents
with specified requirements. E2234
2.1 ASTM Standards:
3.1.6 inspection, n—the process of measuring, examining,
E456 Terminology Relating to Quality and Statistics
testing, or otherwise comparing the unit of product with the
E2234 Practice for Sampling a Stream of Product by Attri-
requirements. E2234
butes Indexed by AQL
E2586 Practice for Calculating and Using Basic Statistics
3.1.7 inspection by variables, n—inspection wherein the
unit of product is measured on a continuous scale with respect
to a given requirement or set of requirements.
This practice is under the jurisdiction ofASTM Committee E11 on Quality and
3.1.8 inspection lot, n—a collection of units of product
Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical
produced under conditions that are considered uniform and
Quality Control.
from which a sample is drawn and inspected. E2234
Current edition approved Jan. 1, 2020. Published February 2020. Originally
approved in 2010. Last previous edition approved in 2014 as E2762 – 10 (2014).
DOI 101520/E2762-10R20.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Available from Standardization Documents Order Desk, DODSSP, Bldg. 4,
Standards volume information, refer to the standard’s Document Summary page on Section D, 700 Robbins Ave., Philadelphia, PA 19111-5098, http://
the ASTM website. dodssp.daps.dla.mil.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2762 − 10 (2020)
3.1.9 major defect, n—a defect, other than critical, that is A1.3) have been computed for the sampling plans based on the
likely to result in failure, or to reduce materially the usability estimate of lot standard deviation of unknown variability.They
of the unit of product for its intended purpose. E2234 are equally applicable for sampling plans based on the average
range of the sample of unknown variability and those based on
3.1.10 minor defect, n—a defect that is not likely to reduce
known variability.
materially the usability of the unit of product for its intended
purpose, or is a departure from established standards having 4.5 Certain characteristics concerning the sampling plans in
little bearing on the effective use or operation of the unit. Sections 7 and 8 and those in Section 9 should be noted. Plans
E2234 based on the estimate of unknown variability require fewer
sampleunitsforcomparableassurancewhentheestimateoflot
3.1.11 operating characteristic, n—probability of accep-
standard deviation is used than when the average range of the
tance using a specified acceptance sampling plan, as a function
sample is used; on the other hand, plans using the average
of parameters describing quality of the lot. E2234
range of the sample require simpler computations. Plans using
3.1.12 sample, n—a group of observations, test results,
known variability require considerably fewer sample units for
taken from a large collection of observations, test results,
comparable assurance than either of the plans when variability
whichservestoprovideinformationthatmaybeusedasabasis
is unknown; however, the requirement of variability is a
for making a decision concerning the larger collection. E2586
stringent one. The user is advised to consult his technical
3.1.12.1 Discussion—A sample consists of one or more
agency before applying sampling plans using known variabil-
units of product drawn from an inspection lot, the units of the
ity.
sample being selected at random without regard to their
4.6 Table B-8 (see Fig. A1.11) provides values of the
quality. The number of units of product in the sample is the
factor F to compute the maximum standard deviation MSD.
sample size.
The MSD serves as a guide for the magnitude of the estimate
4. Summary of Practice
of lot standard deviation when using plans for the double
specification limit case, based on the estimate of lot standard
4.1 The main body of this practice is divided into four
deviationofunknownvariability.Similarly,TableC-8(seeFig.
sections. Section 6 (Section A in MIL-STD-414) describes
A1.19) provides values of the factor f to compute the maxi-
general procedures of the sampling plans. Sections 7 and 8
mum average range MAR. The MAR serves as a guide for the
(Sections B and C in MIL-STD-414) describe specific proce-
magnitudeoftheaveragerangeofthesamplewhenusingplans
dures and applications of the sampling plans when variability
for the double specification limit case, based on the average
is unknown. In Section 7 (Section B in MIL-STD-414) the
range of the sample of unknown variability.The estimate of lot
estimate of lot standard deviation is used as the basis for an
standard deviation or average range of the sample, if it is less
estimate of the unknown variability, and in Section 8 (Section
than the MSD or MAR respectively, helps to insure, but does
C in MIL-STD-414) the average range of the sample is used.
not guarantee, lot acceptability.
Section 9 (Section D in MIL-STD-414) describes the plans
when variability is known. 4.7 All symbols and their definitions are given in AnnexA1
for their applicable section.An illustration of the computations
4.2 Each of Sections 7, 8, and 9 is divided into three parts:
and procedures used in the sampling plans is given in the
(I) Sampling Plans for the Single Specification Limit Case, (II)
examples of Parts I and II of the applicable section. The
Sampling Plans for the Double Specification Limit Case, and
computations involve simple arithmetic operations such as
(III) Procedures for Estimation of ProcessAverage and Criteria
addition, subtraction, multiplication, and division of numbers,
for Tightened and Reduced Inspection. For the single specifi-
or at most, the taking of a square root of a number. The user
cation limit case, the acceptability criterion is given in two
should become familiar with the general procedures of Section
forms: Form 1 and Form 2. Either of the forms may be used,
6, and refer to the applicable section for detailed instructions
since they are identical as to sample size and decision for lot
regarding specific procedures, computations, and tables for the
acceptabilityorrejectability.IndecidingwhethertouseForm 1
sampling plans.
or Form 2, the following point should be borne in mind.
Form 1 provides the lot acceptability criterion without estimat-
5. Significance and Use
ing lot percent defective.The Form 2 lot acceptability criterion
5.1 This practice was prepared to meet a growing need for
requiresestimatesoflotpercentdefective.Theseestimatesalso
the use of standard sampling plans for inspection by variables
are required for estimation of the process average.
in customer procurement, supply and storage, and maintenance
4.3 Operating Characteristic Curves in Table A-3 (see Fig.
inspection operations. The variables sampling plans apply to a
A1.3)showtherelationshipbetweenqualityandpercentoflots
single quality characteristic which can be measured on a
expected to be acceptable for the quality characteristic in-
continuousscale,andforwhichqualityisexpressedintermsof
spected. As stated, these Operating Characteristic Curves are
percent defective. The theory underlying the development of
based on the assumption that measurements are selected at
the variables sampling plans, including the operating charac-
random from a normal distribution.
teristic curves, assumes that measurements of the quality
characteristic are independent, identically distributed normal
4.4 The corresponding sampling plans in Sections 7, 8, and
random variables.
9 were matched as closely as possible under a system of fixed
sample size with respect to their Operating Characteristic 5.2 In comparison with attributes sampling plans, variables
Curves. Operating Characteristic Curves in TableA-3 (see Fig. sampling plans have the advantage of usually resulting in
E2762 − 10 (2020)
considerable savings in sample size for comparable assurance These plans may be used whether procurement inspection is
as to the correctness of decisions in judging a single quality performed at the plant of a prime contractor, subcontractor or
characteristic, or for the same sample size, greater assurance is
vendor, or at destination, and also may be used when appro-
obtained using variables plans.Attributes sampling plans have priate in supply and storage, and maintenance inspection
the advantage of greater simplicity, of being applicable to
operations.
either single or multiple quality characteristics, and of requir-
6.2 Classification of Defects:
ing no knowledge about the distribution of the continuous
6.2.1 Method of Classifying Defects—A classification of
measurements of any of the quality characteristics.
defects is the enumeration of defects of the unit of product
5.3 It is important to note that variables sampling plans are
classified according to their importance.Adefect is a deviation
not to be used indiscriminately, simply because it is possible to
of the unit of product from requirements of the specifications,
obtain variables measurement data. In considering applications
drawings,purchasedescriptions,andanychangestheretointhe
where the normality or independence assumptions may be
contract or order. Defects normally belong to one of the
questioned, the user is advised to consult his technical agency
following classes; however, defects may be placed in other
to determine the feasibility of application.
classes.
5.4 Application—Sampling plans designated in this publi-
6.2.1.1 Critical Defects—A critical defect is one that judg-
cation are applicable, but not limited, to inspection of the
ment and experience indicate could result in hazardous or
following: (1)enditems, (2)componentsandrawmaterials, (3)
unsafe conditions for individuals using or maintaining the
operations or services, (4) materials in process, (5) supplies in
product; or, for major end items units of product, such as ships,
storage, (6) maintenance operations, (7) data or records, and
aircraft, or tanks, a defect that could prevent performance of
(8) administrative procedures.
their tactical function.
6.2.1.2 Major Defects—A major defect is a defect, other
6. General Description of Sampling Plans
than critical, that could result in failure, or materially reduce
6.1 Scope:
the usability of the unit of product for its intended purpose.
6.1.1 Purpose—This practice establishes sampling plans
6.2.1.3 Minor Defects—A minor defect is one that does not
and procedures for inspection by variables for use in customer
materially reduce the usability of the unit of product for its
procurement, supply and storage, and maintenance inspection
intended purpose, or is a departure from established standards
operations.Whenapplicablethispracticeshallbereferencedin
having no significant bearing on the effective use or operation
the specification, contract, or inspection instructions, and the
of the unit.
provisions set forth herein shall govern.
6.1.2 Inspection—Inspection is the process of measuring,
6.3 Percent Defective:
examining,testing,gaging,orotherwisecomparingthe“unitof
6.3.1 Expression of Nonconformance—The extent of non-
product” (see 6.1.4) with the applicable requirements.
conformance of product that shall be expressed in terms of
6.1.3 Inspection by Variables—Inspection by variables is
percent defective.
inspection wherein a specified quality characteristic (see 6.1.5)
6.3.2 Percent Defective—The percent defective for a quality
on a unit of product is measured on a continuous scale, such as
characteristic of a given lot of product is the number of units of
pounds, inches, feet per second, etc., and a measurement is
product defective for that characteristic divided by the total
recorded.
number of units of product and multiplied by one hundred.
6.1.4 Unit of Product—The unit of product is the entity of
Expressed as an equation:
product inspected in order to determine its measurable quality
characteristic. This may be a single article, a pair, a set, a number of defectives 3100
Percent defective 5 (1)
component of a product, or the end product itself. The unit of number of units
product may or may not be the same as the unit of purchase,
6.4 Acceptance Quality Level:
supply, production, or shipment.
6.4.1 Acceptance Quality Level—The acceptance quality
6.1.5 Quality Characteristic—The quality characteristic for
level (AQL) is a nominal value expressed in terms of percent
variables inspection is that characteristic of a unit of product
defective specified for a single quality characteristic. Certain
that is actually measured to determine conformance with a
numerical values of AQL ranging from 0.04 to 15.00 percent
given requirement.
are shown in TableA-1 (see Fig.A1.1). When a range ofAQL
6.1.6 Specification Limits—The specification limit(s) is the
values is specified, it shall be treated as if it were equal to the
requirement that a quality characteristic should meet. This
value of AQL for which sampling plans are furnished and
requirement may be expressed as an upper specification limit;
which is included within the AQL range. When the specified
or a lower specification limit, called herein a single specifica-
AQL is a particular value other than those for which sampling
tion limit; or both upper and lower specification limits, called
plans are furnished, the AQL, which is to be used in applying
herein a double specification limit.
the provisions of this practice, shall be as shown in Table A-1
6.1.7 Sampling Plans—A sampling plan is a procedure
(see Fig. A1.1).
whichspecifiesthenumberofunitsofproductfromalotwhich
aretobeinspected,andthecriterionforacceptabilityofthelot. 6.4.1.1 The term “acceptable” was changed to “acceptance”
Sampling plans designated in this practice are applicable to the after publication of MIL-STD-105E, so where possible this
inspectionofasinglequalitycharacteristicofaunitofproduct. termhasbeeneditedinthecaseofdirectreferencestotheAQL
E2762 − 10 (2020)
asampledrawntherefromisfoundtocontainoneormorecriticaldefects.
value. The notable exceptions are the original tables in Annex
A1 which show the original wording as they appeared in
6.7.2 Drawing of Samples—A sample is one or more units
MIL-STD-105E.
of product drawn from a lot. Units of the sample shall be
6.4.2 Specifying AQL’s—The particular AQL value to be
selected without regard to their quality.
used for a single quality characteristic of a given product must
6.8 Estimation of Process Average and Severity of Inspec-
be specified. In the case of a double specification limit, either
tion:
anAQLvalueisspecifiedforthetotalpercentdefectiveoutside
6.8.1 Procedures for estimating the process average and
of both upper and lower specification limits, or two AQL
criteria for tightened and reduced inspection based on the
values are specified, one for the upper limit and another for the
inspection results of preceding lots are provided in Part III of
lower limit.
Sections 7, 8, and 9.
6.5 Submittal of Product:
6.9 Special Procedure for Application of Mixed Variables-
6.5.1 Lot—The term “lot” shall mean “inspection lot,” that
Attributes Sampling Plans:
is, a collection of units of product from which a sample is
6.9.1 Applicability—A mixed variables and attributes sam-
drawn and inspected to determine compliance with the accept-
pling plan may be used under either of the two following
ability criterion.
conditions:
6.5.1.1 Formation of Lots—Each lot shall, as far as is
practicable, consist of units of product of a single type, grade,
NOTE 2—No Operating Characteristic Curves are provided for the
class, size, or composition manufactured under essentially the mixed variables-attribute sampling plans herein and that those in Table
A-1 (see Fig. A1.1) are not applicable.
same conditions.
6.5.2 Lot Size—The lot size is the number of units of
6.9.1.1 Condition A—Ample evidence exists that the prod-
product in a lot, and may differ from the quantity designated in
uct submitted for inspection is selected by the supplier to meet
the contract or order as a lot for production, shipment, or other
the specification limit(s) by a screening process from a larger
purposes.
quantity of product which is not being produced within the
specification limit(s).
6.6 Lot Acceptability:
6.9.1.2 Condition B—Otherconditionsexistthatwarrantthe
6.6.1 Acceptability Criterion—The acceptability of a lot of
use of a variables-attributes sampling plan.
material submitted for inspection shall be determined by use of
6.9.2 Definitions:
one of the sampling plans associated with a specified value of
6.9.2.1 Inspection by Attributes—Inspection by attributes is
the AQL(s). This practice provides sampling plans based on
inspection wherein the unit of product is classified simply as
known and unknown variability. In the latter case, two alter-
defective or nondefective with respect to a given requirement
native methods are provided, one based on the estimate of lot
or set of requirements.
standard deviation and the other on the average range of the
6.9.2.2 Mixed Variables—Attributes Inspection. Mixed
sample. These are referred to as the standard deviation method
variables-attributes inspection is inspection of a sample by
and the range method. For the case of a single specification
attributes, in addition to inspection by variables already made
limit, the acceptability criterion is given in two forms. These
of a previous sample, before a decision as to acceptability or
are identified as Form 1 and Form 2.
rejectability of a lot can be made.
6.6.2 Choice of Sampling Plans—Sampling plans and pro-
6.9.3 Selection of Sampling Plans—The mixed variables-
cedures are provided in Section 7 if variability is unknown and
attributes sampling plan shall be selected in accordance with
the standard deviation method is used, in Section 8 if variabil-
the following:
ity is unknown and the range method is used, and in Section 9
if variability is known. Unless otherwise specified, unknown 6.9.3.1 Select the variables sampling plan in accordance
with Section 7, 8,or 9.
variability, standard deviation method sampling plans, and the
acceptability criterion of Form 2 (for the single specification 6.9.3.2 Select the attributes sampling plan from Practice
E2234, 6.9, using a single sampling plan and tightened
limit case) shall be used.
inspection. The same AQL value(s) shall be used for the
6.7 Sample Selection:
attributes sampling plan as used for the variables plan of
6.7.1 Determination of Sample Size—The sample size is the
6.9.3.1. (Additional sample items may be drawn, as necessary,
number of units of product drawn from a lot. Relative sample
to satisfy the requirements for sample size of the attributes
sizesaredesignatedbycodeletters.Thesamplesizecodeletter
sampling plan. Count as a defective each sample item falling
depends on the inspection level and the lot size. There are five
outside of specification limit(s).)
inspection levels: I, II, III, IV, and V. Unless otherwise
6.9.4 Determination of Acceptability—A lot meets the ac-
specified, inspection level IV shall be used. The sample size
ceptability criterion if one of the following conditions is
code letter applicable to the specified inspection level and for
satisfied:
lots of given size shall be obtained from Table A-2 (see Fig.
6.9.4.1 Condition A—The lot complies with the appropriate
A1.2).
variables acceptability criterion of Section 7, 8,or 9.
NOTE 1—Special Reservation for Critical Characteristics—The cus-
6.9.4.2 Condition B—The lot complies with the acceptabil-
tomer reserves the right to inspect every unit submitted by the supplier for
ity criterion of Practice E2234, 6.10.
critical characteristics, and to reject the remainder of the lot immediately
6.9.4.3 IfConditionAisnotsatisfied,proceedinaccordance
after a defect is found. The customer also reserves the right to sample for
critical defects every lot submitted by the supplier, and to reject any lot if with the attributes sampling plan to meet Condition B.
E2762 − 10 (2020)
6.9.4.4 If Condition B is not satisfied, the lot does not meet 7.3 Lot-by-Lot Acceptability Procedures When Form 1 is
the acceptability criterion. Used (see Example 7-1 (Fig. 1) for a complete example of this
6.9.5 Severity of Inspection—The procedures for severity of procedure):
inspection referred to in 6.8 are not applicable for mixed 7.3.1 Acceptability Criterion—The degree of conformance
variables-attributes inspection.
of a quality characteristic with respect to a single specification
¯ ¯
limit shall be judged by the quantity (U–X)/s or (X – L)/s.
NOTE 3—When customer drawings, specifications, or other data are
7.3.2 Computation—The following quantity shall be com-
used for any purpose other than in connection with a definitely related
¯ ¯
puted: (U –X)/s or (X – L)/s depending on whether the
customer procurement operation, the customer thereby incurs no respon-
sibility or any obligation whatsoever; and the fact that the customer may
specification limit is an upper or lower limit,
have formulated, furnished, or in any way supplied the said drawings,
specifications, or other data is not to be regarded by implication or where:
otherwise as in any manner licensing the holder or any other person or
U = the upper specification limit,
corporation, or conveying any rights or permission to manufacture, use, or
L = the lower specification limit,
sell any patented invention that may in any way be related thereto.
¯
X = the sample mean, and
s = the estimate of lot standard deviation.
7. Variability Unknown—Standard Deviation Method
7.3.3 Acceptability Criterion—Compare the quantity (U –
Part I–Single Specification Limit
¯ ¯ ¯
X)/s or (X – L)/s with the acceptability constant k. If (U–X)/s
¯
7.1 Sampling Plan for Single Specification Limit—This part
or (X – L)/s is equal to or greater than k, the lot meets the
¯ ¯
of the practice describes the procedures for use with plans for
acceptability criterion; if (U–X)/s or (X – L)/s is less than k
a single specification limit when variability of the lot with
or negative, then the lot does not meet the acceptability
respect to the quality characteristic is unknown and the
criterion.
standard deviation method is used. The acceptability criterion
7.4 Summary for Operation of Sampling Plan When Form 1
is given in two equivalent forms. These are identified as
is Used:
Form 1 and Form 2.
7.4.1 The following steps summarize the procedures to be
7.1.1 Use of Sampling Plans—To determine whether the lot
followed:
meets the acceptability criterion with respect to a particular
(1) Determine the sample size code letter from Table A-2
quality characteristic and AQL value, the applicable sampling
(see Fig. A1.2) by using the lot size and inspection level.
plan shall be used in accordance with the provisions of Section
(2) Obtain plan from Master Table B-1 or B-2 (see Figs.
6,GeneralDescriptionofSamplingPlans,andthoseinthispart
A1.4 and A1.5) by selecting the sample size n and the
of the practice.
acceptability constant k.
7.1.2 Drawing of Samples—All samples shall be drawn in
(3) Select at random the sample of n units from the lot;
accordance with 6.7.2.
inspect and record the measurement of the quality character-
7.1.3 Determination of Sample Size Code Letter—The
istic for each unit of the sample.
sample size code letter shall be selected from Table A-2 (see
¯
(4) Compute the sample mean X and estimate of lot
Fig. A1.2) in accordance with 6.7.1.
¯
standard deviation s, and also compute the quantity U–X)/ s
7.2 Selecting the Sampling Plan When Form 1 is Used: ¯
for an upper specification limit U or the quantity X – L)/s for
7.2.1 Master Sampling Tables—The master sampling tables
a lower specification limit L.
for plans based on variability unknown for a single specifica- ¯ ¯
(5) If the quantity (U–X)/s or (X – L)/s is equal to or
tion limit when using the standard deviation method areTables
greater than k, the lot meets the acceptability criterion; if (U –
B-1 and B-2 (see Figs. A1.4 and A1.5). Table B-1 is used for ¯ ¯
X)/ s or (X – L)/s is less than k or negative, then the lot does
normal and tightened inspection and Table B-2 for reduced
not meet the acceptability criterion.
inspection.
7.5 Selecting the Sampling Plans When Form 2 is Used:
7.2.2 Obtaining the Sampling Plan—The sampling plan
7.5.1 Master Sampling Tables—The master sampling tables
consists of a sample size and an associated acceptability
for plans based on variability unknown for a single specifica-
constant. The sampling plan is obtained from Master Table
tion limit when using the standard deviation method areTables
B-1 or B-2 (see Figs. A1.4 and A1.5).
B-3 and B-4 (see Figs. A1.6 and A1.7) of Part II. Table B-3 is
7.2.2.1 Sample Size—The sample size n is shown in the
used for normal and tightened inspection and Table B-4 for
master table corresponding to each sample size code letter.
reduced inspection.
7.2.2.2 Acceptability Constant—The acceptability constant,
7.5.2 Obtaining the Sampling Plan—The sampling plan
k, corresponding to the sample size mentioned in 7.2.2.1,is
consists of a sample size and an associated maximum allow-
indicated in the column of the master table corresponding to
able percent defective. The sampling plan is obtained from
the applicableAQLvalue. Table B-1 (see Fig.A1.4) is entered
Master Table B-3 or B-4 (see Figs. A1.6 and A1.7).
from the top for normal inspection and from the bottom for
7.5.2.1 Sample Size—The sample size n is shown in the
tightened inspection. Sampling plans for reduced inspection
master table corresponding to each sample size code letter.
are provided in Table B-2 (see Fig. A1.5).
7.5.2.2 Maximum Allowable Percent Defective—The maxi-
mum allowable percent defective M for sample estimates
corresponding to the sample size mentioned in 7.5.2.1 is
See Section 7 Definitions in AnnexA1 for definitions of all symbols used in the
sampling plans based on variability unknown-standard deviation method. indicated in the column of the master table corresponding to
E2762 − 10 (2020)
FIG. 1 Example 7-1
the applicableAQLvalue. Table B-3 (see Fig.A1.6) is entered 7.6.3 Estimate of Percent Defective in Lot—The quality of a
from the top for normal inspection and from the bottom for lot shall be expressed by p , the estimated percent defective in
U
tightened inspection. Sampling plans for reduced inspection
the lot above the upper specification limit, or by p , the
L
are provided in Table B-4 (see Fig. A1.7).
estimatedpercentdefectivebelowthelowerspecificationlimit.
The estimated percent defective p or p is obtained by
7.6 Lot-by-Lot Acceptability Procedures When Form 2 is U L
entering Table B-5 (see Fig. A1.8) with Q or Q and the
Used (see Example 7-2 (Fig. 2) for a complete example of this
U L
appropriate sample size.
procedure):
7.6.1 Acceptability Criterion—The degree of conformance
7.6.4 Acceptability Criterion—Compare the estimated lot
of a quality characteristic with respect to a single specification
percent defective p or p with the maximum allowable
U L
limit shall be judged by the percent of nonconforming product
percent defective M. If p or p is equal to or less than M, the
U L
outside the upper or lower specification limit. The percentage
lot meets the acceptability criterion; if p or p is greater than
U L
of nonconforming product is estimated by entering Table B-5
MorifQ or Q is negative, then the lot does not meet the
U L
(see Fig. A1.8) with the quality index and the sample size.
acceptability criterion.
7.6.2 Computation of Quality Index—The Quality index
7.7 Summary for Operation of Sampling Plan When Form 2
¯
Q =(U–X)/s shall be computed if the specification limit is
U
¯ is Used:
an upper limit U, or Q =(X – L)/s if it is a lower limit L. The
L
¯
7.7.1 The following steps summarize the procedures to be
quantities, X and s, are the sample mean and estimate of lot
standard deviation, respectively. followed:
E2762 − 10 (2020)
FIG. 2 Example 7-2
(1) Determine the sample size code letter from Table A-2 (6) Determine the estimated lot percent defective p or p
U L
(see Fig. A1.2) by using the lot size and the inspection level.
from Table B-5 (see Fig. A1.8).
(2) Obtain plan from Master Table B-3 or B-4 (see Figs.
(7) If the estimated lot percent defective p or p is equal
U L
A1.6 and A1.7) by selecting the sample size n and the
toorlessthanthemaximumallowablepercentdefectiveM,the
maximum allowable percent defective M.
lot meets the acceptability criterion; if p or p is greater than
U L
(3) Select at random the sample of n units from the lot;
MorifQ or Q is negative, then the lot does not meet the
U L
inspect and record the measurement of the quality character-
acceptability criterion.
istic on each unit of the sample.
¯
(4) Compute the sample mean X and the estimate of lot Part II–Double Specification Limit
standard deviation s.
7.8 Sampling Plan for Double Specification Limit—This
¯
(5) Compute the quality index Q =(U–X)/s if an upper
U
part of the practice describes the procedures for use with plans
¯
specification limit U is specified, or Q =(X – L)/s if a lower
L
for a double specification limit when variability of the lot with
specification limit L is specified.
E2762 − 10 (2020)
respect to the quality characteristic is unknown and the
s = the estimate of lot standard deviation.
standard deviation method is used.
7.11.3 Percent Defective in the Lot—The quality of a lot
7.8.1 Use of Sampling Plans—To determine whether the lot
shall be expressed in terms of the lot percent defective. Its
meets the acceptability criterion with respect to a particular
estimate will be designated by p ,p , or p. The estimate p
L U U
quality characteristic and AQL value(s) the applicable sam-
indicates conformance with respect to the upper specification
pling plan shall be used in accordance with the provisions of
limit, p with respect to the lower specification limit, and p for
L
Section 6, General Description of Sampling Plans, and those in
both specification limits combined. The estimates p and p
L U
this part of the practice.
shall be determined by entering Table B-5 (see Fig. A1.8),
7.9 Selecting the Sampling Plan—Asampling plan for each respectively,withQ andQ andthesamplesize.Theestimate
L U
AQL value shall be selected from Table B-3 or B-4 (see Figs.
p shall be determined by adding the corresponding estimated
A1.6 and A1.7) as follows:
percent defectives p and p found in the table.
L U
7.9.1 Determination of Sample Size Code Letter—The
7.12 Acceptability Criterion and Summary for Operation of
sample size code letter shall be selected from Table A-2 (see
Sampling Plans:
Fig. A1.2) in accordance with 6.7.1.
7.12.1 One AQL Value for both Upper and Lower Specifi-
7.9.2 Master Sampling Tables—The master sampling tables
cation Limit Combined:
for plans based on variability unknown for a double specifica-
7.12.1.1 Acceptability Criterion (see Example 7-3 (Fig. 3)
tion limit when using the standard deviation method areTables
for a complete example of this procedure): Compare the
B-3 and B-4 (see Figs. A1.6 and A1.7). Table B-3 is used for
estimated lot percent defectivep=p +p with the maximum
U L
normal and tightened inspection and Table B-4 for reduced
allowable percent defective M. If p is equal to or less than M,
inspection.
the lot meets the acceptability criterion; if p is greater than M
7.9.3 Obtaining Sampling Plan—A sampling plan consists
or if either Q or Q or both are negative, then the lot does not
U L
of a sample size and the associated maximum allowable
meet the acceptability criterion.
percent defective(s). The sampling plan to be applied in
7.12.1.2 Summary for Operation of Sampling Plan—In
inspection shall be obtained from MasterTable B-3 or B-4 (see
caseswhereasingleAQLvalueisestablishedfortheupperand
Figs. A1.6 and A1.7).
lower specification limit combined for a single quality
7.9.3.1 Sample Size—The sample size n is shown in the
characteristic, the following steps summarize the procedures to
master tables corresponding to each sample size code letter.
be used:
7.9.3.2 Maximum Allowable Percent Defective—The maxi-
(1) Determine the sample size code letter from Table A-2
mum allowable percent defective for sample estimates of (see Fig. A1.2) by using the lot size and the inspection level.
percent defective for the lower, upper, or both specification
(2) Select plan from Master Table B-3 or B-4 (see Figs.
limits combined, corresponding to the sample size mentioned A1.6 and A1.7). Obtain the sample size n and the maximum
in 7.9.3.1, is shown in the column of the master table
allowable percent defective M.
corresponding to the applicable AQL value(s). If different (3) Select at random the sample of n units from the lot;
AQL’s are assigned to each specification limit, designate the
inspect and record the measurement of the quality character-
maximum allowable percent defective by M for the lower istic on each unit of the sample.
L
¯
limit, and by M for the upper limit. If oneAQLis assigned to
(4) Compute the sample mean X and estimate of lot
U
both limits combined, designate the maximum allowable per- standard deviation s.
¯
cent defective by M. Table B-3 (see Fig.A1.6) is entered from
(5) Compute the quality indices Q =(U–X)/s and Q =
U L
¯
thetopfornormalinspectionandfromthebottomfortightened (X – L)/s.
inspection. Sampling plans for reduced inspection are provided
(6) Determine the estimated lot percent defectivep=p +
U
in Table B-4 (see Fig. A1.7). p from Table B-5 (see Fig. A1.8).
L
(7) If the estimated lot percent defective p is equal to or
7.10 Drawing of Samples:
less than the maximum allowable percent defective M, the lot
7.10.1 Samples shall be selected in accordance with 6.7.2.
meets the acceptability criterion; if p is greater than M or if
7.11 Lot-by-Lot Acceptability Procedures:
either Q or Q or both are negative, then the lot does not meet
U L
7.11.1 Acceptability Criterion—The degree of conformance the acceptability criterion.
of a quality characteristic with respect to a double specification
7.12.2 Different AQL Values for Upper and Lower Specifi-
limit shall be judged by the percent of nonconforming product. cation Limit:
The percentage of nonconforming product is estimated by
7.12.2.1 Acceptability Criteria(seeExample7-4(Fig.4)for
entering Table B-5 (see Fig. A1.8) with the quality index and a complete example of this procedure)—Compare the esti-
the sample size.
mated lot percent defectives p and p with the corresponding
L U
7.11.2 Computation of Quality Indices—The quality indices maximum allowable percent defectives M and M ; also
L U
¯ ¯
Q =(U–X)/s and Q =(X – L)/s shall be computed, comparep=p +p with the larger of M and M .Ifp is
U L L U L U L
equal to or less than M ,p is equal to or less than M , and p
L U U
where:
is equal to or less than the larger of M and M , the lot meets
L U
U = the upper specification limit,
the acceptability criteria; otherwise, the lot does not meet the
L = the lower specification limit,
acceptability criteria. If either Q or Q or both are negative,
L U
¯
X = the sample mean, and
then the lot does not meet the acceptability criteria.
E2762 − 10 (2020)
FIG. 3 Example 7-3
7.12.2.2 Summary for Operation of Sampling Plan—In (3) Select at random the sample of n units from the lot;
cases where a differentAQL value is established for the upper inspect and record the measurement of the quality character-
and lower specification limit for a single quality characteristic, istic on each unit in the sample.
¯
the following steps summarize the procedures to be used: (4) Compute the sample mean X and estimate a lot stan-
(1) Determine the sample size code letter from Table A-2 dard deviation s.
¯
(see Fig. A1.2) by using the lot size and inspection level. (5) Compute the quality indices Q =(U–X)/s and Q =
U L
¯
(2) Select the sampling plan from Master Table B-3 or B-4 (X – L)/s.
(see Figs. A1.6 and A1.7). Obtain the sample size n and the (6) Determine the estimated lot percent defectives p and
U
maximum allowable percent defectives M and M , corre- p , corresponding to the percent defectives above the upper
U L L
sponding to the AQL values for the upper and lower specifi- and below the lower specification limits. Also determine the
cation limits, respectively. combined percent defectivep=p +p .
U L
E2762 − 10 (2020)
FIG. 4 Example 7-4
(7) If all three of the following conditions are satisfied, the (c) p is equal to or less than the larger of M and M
L U
lot meets the acceptability criteria; otherwise the lot does not
Part III–Estimation of Process Average and Criteria for
meet the acceptability criteria. If either Q or Q or both are
L U
Reduced and Tightened Inspection
negative, then the lot does not meet the acceptability criteria.
(a) p is equal to or less than M 7.13 Estimation of Process Average—The average percent
U U
(b) p is equal to or less than M defective, based upon a group of lots submitted for original
L L
E2762 − 10 (2020)
inspection, is called the process average. Original inspection is 7.14.1 At Start of Inspection—Normal inspection shall be
thefirstinspectionofaparticularquantityofproductsubmitted used at the start of inspection unless otherwise designated.
for acceptability as distinguished from the inspection of 7.14.2 During Inspection—During the course of inspection,
product which has been resubmitted after prior rejection. The normal inspection shall be used when inspection conditions are
process average shall be estimated from the results of inspec- such that tightened or reduced inspection is not required in
tion of samples drawn from a specified number of preceding accordance with 7.14.3 and 7.14.4.
lots for the purpose of determining severity of inspection 7.14.3 Tightened Inspection—Tightened inspection shall be
during the course of a contract in accordance with 7.14.3.Any instituted when the estimated process average computed from
lot shall be included only once in estimating the process the preceding ten (10) lots (or such other number of lots
average. The estimate of the process average is designated by designated) in accordance with 7.13.2 is greater than theAQL,
p¯ when computed with respect to an upper specification limit, and when more than a certain number T of these lots have
U
by p¯ when computed with respect to a lower specification estimates of the percent defective exceeding the AQL. The
L
limit, and by p¯ when computed with respect to a double T-values are given in Table B-6 (see Fig.A1.9) for the process
specification limit. average computed from 5, 10, or 15 lots. Normal inspection
7.13.1 Abnormal Results—Theresultsofinspectionofprod- shall be reinstated if the estimated process average of lots
uct manufactured under conditions not typical of usual produc- under tightened inspection is equal to or less than the AQL.
tion shall be excluded from the estimated process average. 7.14.4 Reduced Inspection—Reduced inspection may be
7.13.2 Computation of the Estimated Process Average—The instituted provided that all of the following conditions are
estimated process average is the arithmetic mean of the satisfied:
estimated lot percent defectives computed from the sampling 7.14.4.1 Condition A—The preceding ten (10) lots (or such
inspection results of the preceding ten (10) lots or as may be other number of lots designated) have been under normal
otherwise designated. In order to estimate the lot percent inspection and none has been rejected.
defective, the quality indices Q and/or Q shall be computed 7.14.4.2 Condition B—The estimated percent defective for
U L
¯ ¯
foreachlot.Theseare: Q =(U–X)/sand Q =(X– L)/s.(See each of these preceding lots is less than the applicable lower
U L
7.11.2.) limit shown in Table B-7 (see Fig. A1.10); or for certain
7.13.2.1 Single Specification Limit —The estimated lot per- sampling plans, the estimated lot percent defective is equal to
cent defective shall be determined from Table B-5 (see Fig. zeroforaspecifiednumberof consecutivelots(seeTableB-7).
A1.8) for the plans based on known variability. The quality 7.14.4.3 Condition C—Production is at a steady rate.
index Q shall be used for the case of an upper specification 7.14.4.4 Normal inspection shall be reinstated if any one of
U
limit, or Q for the case of a lower specification limit. Table the following conditions occurs under reduced inspection:
L
B-5 is entered with Q or Q and the corresponding estimated 7.14.4.5 Condition D—A lot is rejected.
U L
lot percent defective p or p , respectively, is read from the 7.14.4.6 Condition E—The estimated process average is
U L
table. The estimated process average p¯ is the arithmetic mean greater than the AQL.
U
of the individual estimated lot percent defectives p ’s. 7.14.4.7 Condition F—Production becomes irregular or de-
U
Similarly, the estimated process average p¯ is the arithmetic layed.
L
mean of the individual estimated lot percent defectives p ’s. 7.14.4.8 Condition G—Otherconditionsasmaywarrantthat
L
7.13.2.2 Double Specification Limit—The estimated lot per- normal inspection should be reinstated.
cent defective shall be determined from Table B-5 (see Fig. 7.14.5 Sampling Plans for Tightened or Reduced
A1.8) for the plans based on variability known.
...