military standard procedures and tables ......mil-std-105d 29april1963 superseding mil-std-105c...
TRANSCRIPT
MIL-STD-105D
29 April 1963
SUPERSEDINGMIL-STD-105C
18 July 1961
MILITARY STANDARD
SAMPLING PROCEDURES AND TABLES
FOR INSPECTION BY ATTRIBUTES
MXL-STD~105D29 APRIL 1963
SAMPLING PROCEDURES AND
MIL-STD-105D
DEFENSE
5, D. C.
INSPECTION BI ATTRIBUTES
29 APRIL 1963
!• This standard has been approved by the Department of Defense and ismandatory for use by the Departments of the Army* the Navy, the Air Forceand the Defense Supply Agency • This revision supersedes M3X-STD-105C,dated 18 July 196I.
2. This publication provides sampling procedures and reference tablesfor use in planning and conducting inspection by attributes. Thispublication was developed by a working group representing the militaryservices of Canada, the United Kingdom and the United States of Americawith the assistance and cooperation of American and European organizationsfor quality control* The international designation of this document isABC-STD-105* When revision or cancellation of this standard is proposed,the departmental custodians win infoim their respective DepartmentalStandardization Office so that appropriate action may be taken respectingthe international agreement concerned*
3. The U.S. Army Munitions Command is designated as preparing activity forthis standard* Recommended corrections, additions, or deletions should beaddressed to the Commanding Officer, U. S. Array CBR Engineering Office,Attn: SftJCE-ED-S, Army Chemical Center, Maryland.
For sale by the Superintendent of Documents, U.S. (Jovornmont Printing Office
Washington, D.C. 20402 - Price 65 cents
MIL-STD-105DChange Notice 2
20 March 1964
MILITARY STANDARD
SAMPLING PROCEDURES AND TABLES FOR INSPECTION
BY ATTRIBUTESTO ALL ACTIVITIES:
1. The following corrections should be made to MIL-STD-105D:(a) Page %%, lines 2, 3, and 4: Change to read "Recommended corrections, additions or
deletions should be addressed to Director of Quality Assurance, U.S. Army Edgewood Arsenal,
ATTN: SMUEA-QA-E, Edgewood Arsenal, Md., 21010."
(b) Page 2, paragraph 3.2, line 3: Change "hunderd" to read "hundred".
(c) Page 4> paragraph 6.4, line 9 Change "for" to read "only".
(d) Page 5, paragraph 8.2, line 5: Change "batchs" to read "batches".
(e) Page 5, paragraph 8.2, line 6: Change "require change" to read "require a change".
(f) Page 5, paragraph 8.2, lines 6, 7, and 8: Delete the sentence that reads,"The switching
procedures given below require a change".
(g) Page 7, paragraph 10.1, lines 5 and 6: Change "10.1.3, 10.1.4, and 10.1.5" to read
"10.1.3 and 10.1.4". Delete reference to 10.1.5.
(h) Page 8, paragraph 11.1, line 2: Change "larger then 80" to read "larger than 80".
(i) Page 9, table I: Add the following footnote beneath table I:
Convert to these
specialNote., Small sample inspection levels of MIL-STD-1Q6C inspection levels
L-l and L-2 S-l
L-3andL-4 _.. S-2
L-5 and L-6 _ S-3
L~7andL-8_ S-4
(j) Page 29, table IX, vertical scale on three charts: Change "%n, %n, #n" to read ".75n,
.50n, 25n".
(k) Page 36, table X-D-l: Add footnote, "Note: Binomial distribution used for percent
defective computations; Poisson for defects per hundred units".
(1) Page 46 rtable X-J-l: Change footnote to read, "Note: Binomial distribution used for
percent defective computations; Poisson for defects per hundred units".
(m) Page 48, table X-K-l: For Pa=75.0 and AQL=0.65, change "0.382" to read "1.382".
(n) Page 62, table X-M-l: In line below row of AQL values, change "dejects" to read
"defects".
(o) Page 54, table X-N-l: In the footnote, change "Pisson" to read "Poisson".
(p) Page 56, table X-P-l: In the footnote, change "Poission" to read "Poisson".
(q) Page 68, for the term Reduced inspection: Change paragraph references from "8.2 and8.3.3" to read "8.2, 8.3.3 and 10.1.4".
(r) Page 64, mailing address for the U.S. Government Printing Office: Delete reference to
zone 25 and, after D.C., add the ZIP code "20402".
2. The following is a cumulative list of earlier changes: Notice 1 (Navy) dated 1 November1963 provided a table of conversion from the small sample inspection levels (L-l, L-2, etc.) of
MIL-STD-105C, to the special inspection levels (S-l, etc.) of MIL-STD-105D. The same con-
version information is covered by correction 1 (i) above to page 9, table I.
3. Retain this notice and insert before the table of contents.
4. Holders of MIL-STD-105D will verify that corrections indicated above have been entered
and will destroy the previous notice. Activities which stock these notices for issue are warnedthat each notice, together with its appended revised pages if any, is in effect a separate publication
to be retained until the military standard is completely revised or canceled.
Paragraph
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Table I
Table II-A
Table II-B
Table II-C
Table III-A
Table III-B
Table III-C
Table IV-ATable IV-B
Table IV-C
Table V-A
Table V-B
Table VI-A
Table VI-B
Table VII-A
Table VII-B
Table VIII
Table IX
Table X-ATable X-BTable X-C
CONTENTSPage
SCOPE 1
CLASSIFICATION OF DEFECTS AND DEFECTIVES 2
PERCENT DEFECTIVE AND DEFECTS PER HUNDRED UNITS 2
ACCEPTABLE QUALITY LEVEL (AQL) 3
SUBMISSION OF PRODUCT 3
ACCEPTANCE AND REJECTION 4
DRAWING OF SAMPLES 4
NORMAL, TIGHTENED, AND REDUCED INSPECTION 5
SAMPLING PLANS 6
DETERMINATION OF ACCEPTABILITY 7
SUPPLEMENTARY INFORMATION 7
TABLES
Sample Size Code Letters 9
Single Sampling Plans for Normal Inspection (Master Table) 10
Single Sampling Plans for Tightened Inspection (Master Table) .... 11
Single Sampling Plans for Reduced Inspection (Master Table) .... 12
Double Sampling Plans for Normal Inspection (Master Table) .... 13
Double Sampling Plans for Tightened Inspection (Master Table) .. 14
Double Sampling Plans for Reduced Inspection (Master Table) .. 15
Multiple Sampling Plans for Normal Inspection (Master Table) .. 16
Multiple Sampling Plans for Tightened Inspection
(Master Table) 18
Multiple Sampling Plans for Reduced Inspection (Master Table) .. 20
Average Outgoing Quality Limit Factors for Normal Inspection
(Single Sampling) 22
Average Outgoing Quality Limit Factor for Tightened
Inspection (Single Sampling) 23
Limiting Quality (in percent defective) for which the Pa = 10 9J
(for Normal Inspection, Single Sampling) 24
Limiting Quality (in defects per hundred units) for which the
Pa = 10% (for Normal Inspection, Single Sampling) 25
Limiting Quality (in percent defective) for which the Pa = 5%(for Normal Inspection, Single Sampling) 26
Limiting Quality (in defects per hundred units) for whichPa = 5% (for Normal Inspection, Single Sampling) 27
Limit Numbers for Reduced Inspection 28
Average Sample Size Curves for Double and Multiple Sampling .. 29
Sampling Plans and Operating Characteristic Curves(and Data) for:
Sample Size Code Letter A 30
Sample Size Code Letter B 32
Sample Size Code Letter C 34
Ml
Table X-D Sample Size Code Letter D 36Table X-E Sample Size Code Letter E 38Table X-F Sample Size Code Letter F 40Table X-G Sample Size Code Letter G 42Table X-H Sample Size Code Letter H 44Table X-J Sample Size Code Letter J 46Table X-K Sample Size Code Letter K [[[[[[[[ 48Table X-L Sample Size Code Letter L 50Table X-M Sample Size Code Letter M 52Table X-N Sample Size Code Letter N 54Table X-P Sample Size Code Letter P 56Table X-Q Sample Size Code Letter Q 58Table X-R Sample Size Code Letter R 60Table X-S Sample Size Code Letter S 62
INDEX OF TERMS WITH SPECIAL MEANINGS 63
<*$g)K<2$*>
IV
<4Sm<5kfi
SAMPLING PROCEDURES AND TABLES
FOR INSPECTION BY ATTRIBUTES
<*tgto&*
1. SCOPE
1.1 PURPOSE. This publication estab-
lishes sampling plans and procedures for
inspection by attributes. When specified by
the responsible authority, this publication
shall be referenced in the specification, con-
tract, inspection instructions, or other docu-
ments and the provisions set forth herein
shall govern. The "responsible authority"
shall be designated in one of the above
documents.
1.2 APPLICATION, Sampling plans des-
ignated in this publication are applicable, but
not limited, to inspection of the following:
a. End items.
b. Components and raw materials.
c. Operations.
d. Materials in process.
e. Supplies in storage.
f. Maintenance operations.
g. Data or records.
h. Administrative procedures.
These plans are intended primarily to be
used for a continuing series of lots or batches.
The plans may also be used for the inspection
of isolated lots or batches, but, in this latter
case, the user is cautioned to consult the
operating characteristic curves to find a plan
which will yield the desired protection (see
11.6).
1 .3 INSPECTION. Inspection is the proc-
ess of measuring, examining, testing, or
otherwise comparing the unit of product (see
1.5) with the requirements.
1.4 INSPECTION BY ATTRIBUTES. In-
spection by attributes is inspection whereby
either the unit of product is classified simply
as defective or nondefective, or the number
of defects in the unit of product is counted,
with respect to a given requirement or set
of requirements.
1.5 UNIT OF PRODUCT. The unit of
product is the thing inspected in order to
determine its classification as defective or
nondefective or to count the number of de-
fects. It may be a single article, a pair, a set,
a length, an area, an operation, a volume, a
component of an end product, or the end
product itself. The unit of product may or
may not be the same as the unit of purchase,
supply, production, or shipment.
2. CLASSIFICATION OF DEFECTS AND DEFECTIVES
2.1 METHOD OF CLASSIFYING DEFECTS.A classification of defects is the enumerationof possible defects of the unit of productclassified according to their seriousness. Adefect is any nonconformance of the unit of
product with specified requirements. Defects
will normally be grouped into one or moreof the following classes; however, defects
may be grouped into other classes, or into
subclasses within these classes.
2.1.1 CRITICAL DEFECT. A critical de-
fect is a defect that judgment and experienceindicate is likely to result in hazardous or
unsafe conditions for individuals using,
maintaining, or depending upon the product;or a defect that judgment and experienceindicate is likely to prevent performance of
the tactical function of a major end item suchas a ship, aircraft, tank, missile or spacevehicle. NOTE: For a special provision re-
lating to critical defects, see 6.3.
2.1.2 MAJOR DEFECT. A major defectis a defect, other than critical, that is likely
to result in failure, or to reduce materiallythe usability of the unit of product for its
intended purpose.
2.1.3 MINOR DEFECT. A minor defectis a defect that is not likely to reduce ma-terially the usability of the unit of productfor its intended purpose, or is a departurefrom established standards having little bear-ing on the effective use or operation of theunit.
2.2 METHOD OF CLASSIFYING DEFEC-TIVES. A defective is a unit of product whichcontains one or more defects. Defectives will
usually be classified as follows:
2.2.1 CRITICAL DEFECTIVE. A critical
defective contains one or more critical de-fects and may also contain major and orminor defects. NOTE: For a special provi-sion relating to critical defectives, see 6.3.
2.2.2 MAJOR DEFECTIVE. A major de-fective contains one or more major defects,
and may also contain minor defects but con-tains no critical defect.
2.2.3 MINOR DEFECTIVE. A minor de-fective contains one or more minor defects
but contains no critical 6r major defect.
3. PERCENT DEFECTIVE AND DEFECTS PER HUNDRED UNITS
3.1 EXPRESSION OF NONCONFORM-ANCE. The extent of nonconformance of
product shall be expressed either in termsof percent defective or in terms of defects perhundred units.
3.2 PERCENT DEFECTIVE. The percentdefective of any given quantity of units of
product is one hunderd times the number of
defective units of product contained thereindivided by the total number of units of prod-uct, i.e.:
Percent defective = XT"""***. °f defectives
Number of units inspectedx 100
3.3 DEFECTS PER HUNDRED UNITS. Thenumber of defects per hundred units of any
given quantity of units of product is one
hundred times the number of defects con-
tained therein (one or more defects being
possible in any unit of product) divided by
the total number of units of product, i.e.:
Number of defectsDefects per
hundred units= Number of units inspected
X 100
4. ACCEPTABLE QUALITY LEVEL (AQL)
4.1 USE. The AQL, together with the
Sample Size Code Letter, is used for index-
ing the sampling plans provided herein.
4.2 DEFINITION. The AQL is the max-imum percent defective (or the maximumnumber of defects per hundred units) that,
for purposes of sampling inspection, can be
considered satisfactory as a process average
(see 11.2).
4.3 NOTE ON THE MEANING OF AQLWhen a consumer designates some specific
value of AQL for a certain defect or group
of defects, he indicates to the supplier that
his (the consumers) acceptance sampling
plan will accept the great majority of the lots
or batches that the supplier submits, pro-
vided the process average level of percent
defective (or defects per hundred units) in
these lots or batches be no greater than the
designated value of AQL. Thus, the AQLis a designated value of percent defective (or
defects per hundred units) that the consumer
indicates will be accepted most of the time
by the acceptance sampling procedure to be
used. The sampling plans provided herein
are so arranged that the probability of ac-
ceptance at the designated AQL value de-
pends upon the sample size, being generally
higher for large samples than for small ones,
for a given AQL. The AQL alone does not
describe the protection to the consumer for
individual lots or batches but more directly
relates to what might be expected from a
series of lots or batches, provided the steps
indicated in this publication are taken. It is
necessary to refer to the operating character-
istic curve of the plan, to determine whatprotection the consumer will have.
4.4 LIMITATION. The designation of anAQL shall not imply that the supplier has
the right to supply knowingly any defective
unit of product.
4.5 SPECIFYING AQLs. The AQL to be
used will be designated in the contract or bythe responsible authority. Different AQLsmay be designated for groups of defects con-
sidered collectively, or for individual defects.
An AQL for a group of defects may be des-
ignated in addition to AQLs for individual
defects, or subgroups, within that group.
AQL values of 10.0 or less may be expressed
either in percent defective or in defects per
hundred units; those over 10.0 shall be ex-
pressed in defects per hundred units only.
4.6 PREFERRED AQLs. The values of
AQLs given in these tables are known as
preferred AQLs. If, for any product, an AQLbe designated other than a preferred AQL,these tables are not applicable.
5. SUBMISSION OF PRODUCT
5.1 LOT OR BATCH. The term lot or
batch shall mean "inspection lot" or "inspec-
tion batch, " i.e., a collection of units of prod-
uct from which a sample is to be drawn and
inspected to determine conformance with the
acceptability criteria, and may differ from a
collection of units designated as a lot or batch
for other purposes (e.g., production, ship-
ment, etc.).
5.2 FORMATION OF LOTS OR BATCHES.The product shall be assembled into identi-
fiable lots, sublots, batches, or in such other
manner as may be prescribed (see 5.4). Eachlot or batch shall, as far as is practicable,
5. SUBMISSION OF PRODUCT (Continued)
consist of units of product of a single type,
grade, class, size, and composition, manu-
factured under essentially the same condi-
tions, and at essentially the same time.
5.3 LOT OR BATCH SIZE. The lot or
batch size is the number of units of product
in a lot or batch.
5.4 PRESENTATION OF LOTS ORBATCHES. The formation of the lots or
batches, lot or batch size, and the mannerin which each lot or batch is to be presented
and identified by the supplier shall be des-
ignated or approved by the responsible au-
thority. As necessary, the supplier shall
provide adequate and suitable storage space
for each lot or batch, equipment needed for
proper identification and presentation, and
personnel for all handling of product re-
quired for drawing of samples.
6. ACCEPTANCE AND REJECTION
6.1 ACCEPTABILITY OF LOTS ORBATCHES. Acceptability of a lot or batch
will be determined by the use of a sampling
plan or plans associated with the designated
AQL or AQLs.
6.2 DEFECTIVE UNITS. The right is re-
served to reject any unit of product found
defective during inspection whether that
unit of product forms part of a sample or
not, and whether the lot or batch as a whole
is accepted or rejected. Rejected units maybe repaired or corrected and resubmitted for
inspection with the approval of, and in the
manner specified by, the responsible au-
thority.
6.3 SPECIAL RESERVATION FOR CRITI-
CAL DEFECTS. The supplier may be required
at the discretion of the responsible authority
to inspect every unit of the lot or batch for
critical defects. The right is reserved to in-
spect every unit submitted by the supplier for
critical defects, and to reject the lot or batch
immediately, when a critical defect is found.
The right is reserved also to sample, for crit-
ical defects, every lot or batch submitted bythe supplier and to reject any lot or batch
if a sample drawn therefrom is found to con-
tain one or more critical defects.
6.4 RESUBMITTED LOTS OR BATCHES.Lots or batches found unacceptable shall be
resubmitted for reinspection only after all
units are re-examined or retested and all de-
fective units are removed or defects cor-
rected. The responsible authority shall deter-
mine whether normal or tightened inspection
shall be used, and whether reinspection shall
include all types or classes of defects or for
the particular types or classes of defects
which caused initial rejection.
7. DRAWING OF SAMPLES
7.1 SAMPLE. A sample consists of oneor more units of product drawn from a lot or
batch, tho units of the sample being selected
at random without regard to their quality.
The number of units of product in the sampleis the sample size.
7.2 REPRESENTATIVE SAMPLING. Whenappropriate, the number of units in the sam-
ple shall be selected in proportion to the size
of sublots or subbatches, or parts of the lot or
batch, identified by some rational criterion.
7. DRAWING OF SAMPLES (Continued)
When representative sampling is used, the
units from each part of the lot or batch shall
be selected at random.
7.3 TIME OF SAMPLING. Samples maybe drawn after all the units comprising the
lot or batch have been assembled, or sam-
ples may be drawn during assembly of the
lot or batch.
7.4 DOUBLE OR MULTIPLE SAMPLING*When double or multiple sampling is to beused, each sample shall be selected over the
entire lot or batch.
8. NORMAL, TIGHTENED AND REDUCED INSPECTION
8.1 INITIATION OF INSPECTION. Nor-
mal inspection will be used at the start of
inspection unless otherwise directed by the
responsible authority.
8.2 CONTINUATION OF INSPECTION-
Normal, tightened or reduced inspection
shall continue unchanged, fojr each class of
defects or defectives on successive lots or
batchs except where the switching proce-
dures given below require change. Theswitching procedures given below require a
change. The switching procedures shall be
applied to each class of defects or .defectives^
independently.
8.3 SWITCHING PROCEDURES.
8.3.1 NORMAL TO TIGHTENED. Whennormal inspection is in effect, tightened in-
spection shall be instituted when 2 out of 5
consecutive lots or batches have been re-
jected on original inspection (i.e., ignoring
resubmitted lots or batches for this proce-
dure).
8.3.2 TIGHTENED TO NORMAL. Whentightened inspection is in effect, normal in-
spection shall be instituted when 5 consecu-
tive lots or batches have been considered
acceptable on original inspection.
8.3.3 NORMAL TO REDUCED. Whennormal inspection is in effect, reduced inspec-
tion shall be instituted providing that all of
the following conditions are satisfied:
a. The preceding 10 lots or batches (or
more, as indicated by the note to Table VIII)
have been on normal inspection and nonehas been rejected an original inspection; and
b. The total number of defectives (or de-
fects) in the samples from the preceding 10
lots or batches (or such other number as wasused for condition "a" above) is equal to or
less than the applicable number given in
Table VIII. If double or multiple samplingis in use, all samples inspected should be in-
cluded, not ^ftast" samples only; and
c. Production is at a steady rate; and
d. Reduced inspection is considered de-
sirable by the responsible authority.
8.3.4 REDUCED TO NORMAL. When re-
duced inspection is in effect, normal inspec-
tion shall be instituted if any of the following
occur on original inspection:
a. A lot or batch is rejected; or
b. A lot or batch is considered acceptable
under the procedures of 10.1.4; or
c. Production becomes irregular or de-
layed; or
d. Other conditions warrant that normalinspection shall be instituted.
8.4 DISCONTINUATION OF INSPECTION.In tHe ev£nt that 10 consecutive lots or
batches remain on tightened inspection (or
sucfh other number as may be designated bytfie responsible authority), inspection underthe provisions of this document should bediscontinued pending action to improve the
quality of submitted material.
9. SAMPLING PLANS
9.
1
SAMPLING PLAN. A sampling plan
indicates the number of units of product
from each lot or batch which are to be in-
spected (sample size or series of sample
sizes) and the criteria for determining the
acceptability of the lot or batch (acceptance
and rejection numbers).
9.2 INSPECTION LEVEL. The inspection
level determines the relationship between
the lot or batch size and the sample size. The
inspection level to be used for any particular
requirement will be prescribed by the re-
sponsible authority. Three inspection levels:
I, II, and III, are given in Table I for general
use. Unless otherwise specified, Inspection
Level II will be used. However, Inspection
Level I may be specified when less discrimi-
nation is needed, or Level III may be speci-
fied for greater discrimination. Four addi-
tional special levels: S-l, S-2, S-3 and S-4,
are given in the same table and may be used
where relatively small sample sizes are neces-
sary and large sampling risks can or must be
tolerated.
NOTE: In the designation of inspection
levels S-l to S-4, care must be exercised to
avoid AQLs inconsistent with these inspec-
tion levels.
9.3 CODE LETTERS. Sample sizes are
designated by code letters. Table I shall be
used to find the applicable code letter for the
particular lot or batch size and the prescribed
inspection level.
9.4 OBTAINING SAMPLING PLAN. TheAQL and the code letter shall be used to ob-
tain the sampling plan from Tables II, III or
IV. When no sampling plan i£ available for a
given combination of AQL and code lettg£>
the tables direct the user to a different letter.
The sample size to be used is given by the
new code letter not by the original letter. If
this procedure leads to different sample sizes
for different classes of defects, the code letter
corresponding to the largest sample size de-
rived may be used for all classed of defects
when designated or approved by the respon-
sible authority. As an alternative to a single
sampling plan with an acceptance numberof 0, the plan with an acceptance number of 1
with its correspondingly larger sample size
for a designated AQL (where available) , maybe used when designated or approved by the
responsible authority.
9.5 TYPES OF SAMPLING PLANS. Three
types of sampling plans: Single, Double and
Multiple, are given in Tables II, III and IV,
respectively. When several types of plans are
available for a given AQL and code letter,
any one may be used. A decision as to type
of plan, either single, double, or multiple,
when available for a given AQL and code
letter, will usually be based upon the com-
parison between the administrative difficulty
and the average sample sizes of the available
plans. The average sample size of multiple
plans is less than for double (except in the
case corresponding to single acceptance num-ber 1) and both of these are always less than
a single sample size. Usually thfe administra-
tive difficulty for single sampling and the
cost per unit of the sample are less than -for
double or multiple.
10. DETERMINATION OF ACCEPTABILITY
10.1 PERCENT DEFECTIVE INSPECTION.
To determine acceptability of a lot or batch
under percent defective inspection, the ap-
plicable sampling plan shall be used in
accordance with 10.1.1, 10.1.2, 10.1.3, 10.1.4,
and 10.1.5.
10.1.1 SINGLE SAMPLING PLAN. Thenumber of sample units inspected shall be
equal to the sample size given by the plan.
If the number of defectives found in the
sample is equal to or less than the acceptance
number, the lot or batch shall be considered
acceptable. If the number of defectives is
equal to or greater than the rejection num-ber, the lot or batch shall be rejected.
10.1.2 DOUBLE SAMPLING PLAN. Thenumber of sample units inspected shall beequal to the first sample size given by the
plan. If the number of defectives found in
the first sample is equal to or less than the
first acceptance number, the lot or batch
shall be considered acceptable. If the num-ber of defectives found in the first sample is
equal to or greater than the first rejection
number, the lot or batch shall be rejected.
If the number of defectives found in the first
sample is between the first acceptance andrejection numbers, a second sample of thesize given by the plan shall be inspected. The
number of defectives found in the first andsecond samples shall be accumulated. If the
cumulative number of defectives is equal to
or less than the second acceptance number,the lot or batch shall be considered accept-
able. If the cumulative number of defectives
is equal to or greater than the second rejec-
tion number, the lot or batch shall be rejected.
10.1.3 MULTIPLE SAMPLE PLAN. Undermultiple sampling, the procedure shall besimilar to that specified in 10.1.2, except that
the number of successive samples requiredto reach a decision may be more than two.
1 0. 1 .4 SPECIAL PROCEDURE FOR RE-
DUCED INSPECTION. Under reduced in-
spection, the sampling procedure may termi-
nate without either acceptance or rejection
criteria having been met. In these circum-stances, the lot or batch will be consideredacceptable, but normal inspection will bereinstated starting with the next lot orbatch (see 8.3.4 (b)).
10.2 DEFECTS PER HUNDRED UNITS IN-
SPECTION. To determine the acceptability
of a lot or batch under Defects per HundredUnits inspection, the procedure specified for
Percent Defective inspection above shall beused, except that the word "defects" shall besubstituted for "defectives."
1 1 . SUPPLEMENTARY INFORMATION
11.1 OPERATING CHARACTERISTICCURVES. The operating characteristic curves
for normal inspection, shown in Table X(pages 30-62), indicate the percentage of
lots or batches which may be expected to beaccepted under the various sampling plans
for a given process quality. The curves shownare for single sampling; curves for double
and multiple sampling are matched as closely
as practicable. The O. C. curves shown for
AQLs greater than 10.0 are based on thePoisson distribution and are applicable for
defects per hundred units inspection; thosefor AQLs of 10.0 or less and sample sizes of
80 or less are based on the binomial distri-
bution and are applicable for percent defec-
11. SUPPLEMENTARY INFORMATION (Continued)
tive inspection; those for AQLs of 10.0 or
less and sample sizes larger then 80 are based
on the Poisson distribution and are applica-
ble either for defects per hundred units in-
spection, or for percent defective inspection
(the Poisson distribution being an adequate
approximation to the binomial distribution
under these conditions). Tabulated values,
corresponding to selected values of probabil-
ities of acceptance (Pa , in percent) are given
for each of the curves shown, and, in addi-
tion, for tightened inspection, and for defects
per hundred units for AQLs of 10.0 or less
and sample sizes of 80 or less.
11.2 PROCESS AVERAGE. The process
average is the average percent defective or
average number of defects per hundred units
(whichever is applicable) of product sub-
mitted by the supplier for original inspec-
tion. Original inspection is the first inspec-
tion of a particular quantity of product as
distinguished from the inspection of product
which has been resubmitted after prior
rejection.
11.3 AVERAGE OUTGOING QUALITY(AOQ). The AOQ is the average quality of
outgoing product including all accepted lots
or batches, plus all rejected lots or batches
after the rejected lots or batches have been
effectively 100 percent inspected and all de-
fectives replaced by nondefectives.
11.4 AVERAGE OUTGOING QUALITYLIMIT (AOQL). The AOQL is the maximumof the AOQs for all possible incoming quali-
ties for a given acceptance sampling plan.
AOQL values are given in Table V-A for
each of the single sampling plans for normal
inspection and in Table V-B for each of the
single sampling plans for tightened inspec-
tion.
11.5 AVERAGE SAMPLE SIZE CURVES.Average sample size curves for double andmultiple sampling are in Table DC. Theseshow the average sample sizes which may beexpected to occur under the various sampling
plans for a given process quality. The curves
assume no curtailment of inspection and are
approximate to the extent that they are
based upon the Poisson distribution, and that
the sample sizes for double and multiple
sampling are assumed to be 0.631n and 0.25n
respectively, where n is the equivalent single
sample size.
11.6 LIMITING QUALITY PROTECTION.The sampling plans and associated proce-
dures given in this publication were designed
for use where the units of product are pro-
duced in a continuing series of lots or batches
over a period of time. However, if the lot
or batch is of an isolated nature, it is desira-
ble to limit the selection of sampling plans
to those, associated with a designated AQLvalue, that provide not less than a specified
limiting quality protection. Sampling plans
for this purpose can be selected by choosing
a Limiting Quality (LQ) and a consumer's
risk to be associated with it. Tables VI and
VII give values of LQ for the commonly used
consumer's risks of 10 percent and 5 percent
respectively. If a different value of con-
sumer's risk is required, the O.C. curves and
their tabulated values may be used. The
concept of LQ may also be useful in specify-
ing the AQL and Inspection Levels for a
series of lots or batches, thus fixing minimumsample size where there is some reason for
avoiding (with more than a given consumer's
risk) more than a limiting proportion of de-
fectives (or defects) in any single lot or
batch.
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Index of terms with special meanings
Term Paragraph
Acceptable Quality Level (AQL) 4.2 and 11.1
Acceptance number 9.4 and 10.1.1
Attributes 1.4
Average Outgoing Quality (AOQ) 11.3
Average Outgoing Quality Limit (AOQL) 11.4
Average sample size . 11.5
Batch 5.1
Classification of defects 2.1
Code letters 9.3
Critical defect 2.1.1
Critical defective 2.2.1
Defect 2.1
Defective unit 2.2
Defects per hundred units 3.3
Double sampling plan .. 10.1.2
Inspection 1.3
Inspection by attributes .. 1.4
Inspection level 9.2
Inspection lot or inspection batch 5.1
Isolated lot , 11.6
Limiting Quality (LQ) 11.6
Lot 5.1
Lot or batch size 5.3
Major defect , 2.1.2
Major defective 2.2.2
Minor defect 2.1.3
Minor defective 2.2.3
Multiple sampling plan 10.1.3
Normal inspection 8.1 and 8.2
Operating characteristic curve 11.1
Original inspection 11.2
Percent defective 3.2
Preferred AQLs 4.6
Process average 11.2
Reduced inspection 8.2 and 8.3.3
Rejection number 10.1.1
Responsible authority 1.1
Resubmitted lots or batches 6.4
Sample 7.1
Sample size 7.1
Sample size code letter 4.1 and 9.3
Sampling plan 9.5
Single sampling plan 10.1.1
Small-sample inspection 9.2
Switching procedures 8.3
Tightened inspection 8.2 and 8.3.1
Unit of product 1.5
63
Copies of this standard may be obtained by directing requests to*
Commanding OfficerU.S. Naval Supply DepotATTN; Code DMD5801 Tabor AvenuePhiladelphia 20, Pennsylvania
Copies of this Military Standard may be obtained for other than
official use by individuals, firms, and contractors from the Superintendent
of Documents, U.S. Government Printing Office, Washington 25, D. C.
Both the title and identiiying symbol number should be stipulated
when requesting copies of Military Standards.
Custodians:
Army - Munitions CommandNavy - Bureau of WeaponsAir Force - Air Force Logistics CommandDefense Supply Agency
Preparing Activity:
Army - Munitions Command
64
U. S. GOVERNMENT PRINTING OFFICE : 1971 O - 414-996