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MIL-STD-105D 29 April 1963 SUPERSEDING MIL-STD-105C 18 July 1961 MILITARY STANDARD SAMPLING PROCEDURES AND TABLES FOR INSPECTION BY ATTRIBUTES

MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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Page 1: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

MIL-STD-105D

29 April 1963

SUPERSEDINGMIL-STD-105C

18 July 1961

MILITARY STANDARD

SAMPLING PROCEDURES AND TABLES

FOR INSPECTION BY ATTRIBUTES

Page 2: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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

Page 3: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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.

Page 4: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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

Page 5: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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

Page 6: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

<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.

Page 7: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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

Page 8: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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,

Page 9: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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.

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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.

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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.

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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-

Page 13: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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.

8

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Page 68: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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

Page 69: MILITARY STANDARD PROCEDURES AND TABLES ......MIL-STD-105D 29April1963 SUPERSEDING MIL-STD-105C 18July1961 MILITARYSTANDARD SAMPLINGPROCEDURESANDTABLES FORINSPECTIONBYATTRIBUTES MXL-STD~105D

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