2500_3 5m2a5a

IS 2500 (Part 3) : 1995 IS0 2859-2 : 1985

( Reaffirmed 2004 )

Indian Standard SAMPLING PART 3

ATTRIBUTE

INSPECTION

PROCEDURES

SAMPLING PLANS INDEXED BY LIMITING ISOLATED LOT INSPECTION

IS0 Title : Sampling procedures

QUALITY

for inspection by attributes -

( LQ)

FOR

Part 2 : Sampling

pians indexed by limiting quality ( LQ ) for isolated lot inspection ] ( First Reprint

JULY 1997 )

ICS .No. 03.120.10

0 BIS 1995

BUREAU MANAK

October 1995

OF BHAVAN,

INDIAN

STANDARDS

9 BAHADUR SHAH NEW DELHI 110002

ZAFAR

MARG

Price Group 9

Statistical

Methods for Quality and Reliability

NATIONAL

Sectional

Committee,

MSD 3

FOREWORD

This Indian Standard which is identical with IS0 2859-2 : 1985 ‘Sampling procedures for inspection by attributes - Part 2 : Sampling plans indexed by limiting quality ( LQ ) for isolated lot inspection’, issued by the International Organization for Standardization ( IS0 ), was adopted by the Bureau of Indian Standards on the recommendation of the Statistical. Methods for Quality and Reliability Sectional Committee ( MSD 3 ), and approval of the Management and Systems Division Council. This standard ( Part 3 ) is third in the series of Sampling parts are as follows:

Inspection

Procedures.

The other published

Part 1

Attribute sampling plans indexed by acceptable quality level ( AQL ) for lot-by-lot inspection

Part 2

Inspection

by variables for percent defective

The text of IS0 2859-2 : 1985 has been approved as suitable for publication as Indian Standard without deviations. Certain conventions are, however, not identical to those used in Indian Standards. Attention is particularly drawn to the following: a)

Wherever the words ‘this part of IS0 2859’ appear referring to this standard, they should be read as ‘this part of IS 2500’.

b)

Comma (J has been used as decimal marker while in Indian Standards the current practice is to use a point (.) as the decimal marker.

In the adopted standard, informative reference appears to IS0 2859/i ‘Sampling procedures for inspection by attributes -- Part 1: Sampling plans indexed by acceptable quality level ( AQL ) for lot-bylot inspection’ which has been adopted in foto as IS 2500 ( Part 1 ) : 1992 ‘Sampling inspection procedures: Part 1 Attribute sampling plans indexed by acceptable quality level ( AQL ) for lot-by-lot inspection’.

IS 2500 (Part 3) : 1995 IS0

2859-2 : 1992

Indian Standard SAMPLING PART 3

0

ATTRIBUTE

INSPECTION

PROCEDURES

SAMPLING PLANS INDEXED BY LIMITING ISOLATED LOT INSPECTION

Introduction

Consequently,

QUALITY

in certain of the above cases consumer

tion may need to be attained

0.1

( LQ ) FOR

or measured

protec-

by other methods.

This part of IS0 2859 uses the limiting quality to measure consumer protection. It should be ed, however, that

General

prior information

on the supplier’s

and its effectiveness

IS0 2859 comprises four parts:

quality

assurance

system

may play a major part in deciding whether

or not to accept a single lot. Part 0: General introduction. Part 1 : Sampling IAQL)

plans indexed by acceptable

for lot-by-lot

Part 2: Sampling

quality level

inspection.

Objectives

0.2

plans indexed by limiting quality (LO) for

isolated lot inspection. In an attempt Part 3: Skip lot sampling

IS0 2859/l

plan.

sampling plans, indexed in of AQL,

defined as a process average, assessment

of

a

the following

series

of

lots.

This

a)

the new

LQ plans can be easily integrated

with

the

existing AQL plans in IS0 265911;

where necessary) but also provide an incentive

to the producer

Iby the switch to reduced

inspection)

with a

reduction to test and inspection costs (when consistently quality is achieved). industrial situations

b)

good

not all of which

the LQ indexing

uses a preferred

series of values that

cannot be confused with the preferred series of AQL values;

However, there is little doubt that in many today the switching rules are not applied

for a variety of reasons or excuses, valid

with

principles:

enables

switchingrules to be employed which not only give protection to the consumer (by the switch to tightened inspection and discontinuation

diverse requests for

sectors, this part of IS0 2859 was drawn up in accordance

which is

were primarily designed for the

continuing

to reconcile the somewhat

assistance made over the past few years by committees of international standardizing bodies representing various product

may be

c)

:

the five basic numbers

associated

with a single sampl-

ing plan, i.e. lot size, sample size, acceptance

number,

AQL

(or quality accepted with probability 0,95) and LQ, appear in a)

individual IS0 2859/l

protection

c&x!

is still claimed

the same table, whenever

plans are used alone but “AQL” or AQL

re-defined,

to suit “SO-

unique products”;

product is specia! so IS0 285911 stanb) “our industry.. dard plans need not apply to us”; c)

production

is intermittent

d)

production

is from several different

quantities,

0.3

Summary

(not continuous); The problems associated with acceptance sampiing inspection involve defining unambiguously the criteria used to judge discrete individual items supplied in quantity, the quality level

sources in varying

i.e. “job lots”;

expected e)

purchases

are from

stock-holders

-

no source

data

lots are “small”

(use of hypergeometric

distribution

re-

a purchasing

quired); g)

lots are “isolated”;

h)

lots are resubmitted

from the manufacturing

process,

the discrimination

offered by the plans and the procedure to be followed when a lot is not accepted. Above all, however, it is necessary to design the sampling scheme so that it may easily be invoked in

available; f)

possible.

maximum that

contract.

The plans in this part of IS0 2859 make

use of the established

sub-clause

12.6

directly operational,

of IS0

plans given in IS0 2859/l,

2859/l

(see 1.1)

by providing a rationalized

indexed in of limiting quality (LQ).

after initial rejection.

1

so

can be made series of plans

IS 25.00 (Part 3) : 1995 IS0

: 1992

2859.2

1

Scope

;.l

and field

3.2

of application

Choice

of sampling

procedure

Scope Although

This part of IS0 2859 establishes LQ sampling plans and procedures for inspection by attributes compatible with IS0 2859/l that

can

2B59/lare

be used when

the

switching

rules given

procedure A is based on the hypergeometric

tion for sampling results, this distribution

distribu-

is well approximated

by the binomial distribution for plans with non-zero acceptance

in IS0

numbers in procedure

not applied, for example, when lots are of an isolated

are well approximated

A. Hence the OC curves for these plans by the tabulated

performance

of the

nature.

same plans in procedure

The plans in this part of IS0 2859 are indexed by a preferred

with acceptance number zero and with sample sizes based on the hypergeometric distribution of sampling results while pro-

series of limiting qualities (LO) with a consumer’s risk usually below 10 %, but always below 13 %. This method of indexing permits the “ad-hoc” proceduret) mentioned in sub-clause 12.6 of IS0 2859/l

to be implemented

cedure

procedures

The choice plans

between

the procedures

linking

the

sample

size and acceptance spection

number

levels available

procedure

A resembles

less than 8 % and level

Procedure

shall be used

to use procedure

maintain

probability

Both procedures

can

The overall effect

level II for limiting

of

quality

between

these levels.

unit so they are approxi-

percent

for good quality and underestimate for poor quality.

For sufficiently

B requires 100 % inspection.

treat the limiting

nonconforming

quality

(LO) as the actual

units in the submitted

lots and the

table Dl for procedure A and tables Bl to BlO for procedure B. Procedure B is indicated as the appropriate procedure if the

that

contain

will be concerned

but the individual received.

consumer

sampling

whether

of sampling

not they receive individual lots or a continuing series of lots. This procedure is suitable for inclusion in product standards specifications

for customers

the progression

probability of acc’eptance at this limiting quality can be found in

manufacturer

procedures

the

or

or

consistent

so that a producer

by

OC curves are based on the prob-

of rejection

small lots, procedure

(OC) curves. The plans used are a selection of in IS0 2859/l

size

with lot size is based on the in-

a nonconforming

of acceptance

the probability

risk at the limiting

but random sampling from a process for the prorisk and the tabulated values of the operating

characteristic

lot

mately correct for small sampling fractions but as the sampling fraction increases the curves (and tables) underestimate the

lot as one of continuing series but the consumer considers the lot received in isolation. The tables are based on random sampling from a finite lot for consumer’s

by the at-

B provides greater flexibility in the choice of inspec-

ability of producing

8.

Procedure 8, to be used when the supplier regards the

the plans available

with

I for limiting quality greater than 8 %

tion levels. The tabulated

unless there is a specific instruction

the

in IS0 2859/l.

sumer

quality, ducer’s

them

is dominated

and

inspection

with 8 % being intermediate

Procedure A, to be used when the supplier and con-

risks. This procedure

size

to that limiting quality. Thereafter

sumer both wish to regard ?he lot in isolation. The tables are based on random sampling from finite lots for both con-

b)

replacing

hypergeometric distribution until the proposed plan corresponds to the accept zero plan in IS0 2859/l corresponding

are provided in this part of IS0 2859 to

and producer

plans,

titude towards accept zero plans. Procedure A uses accept zero

cater for two situations often met in practice: a)

zero

A uses plans

as a standard procedure.

Field of application

Alternative

accept

procedure

106 % inspection.

NOTE - The plans in IS0 2859/l are indexed by a preferred series of AQL values and inspection levels. During the inspection of a continuing series of lots the application of switching rules helps to ensure that the process average in that series of lots is kept below the specified AQL. Limiting quality does not have the same direct relationship with the process average (see 3.5.1 I.

1.2

B excludes

B. However,

clauses.

The

withall

of his production,

only with

the particularlot

manufacturer whether

is concerned

with

a continuing

or not these go to the same consumer.

series of lots; Procedure

A is

indicated as the appropriate procedure when the lot is a single lot and shall be used if accept zero plans are required to be part of the sampling scheme.

2

Definitions

The definitions

3 3.1

Choice

given in IS0 2859/l

of sampling

Specifying

a sampling

shall apply.

3.3

plan plan

A (use table A)

A plan is identified by the lot size and the limiting quality (LQ).

When reference is made to this part of IS0 2859 in a contract or specification, it is necessary to specify the procedure to be used (i.e. either A or Pr. In the absence of any reference either procedure, then procedure A shall be used.

Procedure

With

the specified

lot size and

limiting

quality

values, the sampling size (n) and acceptance

to

as indexing

number (AC) are

given in table A.

1) IS0 2859/l sub-clause 12.6.2, states: “If the lot or batch is OTan isolated nature, it may be desirable to limit the selection of sampling plans to those, associated with a designated AQL value, that provide not less than a specified limiting quality protection. Sampling plans for this purpose can be selected by choosing a limiting quality (LO) and a consumer’s risk to be associated with it. Tables 6 and 7 give process levels for which the probabilities of lot acceptance under various sampling plans are 10 % and 5 %, respectively.” This part of IS0 2859 establishes preferred values for the LQ and allows the consumer’s risk tc vary as indicated above.

2

IS

(Part 3) : 1995 2859-2 : 1992

.

2500

IS0

Example:

Although the primary index to these tables is the limiting quality (LQ), the producer/supplier needs guidance on the quality level required if lots are to have a high probability of acceptance. Information on the producer’s risk point is contained in table Dl. Information on the probability of acceptance of relatively good

The limiting quality has previously been set at 3.5 %. This is not a preferred value and the tables shall be entered by using the nominal limiting quality LQ = 3,15 % since

lots by accept zero plans is given in table D2.

3,5 % lies in the range 2,5 % < LO <4,0

3.5.2 3.4

Procedure

Inspection

In the IS0 2859/l procedures, increased sample size corresponds to a greater protection for the consumer. In this part of IS0 2859, consumer supplier greater the consumer

limiting quality is used to select the appropriate

table from tables Bl to B10. Within

occasional

each table the specified lot

size and inspection

level indicate the appropriate

(n) and acceptance

number

(AC). Although

to the table is the limiting quality (LQ), high probability of acceptance. the equivalent curves

AQL

sample size

the primary index

the producer/supplier

Each table gives information

and details

are indexed

of the OC curves.

by the sample

IS0 285911 and the acceptance

size code

on

actual

used in

operating

inspection

cess average

the limiting

well

probability

a smaller probability

when

of

charac-

is concerned

size depending

for

the

quality

Rules

4.1

sampling

procedures

quality

quality) if the

with actual rather than limiting quality,

sampie sizes have to be kept small and other

only on the limiting quality.

for acceptance

and non-acceptance

Sampling

Once the sampling plan has been determined

Limiting

(better

the indicated

4

parameters

are borne by him. A pro-

considerations are secondary, specifying level S-2 has the effect of providing a fixed sample size for all lot sizes, the sample

is < 0,lO.

Choice

below

spection level III provided by IS0 2859/l has not been incorporated in this part of IS0 2859 for limiting qualities greater

teristic will be more discriminating than these curves by accepting with greater probability when the indicated probability is > 0,90 and with

If

provided against an

or if he pays for the sampling costs, then greater inspection levels are not necessarily advantageous. For this reason, in-

number.

the

process averages.

poor lot by the nominal limiting quality, then the in-

than 5 %. When distribution;

in the permitted

is satisfied by the protection

the costs of the sampling

consumer

The OC curves given under tables Bl to BIO are based on the Poisson/binomial

cons-

would allow the use of smaller sample sizes. Conversely,

The OC

letter

latitude

is held approximately

sample size is to permit the

spection level is primarily of interest to the supplier, especially if

needs guidance on the quality level required if lots are to have a

3.5.1

protection

tant and the effect of increasing

used).

3.5

level

B (use tables B)

A plan is identified by the lot size, limiting quality (LQ) and the inspection level (unless otherwise specified, level II shall be

The specified

%.

as in clause 3, the

specified sample units shall now be drawn at random from the lot, and all units in the sample inspected.

(LQI

4.2

Unlike the AQL, which provides a guide for the producer on the level or quality he needs to produce so that he can satisfy the

Acceptance

If the number of nonconforming

acceptance criteria (sampling clause) most of the time, the limiting quality does not provide a reliable guide for the con-

units, or the total number

of

nonconformities, found in the sample is equal to or less than the acceptance number (AC) specified in the plan, the lot shall be accepted.

sumer as to the true quality of the accepted lots. For this reason the limiting quality should be chosen realistically at a minimum of three times the desired quality.

4.3 This

enables

the

producer/supplier

to provide

lots

desired quality and still have a reasonable probability tance for the submitted

lots, at least for acceptance

5, 10 and 18. For acceptance

number

of the

Notwithstanding

of accep-

units found

numbers 3,

of acceptance

units

that the lot is accepted,

during

inspection,

part of the

4.4

Non-acceptance

and

If the number of nonconforming greater than the acceptance

plans are introduced

table. An unacceptable tion unless

a non-standard

resubmission

The limiting

values are restricted to a set of preferred values and the plans are intended to be used with these preferred values. If these limiting quality is

already specified, the plans should be entered with the preferred value (LO) corresponding to the interval containing the non-standard

any nonconforming forming

1 plans the lots have to

rises to 0,95 or greater.

where

whether

sample or not, shall be rejected.

have a quality better than LQ,, and for acceptance number zero plans the lots have to be perfect or nearly perfect before the probability

Nonconforming

value (L) listed in column 4 of table C. Columns 2

units found

number

lot may not be resubmitted

a)

the Responsible

Autho*

b)

all units in the lot have been re-examined

for inspec-

agrees, and

and 3 of table C contain information on the consumer’s risk qualities (CRQ) found in tables Bl to BlO for consumer’s risks

and all nonconforming

of 10 % and 5 %.

by good units or nonconformities

3

in the sample is

(AC), the lot is unaccep-

or retested

units have been removed or replaced have been corrected.

.

IS 2500 (Part 3) : 1995 IS0

: 1992

2859-2

If the Responsible

Authority

agrees to the resubmission

produce the bookcase kit, but he decides that if 5 % of the s were scarred this would present problems during the

of an

unacceptable lot, he shall determine the method of acceptance inspection to be applied (i.e. LO and/or inspection level) and

processing.

whether re-inspection shall include all types or classes of nonconformities or only those that caused the initial rejection.

The

consumer

and supplier

agree

that

procedure

B is ap-

propriate and select nominal limiting quality 5,0 % with inspection level S-4. The parameters of the sampling plan for a lot size

5

Double

and multiple

sampling

plans

of 7 500 is n = 80, AC = 1. With acceptance

this plan the probability

of

with the current process average is less than 0,5. A

lot which is unacceptable

has to be 100 % inspected before use

terns for the double and multiple sampling plans in IS0 2859/l

and this high probability

of non-acceptance

equivalent to the single sampling plans given in tables 61 to 810. The sample size code agrees with that in IS0 285911 and

costs larger than desirable.

Tables D3 and D4 provide the sample sizes and acceptance

the acceptance

pattern

corresponding’single

code is the acceptance

pat-

Inspection

number in the

size plans. Since procedure

process

produce lots with a probability of acceptance

cedure B plans have similar OC curves for non-zero acceptance numbers,

level III would have provided a sampling

n = 315 and AC = 10. The current

A and pro-

implies inspection

A supplier with a better process average,

these double and multiple plans can also be used in

of acceptance

plan with

average

would

greater than 080.

say 1 %, would ob-

procedure A to replace the corresponding single sampling plan. The is referred to 11.1.2 and 11.1.3 in IS0 2859/l for the

tain a similar probability

with

inspection

level

operation

smaller sample sizes whilst still meeting the same limiting qual-

S-4. This illustrates the ability of better suppliers to work with

of these double and multiple sampling plans.

ity criterion.

6 Examples of IS0 2659 6.1

illustrating

how to use this part 7

A consumer

wishes

to purchase

screws to include in the self-assembly

prepacked

sets of 10

Compatibility

7.1

with

IS0

2659/l

General

bookcase kits he plans to

sell. While he prefers each set to contain exactly 10 screws, he

Within

can tolerate

pling,

1 % of packs with fewer screws but he does not

want to risk accepting a much higher percentage of deficient packs. He plans to produce 5 000 kits in lots of 1 250.

the probability the

LQ

plans

indexed plans of IS0 2859/l.

A with nominal limiting

quality 3.15 %. For lots of size 1 250, the selected n = 125, AC = 1.

constraints

tables B provide a rationalized non-acceptance

The supplier agrees to use procedure

indexed

in attribute in table A

samand

selection from the existing AQL Similar rules for acceptance

and the IS0 2859/l

also been retained for compatibility.

plan has

inherent

standardized

lot size categories Significant

deviations

and have are

given in 7.2 and 7.3.

7.2

The supplier offers to provide the packs needed for all 5 000 kits

Procedure

A (see table A)

as a single lot. The new sampling plan has n = 200, AC = 3. For unique lots with a relatively high sample size/lot

size ratio,

The single lot requires proportionately fewer tested items and yet the sampling plan still provides a high probability of rejec-

it becomes necessary to use the hypergeometric distribution. Consequently, there are an additional 39 (AC = 0) plans in

tion for quality as poor as 3,15 %, while increasing the prob-

table A for which

ability of acceptance

given in table D2. The remaining 80 plans of table A have been taken from IS0 285911.

6.2

The

components

same

for a lot of quality 1 % from O&l to 088.

consumer

wishes

of his self-assembly

to purchase

general

stream

7.3

(OCI curve data is

Procedure

B (see tables B)

All the plans in tables B have been selected from IS0 2859/l by using a sliding scale for the consumer’s risk (usually below

for each lot of 1 250 kits as single lots in the of supply to DIY shops.

characteristic

the wooden

bookcase kit as standard-size,

plastic-faced chipboard s. The supplier produces these s as part of his regular production and regards the 7 500 s needed

operating

10 %) at the specified limiting quality (LO). IS0 2859/l

Scars to the plastic

inspec-

facing occur with probability 0,025 according to quality control checks. The consumer can tolerate some scarred s since

tion levels are also included (see 3.5.2) but AC = 0 plans have not been included in tables B, as table A can be used, if

these can be detected

AC = 0 plans are considered

and set aside during the processing to

4

essential.

IS 2500 (Part 3) : 1995 IS0

Table A - Single sampling

by limiting quality (LQ) (Procedure

plans indexed

2859-2

: 1992

A)

Limiting qualityin percent (LQ) Lot size

0.5

16to

25

+

+

+

+

+

+

+

+

-+

60

51to

90

" AC

91 to

150

" AC

151 to

280

n AC

281to

500

1201to

3200

3201to

10000

10001

to

35000

35001

to150000

150001

to500000

> 500000 1)

AC

26to

1200

When

1.25

n n AC

501 to

0,8

2.0

3,15

+

5.0

20

32

25"

8,O 17"

12,5 13

9

6

0

0

0

0

0

50" 0

50" 0

28" 0

22 0

15 0

10 0

6 0

90" 0

50 0

44 0

34 0

24 0

16 0

10 0

8 0

150" 0

90 0

80 0

55 0

38 0

26 0

18 0

13 0

13 1

200" 0

170" 0

130 0

95 0

65 0

42 0

28 0

20 0

20 1

13 1 20

n

280

220

155

105

80

50

32

32

20

AC

0

0

0

0

0

0

0

1

1

3

n

380

255

170

125

125

80

50

32

32

32

AC

0

0

0

0

1

1

1

1

3

5

n

430

280

200

200

125

125

80

50

50

50

AC

0

0

0

1

1

3

3

3

5

10 80

n

450

315

315

200

200

200

125

80

80

AC

0

0

1

1

3

5

5

5

10

n

500

500

315

0

1

800 1

AC ” AC n

800

AC n AC

315

315

200

125

125

80

1

3

5

10

10

10

18

18

500

500

500

500

500

315

200

125

80

1

3

5

10

18

18

18

18

18

800

800

800

800

500

315

200

125

80

3

5

10

18

18

18

18

18

18

500

500

315

200

125

80

18

18

18

18

18

18

1 1250

1250 3

18

315

1 250 5

1250

10

18

n exceeds the lot size, use 100 % inspection with zero acceptance

Limiting quality implies less than one nonconforming

number.

item in the lot. Use first available plan for higher LQ.

5

.

Table

Bl

-

Sampling

plans

for limiting

quality

0.5 %

IS0 2859/l Lot sizes for inspection

levels

Single

sampling

(Normal S-l

to

s-3

> 80031

I

s-4 >

8003’

II

> 8003)

III

8013’ to 500 OOCI8013) to 150 000

Tabulated plan

Code

accepted

letter

(quality

inspection)

AQL

n

0,065

800

values with

AC

0,95

of submitted

designated

as percent

0.90

1

P

0,044 4

0,066

5

Acceptance probabilities

quality

probabilities’)

for

limiting

nonconforming)

quality21

050

0,lO

0,05

max.

min.

0,210

0,486

0,593

0,091

0,000

150 001

>500000

to 0.10

1250

3

Q

0,109

0,140

0,294

0,534

0,620

0,129

0,129

>5OOOCO

0,lO

2600

5

R

0,131

0,158

0,284

0,464

0,526

0,966

0,666

1)

Probability calculated

by the Poisson approximation.

2)

The exact acceptance

probabilities calculated from the hypergeometric

31

For fewer than 801 in the lot, 100 % inspect the lot.

Operating 0

500006

(Curves

characteristic

are identified

curves

by sample

for single

sampling

distribution vary with lot size, the maximum and minimum values attained for permitted

plans

size code)

0.8

0,2

O/L

0,6

Quality

0,8

of submitted

0,2

lots (percent

nonconforming)

0,C

0,6

0,8

lot sizes are given for each plan.

Table

Lot sizes for inspection

&? -

levels

Single

Single

IS0 285911 sampling

INormal s-1 to s-3

I

II

5013)

5013’

s-4

> 50031

>

50031

to

III

AQL

sampling

plans

for

limiting

quality

0,8

Tabulated plan

Code

letter

accepted

inspection) n

%

(quality AC

0,95

values with

of submitted

designated

as percent

0.90

Acceptance

quality

probabilities

probabilities11

for limiting

nonconforming)

0.50

0.10

quality*’ I

0,05

I

max.

j

min.

501 3’

to

150000

>500000

ot?l

o,1c6 -

o,336_

0,778

0,949

0,091

0,000

150 001 to

I

I

>500000

1

-J

>15oooo

0.15

Probability calculated

by the Poisson approximation.

21

The exact acceptance

probabilities calculated from the hypergeometric

3)

For fewer than 501 in the lot, 100 % inspect the lot.

Operating (Curves

characteristic are identified

)

500000

Ti

curves

by sample

for

single

sampling

1250

5

0,171

1

Q

1

0,218

I

0,209

/

0,459

0,835

0,969

0,118

0,115

0,454

0,742

0,841

0,066

0,066

I

0,252

1

distribution vary with lot size, the maximum and minimum values attained for permitted

plans

size code)

Quality

of submitted

lots lpercent

nonconforming)

lot sizes are given for each

plan.

Table

83 -

Single

sampling

plans

for

limiting

quality

IS0 Lot sizes for inspection

levels

Single (Normal

S-l t3 s, >31531

s-4

j

>31531

I

III

----II 3163’

3163’

to

It0

285Wl sampling

%

Tabulated plan

Code

accepted

letter

inspection)

values with

(quality

of submitted

designated

as percent

Acceptance

quality

probabilities limiting

probabilitiesl’

nonconforming)

n

0.95

AC

0.90

09

for

quality2)

___

1

AQL

0.10

min.

0.05

max.

1,51

0,095

0.~

0,129

0,122

31631

to

/

,,1,~1 150001

1.25

1

/

M

1.23

N

1.34

1.55

1,16

1,31

0.066

0.064

1,36

0,089

0.089

35 001

to 5ooouo

P

>500000

Q

1)

Probability calculated

by the Poisson approximation.

2)

The exact acceptance

probabilities calculated from the hypergeometric

3)

For fewer than 316 in the lot, 100 % inspect the lot.

Operating

characteristic

curves

for single

sampling

0,327 0,494

0,394 0,562

0,709 0,853

distribution vary with lot size, the maximum and minimum values attained

plans

(Curves are identified by sample size code)

0.6

Quality

of submitted

lots (percent

nonconforming)

1.23

for permitted

lot sizes are given for each plan

Tal+

84 -

Single

sampling

plans for limiting quality 2.00 %

IS0 2959/l Lot sizes for inspection

levels

Single

sampling

(Normal s-4

I

II

III

> 20031

20131

20131

2013’

to

to

15OOQO

10 oocl

150 001

10001

to

to

to

5OQOOiI

35 000

10 CQO

1

(quality

inspection) n

as percent

-

1

quality”

0,178

L

t

1

3 201 3

--/

M

0,433

0,533

1,17

2.12

2,46

0,124

0,111

N

0,523

0,630

1,13

1,86

2.10

0,065

0,061

P

0,771

0,878

1.33

1,93

2.12

0,075

0,073

i

by the Poisson approximation.

Proba

21

The exact acceptance

3)

For fewer than 201 in the lot, 100 % inspect the lot.

probabilities calculated from the hypergeometric

distribution vary with lot size, the maximum and minimum values attained for permitted

W

characteristic

(Curves are identified

nonconforming)

to 3200

1)

Operating

for

limiting

sl:,:,:r:,s

0,95

AC

;ljzz 1;ilI

~-@j

ity calculated

AQL

Code letter

plan

Acceptance probabilities

Tabulated values of submitted quality accepted with designated probabilities’)

curves

for single

sampling

plans

by sample size code)

0.8

O,L

012 3

1,o

Quality of submitted

2,0

lots (percent nonconforming)

3.0

L.0

lot sizes are given for each plan.

Table

Lot sizes for inspection

) Probability

calculated

The exact acceptance

For fewer than 51 in the lot, 100 % inspect the lot.

(Curves are identified

sampling

plans

probabilities calculated from the hypergeometric

curves

for single

for limiting

sampling

quality

8.0 %

ETii

Tabulated values uf submitted quality accepted with designated probabilities’) (quality as percent nonconforming)

by the Poisson approximation for code letters K and L. Binomial distribl

21

characteristic

Single

IS0 2858/l Single sampling plan (Normal inspection1

levels

31

Opera’ting

87 -

H

0,712

1.07

3.33

756

9.13

0,083

0,000

J

1.73

2.20

4,57

8,16

939

0,109

0,090

K

269

2,52

454

7.42

8.41

0,059

0,051

L

3.09

3.51

533

7.70

8.48

0,069

0,064

an for code letters H and J.

distribution vary with lot size, the maximum and minimum values attained for permitted

plans

by sainpie size code)

0,6

Quality of submitted

lots (percent nonconforming)

lot sizes are given for each plan.

Table

88 -

Single

sampling

plans

for limiting

quality

IS0 2869/l Lot sizes for inspection

levels

single

sampling

lcontrale

12,5 %

Tabulated plan

Code

letter

accepted

normal)

values with

(quality

of submitted

designated

as percent

quality

probabilities11

nonconforming)

_____-

I

II

III

3331

333)

333!

333’

to

to

to

to

5OOOQO

10 ooo

12lxl

280

~5OOooo

10001

1 201

281

to

to

to

35 ooo

3200

500

35 001

3 201

501

to

to

to

500000

10 000

1 200

>500000

>lOooo

S-1 to s-:

s-4

> 323’

>1200

O,W

G

1.13

1.67

5.19

3

H

2,77

3.54

7.30

80

5

J

3.32

3.98

7,M

125

10

K

4.94

5,62

8,53

n

1,5

32

1

2,5

50

2.5 4.0

1)

Probability calculated

by the Poisson approximation

2)

The exact acceptance

probabilities calculated from the hypergeometric

3)

For fewer than 33 in the lot, 100 % inspect the lot.

Ac-

for code letter K. Binomial distribution

characteristic

(Curves are identified

curves

for single

sampling

qualityz’

0,50

distribution vary with lot size, the maximum and minimum values attained for permitted

plans

by sample size code)

Quality of submitted

for

limiting

for code letters G, H and J.

2

Operating

1

0,95

AQL

Acceptance probabilities

lots (percent nonconforming)

lot sizes are given for each plan.

Table

Lot sizes for inspection

S-1 to s-3 >203’

I

I

II

III

213’

213)

213’

2131

to

to

to

to

35 ooo

1200

500

150

35 001

1 201

501

151

to

to

to

to

10 000

1206

280

z

I

/>35OOc1

>32Ocl

>500

(Curves are identified

by sample

sampling

WJ5

max.

min.

F

160

269

8,25

18,l

21.6

0,069

0,000

3

G

4.39

556

11.4

19.7

22.5

0,093

0,072

50

5

H

5.34

6.42

11.3

17.8

19.9

0,046

0,037

80

10

J

7.91

8.95

13.3

18.6

20.3

0,066

0,049

32

4.0 6,5

probabilities calculated from the hypergeometric

for single

0,lO

4,O

For fewer than 21 in the lot, 100 % inspect the lot.

Acceptance probabilities for limiting quality*)

Tabulated values of submitted quality accepted with designated probabilities” (quality as percent nonconforming) 0.50

1

The exact acceptance

20.0 %

0.90

20

3)

quality

0,95

2.5

2)

for limiting

Code letter

AC

by the binomial distribution.

curves

plans

n

Probability calculated

characteristic

sampling

AQL

1I

Operating

Single

IS0 286!l/l Single sampling plan (Normal inspection)

levels

s-4

500000

B9 -

distribution vary with lot size, the maximum and minimum values attainedfor

plans

size code)

1,o

0,6

Quality of submitted

lots (percent nonconforming)

permitted

lot sizes are given for each plan.

Table

BlO -

Single

sampling

plans

for limiting

quality

IS0 2859/l Lot sizes for inspection

levels

Single

sampling

(Normal

32.0 %

Tabulated plan

Code

accepted

letter

inspection)

values of submitted

with

(quality

designated

as percent

\

quality

probabilities”

nonconforming)

Acceptance probabilities limiting

for

quality*)

S-l to s-3

S-4

I

II

Ill

> 133’

143’

143’

1431

143)

to

to

to

to

3Mo

500

280

90

3201

501

281

91

to

to

to

35000

1200

500

to 156

35 001

1 201

501

151

to

to

to

to

500000

10 000

1200

280

6.5

32

5

G

8.5

10,2

17.5

27,l

30,l

0,031

0,022

>5OOooo

>lOOOO

>1200

>280

10.0

50

10

H

12.9

14.5

21.2

29.1

31,6

0,044

0,042

II

AC

4.0

13

1

E

2.81

6.5

20

3

F

7.13

1I

Probability calculated

by the binomial distribution.

2)

The exact acceptance

probabilities calculated from the hypergeometric

3)

For fewer than 14 in the lot, 100 % inspect the lot.

Operating

characteristic

(Curves are identified

curves

by sample

for single

sampling

095

AQL

0.50

0.10

0.05

max.

min.

4.16

12.6

26,8

31.6

0,047

0,000

9.03

18.1

30.4

34.4

0,077

0,062

0.90

distribution vary with lot size, the maximum and minimum values attained for permitted

plans

size code)

0,6

Quality

of submitted

lots (percent

nonconforming)

lot sizes are given for each plan.

IS 2500 (Part 3) : 1995 IS0

2859-2

: 1992 Table

Preferred value of limiting quality (LQ) %

Relation

between

limiting

Corresponding range of CRQ in tables Bl to BlO (at 10 % consumer’s risk)

quality

(LQ) and consumer’s

risk quality

Corresponding range of CRQ in tables Bl to BlO (at 5 % consumers risk1

(CRQ)

Corresponding interval’) for non-standard value of limiting quality IL)

0,5

0.46

< CRQ

<

054

0.52

< CRQ

<

0.62

0.4

0,8

0.74

< CRQ

i

0.84

0.84

< CRQ

<

0,97

0,65 <

1,0

1.25

1.16

< CRQ

<

1.34

1.31

< CRQ

<

1,55

1,0

1.6

2.0

166

< CRQ

<

2.12

2.10

< CRQ

<

2,46

1,6

< L <

2.5

3.15

2.94

< CRQ

<

3.34

334

< CRQ

<

3.88

2.5

< L <

4,0

5,O

4.64

< CRQ

<

5,35

5,26

< CRQ

<

6.20

4.0

< L <

6.5

8.0

7.42

< CRQ

<

8,16

8.41

< CRQ

<

9.39

6.5

< L < 10.0

< L <

< L <

0.65

12.5

11,3

< CRQ

< 12.9

12,7

< CRQ

< 14.8

10,o

< L < 15,0

20.0

17,8

< CRQ

< 19,7

19.9

< CRQ

< 22.5

15,0

< L < 25,5

26.8

< CRQ

< 30.4

30.1

< CRQ

< 34.4

25,0

< L < 40,O

32.0 1)

C -

These plans are intende

quality is already value (Ll.

specified,

o be used with the preterred the plans should be entered

sehes of limlttng qualltres.

with the preferred

16

If these plans are Introduced

value (LQ) corresponding

where a non-standard

to the interval containing

limiting

the non-standard

Table

Sample

size/acceptance

Percent

nonconforming

Dl

.-

Summary

oi sampling

No. (~/AC) (p)

Each cell in the table shows the consumer’s

inspect

91 to 150

every it&n 151to 293 26ttom

Inspect everyitem y/o

y,y

plan properties

for procedure

A

Probability

of acceptance

at the limiting quality 1) (PLQ)

Probability

of acceptance

at quality (p)

risk (PLQ) and the droducer’s

risk point (p, P,).

90/O 0

1.0

80/o 0

0,099 1.0

55/o 0

0,103 1.0

38/O 0

0,103 1.0

26/O 0

0,092 1.0

18/O 0

0,077 1.0

13/o 0

0.046 1.0

13/l 2.67

0,041 0.96

21

170/o 0

0,102 1.0

130/O 0

0,095 1.0

95/o 0

0,069 1.0

65/O 0

0.090 1.0

42/O 0

0,097 1.0

28/O 0

0.0% 1.0

20/O 0

0,062 1.0

20/l 1.79

0.062 0.96

1311 296

0.044 0.96

y0

;y

A5670

yl

implo

y$92

r/o

0061 l'.

50/O o

0067 l'.

32/o o

0066 l'.

3211

1o.

0,071 0.97

20/l 166

0.065 0.95

Ml3 7.20

0.072 0.95

31to1200 51

380/O o

0.101 1.0

256/o 0

0,098 1.0

im/o

0.100

0

1.0

125/O 0

0,069 1.0

12511 0,250

0,061 0.97

@J/l 0,417

0,079 0.96

50/l 0,667

0,078 0.96

32/l 1.06

0,075 0.95

3213 4.42

0.090 0.95

3215 8.50

0,029 0.95

12cnto 3203

430/o 0

0,099 1.0

260/O 0

0,635 1.0

2WO 0

0,074 1.0

MO/l 0,188

0.083 0.95

12511 0,281

0,088 0.95

12513 1.13

0,119 0.95

69/3 1.75

0,106 0.95

5013 2,76

0,112 0.95

5015 538

0,047 0.95

50/10 12.9

0,042 0.95

3201to 10000

450/o 0,010

0,059 0.96

315/o 0,010

0,076 0.97

315/l 0,110

0,091 0.96

200/l 0,180

0.697 0.95

200/3 0,690

0,120 0.95

2cKr/5 1.32

0,061 0.95

125/5 2.12

0,056 0.95

8015 332

0,056 0.95

80110 7.92

0,056 0.95

80/18 16.1

0,041 0.95

10 001 to 35000

500/o 0,009

o.OKJ 0.96

500/l 0,071

0,069 0.95

315/l 0,111

0,094 0.95

31513 0,437

0,123 0.95

315/5 0,834

0,066 0.95

315/10 1.97

0,080 0.95

2al/lO 399

0,069 0.95

125,'lO 0,077 0.95 5.01

125/18 10.2

0,069 0.95

60118 16.1

0,041 0.95

36001to 150000

800/l 0,044

0,090 0.95

500/l 0,071

0,090 0.95

50013 0,273

0,128 0.95

500/5 0,524

0,665 0.95

500/10 1.23

0,083 095

500118 2.50

0,086 0.95

315/18 3.99

0,077 096

260/18 6,31

0,078 0%

125118 lo,2

0,069 0.95

80/18 16.1

0.04~ 0.95

1156cQ1to

am/l 0,044

0,091 095

0,170

80013

0,118 0.96

609/5 0,328

0,060 0.95

&Xl/10 0,771

0,075 0.95

800118 1.56

0,062 0.95

500/18 2,x

0,096 0.95

315118 399

0,077 0.95

266118 6.31

0,078 0.95

125118 10.2

0,069 0.95

0.041 0.95

1250/3 0,109

0,129 0.95

1250/5 0,209

0,066 0,s

1250/10 0.089 0,494 0.95

1250/18 0,090 0.95 1.00

800118 1.56

0,082 0.95

503/18 2.50

0.086 0.95

315/18 399

0,077 0.95

2@3/18 6.31

0,078 0.95

125/18 10.2

0,069 0.95

80/18 16.1 ____~ 60118 16.1

500 WO >500000

1) Thestated probabilityofacceptanceisthe maximumforlotsoflimiting qualityinthesizerangeandthe hypergeometric distribution. The producer’s risk is (p, PJ, the consumer’s risk point is (LQ. PLQ). 21

No lot in this size range can be of limiting quality since this implies a fractional

minimumforlotswith

number of nonconforming.

percentnonconformingp.

0,041 0.95

These probabilities are based on the

2500 (Part 3) : 1995

IS IS0

: 1992

2859-2

Table

D2 -

Selected

hypergeometric

A sample of size n is drawn from a lot containing

data

R nonconforming

for OC cur&s

for zero acceptance

items. The lot is accepted

if there are nonconforming

sample (AC = 0). the probability of acceptance for the lot (fs) is shown below for the minimum range and the various sampling plans “n/O” (printed in bold type).

1,25

3.15

LO

R 0 1 2 3 4 5 6 6

Lot size

Lot size

Lot size

601

lax

501

1200

501

12a

501

1m

pa

pa

Pa

Pa

pa 1.00 0.66 0.44 0.29 O,ul 0.05 0.00 0.w

pa l.Oc 0.86 0.74 0.63 0.40 0.34 0.10 0.05

pa l.Gu 0.75 0.56 0.42 0.10 0.05 0.00 0.W

pa 1.00 0.90 0.80 0.72 0.41 0.33 0.11 0.05

1.00 0.24 0.06 0.01 0.00 0.00 0.00 0.00

1.00 0.66 0.47 0.32 0.22 0.15 0.10 0.05

R 0 1 2 3 4 5 10 13

430/Q

0 1 2 3 5 7 16 21

1201

32ul

pa

pa

1.00 0.64' 0.41 0.26 0.11 0.04 0.00 0.00

1.00 0.67 0.75 0.65 0.49 0.36 0.10 0.05

R 0 1 2 3 9 11 25 33

R 0 1 2 3 6 10 20 27

5.0

1201

3200

Pa

Pa

3201

1000

pa

pa

1,ccl 1.00 0.77 0.91 0;59 0.63 .0.45 0.76 0.09 0.44 0.05 0.36 0.00 0.10 0.00 0.05

12013m pa 1.00 0.63 0.69 0.56 0.09 0.05 0,Ou 0.W

1.00 0.66 0.74 0.63 0.10 0.05 0.00 0.00

1.M) 0.96 0.91 0.67 0.50 0.40 0.10 0.05

3201

0 1 2 3 22 29 72 93

Pa

R

pa 1.00 0.94 0.m 0.62 0.43 0.36 0.10 0.06

0 1 2 3 4 6

1.00 0.90 0.81 0.73 0.10 0.05 0.00 0.00

Pa 1.00 0.97 0.94 0.91 0.49 0.39 0.10 0.05

!iOO/O Lot size

10001 3500 R 0 1 2 3 45 58 El 06

pa 1.00 0.95 0.90 0.66 0.10 0.05 0.00 0.00

pa 1.00 0.99 0.97 0.93 0.52 0.43 0.10 0.05

6t 0 1 2 3 4 5 6 7 -r-

91

150

pa 1.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00

pa 1.00 0.40 0.16 0.06 0.02 0.01 0.00 0.00

Pa

R

16

25

P,

Pa

0 1 2 3 4

1.00 0.32 0.09 0.02 0.01

0 1 2 3 4

1.00 0.19 0.03 0.00 0.00

1.00 0.46 0.22 0.10 0.04

z 7

0.00 i.:

6 5 7

0.00 0.00

0.01 0.M)

Lot size

R 0 1 2 3 4 5 6 7

Lot size

16

25

Pa 1.00 0.44 0.16 0.06 0.02 0.00 0.00 0.00

Pa 1.00 0.64 0.40 0.24 0.14 0.m 0.05 0.02

1

16

25

R 0 1 ;

"a 1.00 0.63 $;

Pa 1.a 0.71 ;;

4 5 7 9

0:12 0.06 0.01 0.00

0.3 0.z 0.11 OS?!

,:

10/O

6/O

Lot size

Lot size

Lot size

Lot size

Lot size

26

50

pa pa Ei 0:19 0.08 0.03

0.01 0.00

0.00

R 0 1 2 3 4 5 6 7

pa 1.00 0.15 0.02 0.00 0.00 0.00 0.00 0.00

50 Pa 1.00 0.56 0.31 0.17 0.09 0.05 0.02 0.01

2% R 0 1 2 3 4 5 6 6

Pa 1.00 0.42 0.17 0.06 0.02 0.01 0.00 0.00

50 "a 1.00 0.70 0.49 0.33 0.23 0.15 0.10 0.04

26 R 0 1 2 3 4 6 9 12

Pa 1.00 0.62 0.37 0.22 0.12 0.03 0,Ou 0.00

50 Pa lsm 0.80 0.64 0.50 0.40 0.24 0.11 0.05

26 R 0 1 2 3 7 9 15 19

Pa 1.00 0.77 0.56 0.44 0.12 0.05 0.00 0.00

50 Pa 1.a o,tii 0.7 0.61 0.31 0.a 0.v o,o!

44/o

34/Q

24/O

16/O

IO/O

610

Lot size

Lot size

Lot size

Lot size

Lot size

Lot size

Lot size

51

90

pa 1.00 0.02 0.00 0.00 0.00 0.00 0.00 0.00

pa 1.00 0.44 0.19 0.08 0.04 0.01 0.01 0.00

R 0 1 2 3 4 5 6 7

Lot size

R 0 1 2 3 4 5 6 7

Pa

Lot size

60/o

51

90

pa 1.00 0.14 0.M 0.00 0.00 0.00 0.00 0.00

pa 1.00 0.51 0.26 0.13 0.06 0.03 0.02 0.01

R 0 1 2 3 4 5 6 7

am

Lot size

25

15/O

7

R 0 1 2 3 4 5 6 7

16

22/o

s

1om

12.5 13/o

2610 26

Lot size

R

R

Lot size !7 0 1 2 3 13 16 35 46

8,‘J 17/Q Lot size

20010

315/o

Lot size

0 1 2 3 15 20 50 65

0 1 2 3 6 7 15 19

Lot size

46010

p

1.00 0.79 0.62 0.49 036 0.30 0.09 0.04

260/o

Lot size

fz

1.00 0.49 0.24 0,12 0.06 0.03 0.w 0.w

Is

items in the

lot sizes in the lot size

I

125/o Lot size

and maximum

tquality (LQ)

Limiting

W3

plans

91

150

pa 1.00 0.12 0.01 0.00 0.00 0.00 0.00 0.00

pa 1.00 0.47 0.22 0.10 0.05 0.02 0.01 0.00

Lot size

R 0 1 2 3 4 5 6 7

91

150

pa 1.00 0.40 0.15 0.06 0.02 0.01 0.00 u,Gu

pa 1.00 0.63 0.40 0.25 0.16 0.10 0.06 0.04

18

R 0 1 2 3 4 5 6 10

51

90

pa 1.00 033 0.11 0.03 0.01 0.00 0.00 0.00

pa 1.00 0.62 0.36 0.24 0.14 0.09 0.05 0.03

R 0 1 2 3 4 5 7 9

51

90

pa 1.00 0.53 0.26 0.14 0.07 0.03 0.01 0.00

pa 1.00 0.73 0.54 0.39 0.26 0.20 0.10 0.05

R 0 1 2 3 6 6 11 14

51

90

pa 1.00 0.69 0.47 0.31 0.09 0.04 0.01 0.00

pa 1,oo 0.62 0.67 0.55 0.30 0,lS 0.10 0.05

38/Q

26/O

16/O

Lot size

Lot size

Lot size

91

150

pa 1.00 0.56 0;34 0.19 0.11 0.06 0.01 0.00

pa 1.00 0.75 ok6 0.41 0.31 0.23 0.09 0.05

R 0 1 2 3 7 6 12 15

91

150

pa 1.00 0.71 0.51 0.36 0.09 0.06 0.01 0.00

Pa 1.00 0.63 0.66 0.56 0.26 0.21 0.09 0.05

R 0 1 2 3 10 13 17 27

R 0 1 2 3 10 12 16 22

51

90

Pa 1.00 0.80 0.64 0.51 0.09 0.05 0.01 0.00

Pa

1.00 0 0.99 1 0.79 2 0.70 3 0.29 12 0.22 15 0.09 22 0.05 27

13/O

91

150

Pa 1.00 0.60 0.64 0.51 0.10 0.w 0.02 0.00

Pa 1.00 0.66 0.77 0.66 0.27 0.16 0.10 0.05

Lot size .Sl R 0 1 2 3 14 17 23 30

Pa 1.00 0.55 0.73 0.63 0.10 0.05 0.02 0.00

R

150 Pa 1.00 0.91 0.63 0.76 0.26 0.20 0.10 0.05

51

90

Pa

f'.

1.00 0.84 0.71 0.59 0.10 0.05 0.01 0.00

l.ln 0.9 0,K 0.7! 0.x 0.2 O,l( O,O!

IS 2500 (Part 3) : 1995 ISO 2859-2 : 1992

Table

D2 -

Selected

hypergeometric

data

for OC curves

Limiting 0.5

R

R

0

1 2 3 4 5 6 7

pa 1,al 0.00 0,Gu 0,Gu 0.00 0.00 0.00 0.00

1,25

2.0

3,15

5,O

8.0

12,5

130/o

95/O

65/O

42/O

20/O

M/O

Lot size

Lot size

Lot size

Lot size

151

260

151

280

151

280

151

2&l

pa

"a

Pa

Pa

Pa

pa

pa

"a

R

R

1.00 0.14 0.00 0.02

1,oo 0.54 0.15 0.29

0 1 3 2

1.00 0.37 0.06 0.14

1.00 0.66 0.29 0.44

0 1 3 2

1.00 0.57 0.18 0.32

1.00 0.77 0.45 0.59

0 1 2 3

4 5 6 7

0.02 0.01 0.00 0.00

4 5 6 7

0,GlJ 0.00 0.00 0.00

0.09 0.04 0.02 0.01

4 5 6 7

0.02 0.01 0.00 0.M)

0.19 0.12 0.09 0.05

4 5 9 11

0.10 o,ce 0.01 0.00

0.35 0.26 0.09 0.05

7 9 14 18

500 Pa

R

0 1 3 2

220/O

1.00 0.44 0.19 0.08 0.04 0.02 0.01 0.00

R

R 0 1 2 3 4 5 6 7

105/O

Lot size

Lot size

151

280

151

280

Pa

Pa

Pa

Pa 1,oo 0.90 0.61 0.73 0.31 0.22 0,lO 0,05

1.00 0.72 0.52 0.37 0.10 0.05 0.01 0,oO

l,oo 0.65 0.72 0.61 0.32 0.23 0.10 0.05

80/O

50/O

Lot size

Lot size

Lot size

Lot size

Lot size

261

261

281

261

500

pa

Pa 1.00 0,64 0.71 0.59 0.29 0.21 0.10 0.05

Pa 1.00 0.22 0.05 0.01 OSQ 0.00 0.00 0.00

155/o

5al P, 1.00 0.56 0.31 0.17 0.10 0.05 0.03 0.02

R 0 1 2 3 4 5 6 6

Pa l.oo 0.45 0.20 0.09 0.W 0.02 0.01 0.00

5co Pa 1.00 0.69 0.46 0.33 0.23 0.15 0.11 0.05

R 0 1 2 3 5 6 10 13

Pa 1.00 0.63 0.39 0.24 0.09 0.06 0.01 0.00

500 pa 1.00 0.79 0.62 0.49 0.31 0.24 0.09 0.04

R 0 1 2 3 7 9 13 17

1.00 0.72 0.51 0.36 0.09 0.05 0.01 0.00

19

(concluded)

(LQ)

O,8

1.00 0.33 0.06 0.15

Lot size

plans

17010

0 1 :

280/O

281

quality

for zero acceptance

R 0 1 3 2 11 14 21 27

l,oo 0.61 0.66 0.54 0.10 0.05 0.01 0.00

32/O Lot size

261

5cm

R

P,

Pa

R

261

Pa

mo

Pa

0 1 2 3 12 15 21 26

l.oo 0.62 0.66 0.55 0.09 0.05 0.01 0.00

1.00 0.90 0.61 0.73 0.28 0,20 0.10 0.05

0 1 2 3 18 24 33 43

1.00 0.69 0.76 0.69 0.11 0.05 0.01 0.00

1.00 0.94 0.66 0.62 0.30 0.x) 0.10 0.05

20,o

Lot size

R 0 1 3 2 15 20 29 36

151

280

f'a 1.00 0.67 0.75 0.65 0.11 0.05 0.01 0,OO

Pa 1.00 0.93 0.66 0.80 0.32 0.22 0.10 0.05

32,0

IS IS0

2500

(Part

2859-2

3) : 1995 : 1992

Table Type

D3 -

l-

of

sampling

Equivalent

E

F

13

20

1st

8

13

2nd

16

26

Single

Multiple

sizes for single,

Sample size code letter

plan

Double

sample

1st

3

5

2nd

6

10

3rd

9

15

4th

12

20

5th

15

25

6th

18

30

7th

21

35

G

double

and cumulative

and multiple sample

sampling

plans

sizes 1’ in accordance

--

M

N

with

H

J

K

32

50

80

125

200 -__

315

500

800

20

32

50

80

125

200

315

500

40 __-

64

100

160

250

400

630

I

L

IS0

P

1000

1

2959/l

Q 1250 800 1600

R zoo0 1250 2500

8

13

20

32

50

80

125

200

315

560

16

26

40

64

100

160

250

400

630

1 000

24

39

60

96

150

240

375

600

945

1 500

32

52

80

128

200

320

500

800

1 260

2 000

40

65

100

160

250

406

625

1 000

1 575

2500

46

78

120

192

300

460

750

1 200

1890

3000

56

91

140

224

350

560

875

1 400

2 205

3 500

1) For double and multiple sampling pians, the tabulated entries are the cumulative sample sizes. In each case the successtve stages ot sampkng take a fresh sample equal in size to that taken in the first stage. This sample is aggregated with the samples from previous stages and the combined sample is then tested by the criterion in table 04

Table

D4 -

Equivalent

numbers

for single,

double

and multiple

sampling

plans

Approximate relative sample sizes at each stage” n

Type of sampling plrin

Single

!

Double

I

Multiple

Discrimination

acceptance

ratio

I

(Procedure

B) P,,lP9,

Probability

of acceptance

(Procedure

BI

1

1

2

3

4

18

0,63

0

2

1

4

9

14

0.63

1

2

4

5

23

24

0.25

31

2

31

3

31

4

0

5

1

8

0,25

3)

2

0

3

1

5

3

8

6

12

19

0,25

0

2

1

4

2

6

6

10

11

17

0,25

0

3

2

5

3

7

8

13

16

22

0,25

1

3

3

6

5

8

11

15

22

25

0.25

1

3

4

6

7

9

14

17

27

29

0.25

2

3

6

7

9

10

18

19

32

33

at AQL

1)

These relative samples are approximate

2)

This acceptance

3)

Acceptance

only. The exact values are given in table D3 for each sample size code letter.

number is only used in procedure

of the lot is not permitted

A.

on the samples examined.

20

IS 2500 (Part 3) : 1995 IS0

Table

D5 -

Correspondence

between

(Inspection

code letter11

to 90

13

91 to 150

13

151 to 280

20

281 to 500

32

501 to 1 200

50

1 201 to 3 200

80

2

AQL

values

in IS0

I and II, procedure AQL

Sample size

Use

Lot size

lot sizes, levels

values

2669/l

2859-2

: 1992

and LQ values

Bl in IS0 2959/l

for limiting

Lilmiti ng quality

1 -

:3,i! j,( i - -

qualities

lLQl2’

ILQI 1 -8S

12,5

I

20.0

I

32.0

4.0

2.5

6.5

1.5

4.0

6.5

1.0

2,5

4.0

10.0

1.5

2.5

6.5

t

‘I

1 0.65

t 3 201 to 10 000

4

0.40

1.0

1.5

0.25

0.65

1.0

2.5

0.15

0.40

0.65

1.5

0.25

0.40

l,O

125

1 10 001 to 35 000

200

4.0 t

T 35001

to 15Oooo

150061

t0500000

315

1500

0.10

,

1 >500006

1,065

800

1250

),lO

2000

1.10

0.15

0,25

0.65

+

1)

The correspondence

between

re and sample size is determined

head of the arrow corresponding

given inspection

by the inspection level. The sample size code letter to use is indicated by the

level, usually up one row for level

I and

down one row for level Il.

2’ When no AQL value appears in the table for a selected code letter and LQ value, an arrow will indicate that the sample size has to be increased if it points downwards and decreased if it points upwards. The sample size and AQL value to be used correspond to the entrv at the head of the arrow When thus sample size is greater than the lot size all items in the lot have to be inspected.

Table

Lot size

D6 -

Correspondence (Inspection levels Special S-l and S-2

2 to 90 91 to 150

E E

151 to 280 281 to 500

E E

501 to 1200 1201 to3200

E E E

3 201 to 10 000 10 001 to 35 000 35001 to150000 150001

to500000

>500000

I

between lot sizes and sample size code S-l to S-4 and I to III, procedure B)

inspection s-3

levels

I

E E E E E E F

E E

G

E E

G H

General

inspection

s-4

I

E E

E E

E F

E E

E F

G H

F

G H J K

J K L M

L M

N P

N

Q

G G H

F

I

letters

J J K

II

levels

I

III F G H J K L M N P 0 R

NOTE - The sample size code letter indicates the appropriate row in table D5; it does not always indicate the sample size to be used directly since this can depend on the limiting quality. Levels S-l and S-2, for example, give sample sizes independent of lot size but dependent on limiting quality. ranging from 13 to 800.

21

Bureau

of Indian

\

Standards

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Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewed periodically; a standard along with amendments is reaffirmed when such review indicates that no changes are needed; if the review indicates that changes are needed, it is taken up for revision. s of Indian Standards should ascertain that they are in possession of the latest amendments or edition by referring to the latest issue of ‘BIS Handbook’ and ‘Standards Monthly Additions’. This Indian Standard has been developed from Dot: No. MSD 3 (106) Amendments

Issued Since Publication

Date of Issue

Amend No.

Text Affected

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