BASIC CONCEPT OFACCEPTANCE SAMPLINGFOR ATTRIBUTES

Prepared By

Joseph E. KenolJoseph E. Kenol

ASQ North Jersey Chapter, Programs Committee Chair

The content of this handout is consistent with theAmerican National Standard ANSI/ASQC Z1.4

Acceptance SamplingBackground

Acceptance sampling is an important field ofstatistical quality control that was popularizedby Dodge and Romig and originally appliedby the U.S. military to the testing of bulletsduring World War II

If every bullet was tested in advance, nobullets would be left to ship. If, on the otherhand, none were tested, malfunctions mightoccur in the field of battle, with potentiallydisastrous results

Acceptance SamplingBackground (Cont…)

Dodge reasoned that a sample should bepicked at random from the lot, and on thebasis of information that was yielded by thesample, a decision should be made regardingsample, a decision should be made regardingthe disposition of the lot

In general, the decision is either to accept orreject the lot. This process is called LotAcceptance Sampling or just AcceptanceSampling

Acceptance SamplingBackground (Cont…)

The acceptance sampling techniqueswere adopted in 1971 by the AmericanNational Standards Institute as ANSINational Standards Institute as ANSIStandard Z1.4 and in 1974 it wasadopted (with minor changes) by theInternational Organization forStandardization as ISO Std. 2859

Acceptance Sampling

Acceptance Sampling is used to determine whetherto accept or reject a lot of material that has alreadybeen produced

A lot is defined as a quantity of product accumulated A lot is defined as a quantity of product accumulatedunder uniform conditions. For example, one shift’sproduction from a machine could be considered as alot

Acceptance Sampling can be thought of as “end-of-line” inspection

When Does AcceptanceSampling Make Sense?

When testing is destructive

When the cost of 100% inspection is too high

When doing 100% inspection would take too long When doing 100% inspection would take too long

When using new suppliers

When new products are produced

When current supplier is in question

When testing entire lot could be harmful

Sampling InspectionTerminology

Inspection by Attributes

Lot or Batch

Sample

Type of Sampling Type of Sampling

Random Sampling

Nonconforming

Nonconformity

Inspection Levels

Acceptable Quality Level (AQL)

Switching Rule

Inspection By Attributes

Inspection where an item is classified asconforming or nonconforming withrespect to a specified requirement or setrespect to a specified requirement or setof requirements (pass-fail, go-no-go)

Expression ofNonconformance

The extent of nonconformance ofproduct shall be expressed either interms of percent nonconforming or interms of percent nonconforming or interms of nonconformities per hundredunits

Nonconforming vs Nonconformity

In inspection general terms,nonconforming is considered to mean aunit that has been classified as defective,unit that has been classified as defective,where as a nonconformity is thought ofas one defect identified in a unitinspected

Lots or Batches

A collection of units accumulated underuniform conditions from which a sample is tobe drawn and inspected to determineconformance with the acceptability criteriaconformance with the acceptability criteria

A Lot or Batch can also be considered to bethe population in acceptance sampling

Sample

A sample is considered to be a subsetof the lot or the population

We determine the disposition of a lot (lotsentence) based on the examination ofthe sample

Random Sampling

Technique for selecting samples from a givenpopulation of units where every member of thepopulation is equally likely to be in the sample

Samples selected randomly are more likely torepresent the entire population

For the sampling to be statistically valid, the samplemust be randomly selected from the population or lot

3 Types of Sampling Plans

Single: In accordance with Tables IIA,B, and C

Double: In accordance with Tables IIIA,Double: In accordance with Tables IIIA,B, and C

Multiple: In accordance with Tables IVA,B, and C

Single Sampling Plan

The number of sample units inspected shallbe equal to the sample size given by the plan

A decision for accept or reject lot shall bemade in accordance with Table IIA, B, or Cdepending on chosen inspection level (LevelII Normal, Level III Tightened, and Level IReduced)

Double Sampling Plan

If the number of nonconforming units in the first sample isless than or equal to the first acceptance number, accept thelot

If the number of nonconforming falls between the accept andreject numbers in the table, select another sample per thetable

Combine the number of nonconforming units found in the 2samples

Accept the lot if the combined nonconforming numbers isequal or less that the second acceptance number

Reject the lot if nonconforming number is equal or greaterthan second rejection number in the table

Multiple Sampling Plan

Under multiple sampling, the procedureshall be similar to that specified in thedouble sampling method, except thatdouble sampling method, except thatthe number of successive samplesrequired to reach a decision might bemore than two. See tables IVA, B, or C

Sampling Plan (Cont…)

The type of sampling used is generallyestablished by contract or designatedby the responsible internal authorityby the responsible internal authority

3 General Inspection Levels

Reduced [Level I]

Normal [Level II]

Tightened [Level III]

The level of inspection used is generallyestablished by contract or designated by theresponsible internal authority

Normal Inspection (Level II)

The use of a sampling plan with inspection level IIspecified is devised to ensure the manufacturer thatthere is a high probability of lot acceptance by theconsumer when the process average is maintained ata level higher than the AQLa level higher than the AQL

The consumer will call out this level in their samplingplan when there is no reason to suspect that theprocess average differs from an acceptable level

Level II will be used unless another inspection level isspecified

Acceptable Quality Limit(AQL)

The AQL is the maximum percent non-conforming (orthe maximum number of nonconformities perhundred units) that, for the purposes of samplinginspection, can be considered satisfactory as aprocess average

AQL does not mean “desirable level”. It is designedto encourage suppliers to have process averagesconsistently better than the AQL, otherwise there is arisk of switching to tighter inspection

The designation of an AQL does not imply that thesupplier has the right knowingly to supply anynonconforming items

AQL (Cont…)

AQL values shall not exceed 10%nonconforming

When the quality level is expressed asWhen the quality level is expressed asnumber of nonconformities (defects) per100 items, AQL values up to 1000nonconformities (defects) per 100 itemsmay be used

Tightened Inspection (LevelIII)

Level III is a sampling plan with an acceptancecriteria that is tighter than that of thecorresponding plan for normal inspection. Thislevel of inspection is usually invoked when theinspection results of consecutive lots indicateinspection results of consecutive lots indicatethat the process average might be poorer thanthe AQL

Level III inspection will be used when greaterdiscrimination is required

Reduced Inspection (Level I)

This level of inspection is generally called outin a sampling plan when a specified number ofpreceding lots were accepted, the productionprocess at manufacturer is steady, and whenprocess at manufacturer is steady, and whenapproved by the responsible internal authority

Level I inspection will be used when lessdiscrimination is required

4 Special Inspection Levels

S1, S2, S3, S4

These four additional special levels aregiven in the same tables and may begiven in the same tables and may beused where relatively small samples arenecessary for destructive or extremelycostly inspections and large samplingrisks can and must be tolerated

Inspection Levels SwitchingProcedures

Normal to Tightened: Shall be implementedas soon as 2 out of 5 (or fewer than 5)consecutive lots have been rejected onoriginal inspectionoriginal inspection

Tightened to Normal: Shall be reinstatedwhen 5 consecutive lots have beenconsidered acceptable on original inspection

Switching Rule (Cont…)

Normal to Reduced: This level of inspection isgenerally called out in a sampling plan when thepreceding 10 lots were accepted, the productionprocess at manufacturer is steady, and whenapproved by the responsible internal authorityapproved by the responsible internal authority

Discontinuation of inspection: Shall beimplemented when the number of lots not accepted ina sequence of consecutive lots on original tightenedinspection reaches 5

Reduced to Normal: Is implemented if a lot is notaccepted or irregular/delayed production

Important Points ToRemember

The purpose of acceptance sampling is to decidewhether or not the lot is likely to be acceptable, not toestimate the quality of the lot

Setting an AQL does not guarantee to the customer Setting an AQL does not guarantee to the customerthat batches of a worse quality will not be accepted orthat batches of good quality will not be rejected

If the average quality of batches being submitted area little worse than the AQL, a number of lots willprobably be accepted before a switch to tightenedinspection is called for

Important Points (Cont…)

In general the customer gets a qualitywhich is, on average, better than theAQL, since the tables are arranged toprovide an economic incentive – Theprovide an economic incentive – Themanufacturer cannot afford to havemore than a small proportion of batchesrejected so, the manufacturer will haveto improve the quality if this proportionis exceed

Sampling Plan for Inspectionby Attributes Individual items in a sample are inspected and

judged to be either acceptable or not acceptable

Information needed to create a sampling planInformation needed to create a sampling plan

Lot size (Given)

Inspection level I, II, III, S1, S2, S3, S4 (Start w/II)

AQL (Provided by contract or established byresponsible internal authority)

Type of sampling (single, double/multiple)

Example of Single SamplingPlan

A lot containing 210 units is to be inspected usingGeneral Inspection Level (II) to a 2.5% AQL. Singlesampling is to be used.

Find the lot size in Table I on next page Find the lot size in Table I on next page

Read across to General Inspection Level II

The sample size code letter is “G”

The sample size for code letter “G” can be found inTable IIA (32 units)

Find the column for 2.5% AQL at the top of Table IIA

We can accept the lot if 2 or fewer are not acceptable

We should reject the lot if 3 or more are notacceptable

Applicable and ReferencedCharts

Copies of all charts and tables from thestandard referenced in this package willstandard referenced in this package willbe provided as hand outs