acceptance sampling types training

Besterfield: Quality Control, 8th ed.. © 2009 Pearson Education, Upper Saddle River, NJ 07458.All rights reserved

QualityQuality Control Control

Chapter 10- Chapter 10- Acceptance Sampling Acceptance Sampling

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OutlineOutline

Lot-by-lot acceptance sampling plans for attributes

Acceptance sampling plans for continuous production

Acceptance sampling plans for variables


Learning ObjectivesLearning Objectives

When you have completed this chapter you should be able to:

Determine the sampling plan using ANSI/ASQ Z1.4.

Know the switching rules for ANSI/ASQ Z1.4. Categorize the various sampling plan

systems in terms of lot-by-lot, continuous production, attributes or variables.


Learning Objectives-cont’d.Learning Objectives-cont’d.


Describe the various sampling plan systems and know their function (advantages, disadvantages, purpose etc.).

Determine the sampling plan using the Dodge Romig Tables

Construct the OC Curve for a chain sampling plan.


Learning Objectives-cont’d.Learning Objectives-cont’d.


Be able to use the Shainin Lot Plot Method. Determine the sampling plan ANSI/ASQ S1 Determine whether a lot is accepted or

rejected using ANSI/ASQ Z1.9


Lot-by-Lot Acceptance Lot-by-Lot Acceptance Sampling Plans for AttributesSampling Plans for Attributes

Devised in 1942 at Bell Labs Later became MIL-STD-105E ISO-2859 ANSI/ASQ Z1.4

Wording & terminology changesAdditional tables added


ANSI/ASQ Z1.4ANSI/ASQ Z1.4 This standard is applicable to:

End itemsComponents and raw materialsOperationsMaterials in processSupplies in storageMaintenance operationsData or records


ANSI/ASQ Z1.4ANSI/ASQ Z1.4 Intended to be used for a continuing series of lots, but may be designed for isolated lots.

Standard provides for single, double, and multiple sampling plans.

Provision is also provided for normal, tightened, or reduced inspection.

Plan is specified by the AQL, and sample-size code.


ANSI/ASQ Z1.4ANSI/ASQ Z1.4 Normal inspection is used at the start of

inspection with changes being a function of recent quality history.

Tightened inspection:Generally used when producer’s recent

quality history has deteriorated.


ANSI/ASQ Z1.4ANSI/ASQ Z1.4

Reduced inspection:Used when the producer’s recent

quality history has been exceptionally good.

Decision concerning what type of plan to use is left to the responsible authority.

Nonconformities are classified such as critical, major…


Sample Size Code LettersSample Size Code Letters


Comparison of Inspection Comparison of Inspection levelslevels

III

1086

Percent Nonconforming (100Pa)

100

95

80

60

40

20

0

100=10

= 0.05

Perc

ent o

f Lot

s Ac

cept

ed (1

00P a

)

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II I

I = 1/2 nII = nIII = 2n


ANSI/ASQ Z1.4ANSI/ASQ Z1.4ANSI/ASQ Z1.4ANSI/ASQ Z1.4

AQLAQLThe AQL is the most important part of the

standard since the AQL and sample size dictate the plan used.

AQL is defined as the maximum percent nonconforming that can be considered satisfactory as a process average.Satisfactory = Producer’s risk, αUsually 0.05



AQLAQLAQL is specified by contract or responsible authority.

AQL may be determine from historical data, empirical judgment, engineering information, experimentation, producer’s capability, consumer’s requirements.



AQLAQL AQL is specified by contract or responsible

authority.AQL may be determine from historical

data, empirical judgment, engineering information, experimentation, producer’s capability, consumer’s requirements.

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Sample SizeSample SizeDetermined by lot size and

inspection levelUse of sample-size code

Inspection level is determined by the responsible authority.

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ANSI/ASQ Z1.4ANSI/ASQ Z1.4 Sample SizeSample Size

Different levels of inspection provide approximately the same protection to the producer, but different protections to the consumer.

Plan provides for “special” levels to be used where relatively small sample sizes are necessary and large sampling risks must be tolerated. (S-1, S-2, S-3, S-4) 18


Implementation

Determine lot sizeDetermine inspection levelFind sample-size code letter in tableDetermine AQL


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Implementation cont’d.

Determine type of sampling planFind sampling plan in appropriate

tableStart with normal inspection and

change to tightened or reduced based on switching rules


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What an AQL means is that as long as a supplier maintains his/her process average (% defective) at the assigned AQL or lower, there is a very high probability that shipments from that supplier, when inspected using ASQ Z1.4 sampling plans, will be accepted.

AQLAQL

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By the same token, there is a very high probability that shipments, when inspected using ASQ Z1.4 sampling plans, will be rejected if a supplier's process average (% defective) remains higher than the assigned AQL.

AQLAQL

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Single sampling plans

Start by identification of AQL, lot size, inspection level, and type of sampling plan.

Locate appropriate plan parameters in tables.

Double and Multiple Sampling

Similar procedures as single sampling


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Normal, Tightened, and Reduced Inspection Start with normal inspection

Switching Procedures Normal to tightened

Institute when 2 out of 5 consecutive lots not accepted on original inspection

Tightened to normalInstitute when 5 consecutive lots acceptedIf not, then discontinue inspection under this

plan


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Switching ProceduresNormal to reduced

Institute when: (all of the following)Preceding 10 lots on normal inspection

have been acceptedTotal nonconforming in preceding 10

samples is less than number identified in Table 10-5.

Production is at a steady rateReduced inspection is considered

desirable by responsible authority


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Switching ProceduresSwitching Procedures Reduced to normalReduced to normal

Institute when: (any of the following)Institute when: (any of the following)A lot is not acceptedA lot is not acceptedSampling procedure terminates with Sampling procedure terminates with

neither acceptance or rejection criteria neither acceptance or rejection criteria have been methave been met

Production is irregular or delayedProduction is irregular or delayedOther conditionsOther conditions


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Standard is designed for use where units of product are produced in a continuing series of lots or batches.

If a sampling plan is desirable for a lot or batch of an isolated nature, it should be chosen based on the Limiting Quality (LQ) and consumer’s risk, b. These tables are included in the standard,

but not the textbook. Or use ANSI/ASQ Standard Q3


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Standard is used for inspection of isolated lots by attributes.

Provides indexed tables by Limiting Quality, LQ.

ANSI/ASQ Standard Q3ANSI/ASQ Standard Q3

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Two Schemes:

1. Used for lots that are isolated or mixed or that have an unknown history as far as all parties know.

Lot size and LQ must be known.Nominal values of the LQ are based on b=0.10


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Two Schemes:

2. Used when a vendor is producing a continuous stream of lots and sends one or a few to a customer who will consider them as isolated lots.

Occurs frequently when purchasing small quantities of raw materials.


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A set of inspection tables for lot-by-lot A set of inspection tables for lot-by-lot acceptance sampling by attributes.acceptance sampling by attributes.

Tables are based on Limiting Quality (LQ) Tables are based on Limiting Quality (LQ) and Average Outgoing Quality Limit (AOQL).and Average Outgoing Quality Limit (AOQL).

Tables for single and double samplingTables for single and double sampling Advantage that the plan provides a Advantage that the plan provides a

minimum amount of inspection for a given minimum amount of inspection for a given inspection procedure.inspection procedure.

Desirable for in-house inspectionDesirable for in-house inspection

Dodge-Romig TablesDodge-Romig Tables

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Limiting Quality – LQ Based on the probability that a particular

lot, which has percent nonconforming equal to the LQ, will be accepted.Probability is the consumer’s risk, β =

0.10LQ plans give assurance that

individual lots of poor quality will rarely be accepted..


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Observations about the LQ tables:

As the lot size increases, the relative sample size decreases.

The tables extend until the process average is one-half of the LQ.

As the process average increases, a corresponding increase occurs in the amount inspected.


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Average Outgoing Quality Limit – AOQL

Applicable when the inspected lot is a convenient subdivision of a flow of product for materials handling purposes (non-homogeneous)

AOQL plan limits the amount of poor outgoing quality on an average basis, but gives no assurance on individual lots.


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Process average Obtained by the same techniques as for p-

chartsFirst 25 lots the average percent

nonconforming is obtained

Type of nonconformance Dodge-Romig tables do not provide for

different categories or tightened inspectionDifferent LQ or AOQL values may be used


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A special type of lot-by-lot acceptance sampling plan for attributes designated as “Chain Sampling Plan ChSP-1”.

Applicable to quality characteristics which involve destructive or costly tests.Use of small sample sizesAcceptance number, c=0

Poor shape of OC curve at the producer’s risk

Chain Sampling Inspection PlanChain Sampling Inspection Plan

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Chain sampling uses the cumulative results of several samples

Determination of the value of i, the number of previous samples, is determined by analysis of the OC curves for a given sample size.

Chain Sampling Inspection Chain Sampling Inspection PlanPlan

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Procedure:

For each lot, select a sample of size n and test each for conformance to specifications.


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Procedure: If the sample has 0 nonconforming

units, accept the lot; if the sample has 2 or more nonconforming units, do not accept the lot; and if the sample has 1 nonconforming unit, it may be accepted provided that there are 0 nonconforming units in the previous

i samples of size n.


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n=5n=5c=0c=0 LastLast LotLot

Second-Second-to-Lastto-Last

LotLot

i previous lotsi previous lotsCurrent LotCurrent Lot

Accept if 0 Nonconforming UnitsAccept if 0 Nonconforming Unitsin in n =5n =5 or if or if 11 Nonconforming Unit Nonconforming Unit

&& Zero Nonconforming Units in Zero Nonconforming Units in iiPrevious LotsPrevious Lots

Chain Sampling DiagramChain Sampling Diagram

Figure 10-4 Chain Sampling Diagram

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Conditions for use of the Chain Sampling Plan:

1.1. The lot should be one of The lot should be one of continuing series of product that continuing series of product that is sampled in substantially the is sampled in substantially the order of productionorder of production

2.2. The consumer can normally The consumer can normally expect the lots to be essentially expect the lots to be essentially the same quality.the same quality.


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Conditions for use of the Chain Sampling Plan:

3.3. The consumer has confidence in the The consumer has confidence in the producer not to occasionally send an producer not to occasionally send an unacceptable lot that would have unacceptable lot that would have the optimum chance of acceptance.the optimum chance of acceptance.

4.4. The quality characteristic is one that The quality characteristic is one that involves destructive or costly tests.involves destructive or costly tests.


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Used for costly or destructive tests Subgroup size of 1 – item by item plan

Sequential sampling is similar to multiple sampling, except sequential sampling can, in theory, continue indefinitely. In practice, the plan is truncated after the

number inspected is equal to three times the number inspected by a corresponding single sampling plan.

Based on the Sequential Probability Ratio Test

Sequential SamplingSequential Sampling

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Sequential Sampling PlanSequential Sampling Plan

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Sequential Sampling PlanSequential Sampling Plan

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Designated SkSP-1 and based on AOQL.Designated SkSP-1 and based on AOQL. A single sampling plan for minimizing A single sampling plan for minimizing

inspection costs when there is a inspection costs when there is a continuing supply of lots of raw continuing supply of lots of raw materials, component parts, materials, component parts, subassemblies, and finished parts subassemblies, and finished parts from from the same sourcethe same source..

Applicable to chemical and physical Applicable to chemical and physical characteristics that require laboratory characteristics that require laboratory analysis.analysis.

Skip Lot SamplingSkip Lot Sampling

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When i consecutive lots areWhen i consecutive lots arefound to be conformingfound to be conforming

Begin by inspecting every lotBegin by inspecting every lot

Discontinue inspection of every lotDiscontinue inspection of every lotInspect a fraction, f, of the lotsInspect a fraction, f, of the lots

In a random mannerIn a random mannerWhen an inspected lot is found When an inspected lot is found

nonconformingnonconforming

Procedure for SkSP-1 PlansProcedure for SkSP-1 Plans

Figure 10-7 Procedure SkSP-1 plans 47


Provides procedures to reduce the inspection effort when the supplier’s quality is superior.

A skip-lot scheme used in conjunction with attribute lot-by-lot plans given in ASQ Z1.4

ANSI/ASQ S1ANSI/ASQ S1

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Requirements to use ANSI/ASQ S1

1. Have a documented system for controlling product quality and design changes

2. Have instituted a system that is capable of detecting and correcting changes that might adversely affect quality.

3. Not have experienced an organizational change that might adversely affect quality


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Additional requirements of the product:Be of stable designHave been manufactured on a continuous

basis for at least 6 months unless agreed to a longer period.

Have been on normal and reduced inspection during the qualification period.

Have maintained a quality level at or less than the AQL for at least 6 months.


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Other:The previous 10 or more consecutive lots

have been acceptedThe min cumulative sample size for the last

10 or more consecutive lots have been met.The acceptance numbers for the last 2 lots

have been met


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Sampling for Continuous Sampling for Continuous ProductionProduction

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Acceptance sampling for continuous production implies that manufacturing operations do not create lots as part of the normal part of the production process.

Parts are produced by a continuous process on a conveyor or similar system..


Plans for continuous production consist of alternating sequences of sampling inspection and screening (100%) inspection.Plans begin with 100% inspection and

convert to sampling after a stated number of items are free of nonconformities.

Sampling continues until a stated number of nonconforming units are found, at which time 100% inspection in reinstated.

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Applicable to attribute, nondestructive inspection of moving product.

Inspection should be easy and rapid Process must be capable of

manufacturing homogeneous product


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Developed by Dodge

CSP-1, CSP-2, CSP-3Later, MIL-STD-1235B


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CSP-1

Begins with 100% inspection of the product in the order of production until a certain number of successive units are free of nonconformities.

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CSP-1

Sampling inspection is then instituted

Samples are selected in such a manner as to minimize any bias

If a nonconformity occurs, sampling is discontinued and 100% inspection begins..


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The Screening Crew Inspects 100% of the Units

When i Consecutive Units Are Found Free ofNonconformities Concerned,

The Screening Crew is Released from 100% Inspectionand the Sampling Inspector Inspects a Fraction, f, ofthe Units, Where the Sample Units are Selected in aRandom Manner.

When the Sampling Inspector Finds One of theNonconformities Concerned,

Start

CSP-1 and CSP-F PlansCSP-1 and CSP-F Plans

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Standard is composed of five different continuous sampling plans.

Designated by code letters

MIL-STD-1235BMIL-STD-1235B

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Inspection is by attributes for nonconforming units using three classes of severity:

CriticalMajorMinor

Each of the plans incorporates a provision for discontinuance of inspection

MIL-STD-1235BMIL-STD-1235B

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Shainin Lot Plot ANSI/ASQ Z1.9-2003

Acceptance Sampling Plans Acceptance Sampling Plans for Variablesfor Variables

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Shainin Lot Plot

Random sample of 10 subgroups of 5 each

Find average and rangeConstruct a histogramCalculate Xdouble bar, R barCalculate ULL and LLLCompare to lot plots in Figure 10-15


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ANSI/ASQ Z1.9-2003 Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming is an acceptance sampling system to be used on a continuing stream of lots for Acceptance Quality Limit (AQL) specified.



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ANSI/ASQ Z1.9-2003 provides tightened, normal, and reduced plans to be used on measurements which are normally distributed. Variation may be measured by sample standard deviation, sample range, or known standard deviation. It is applicable only when the normality of the measurements is assured.

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