acceptance sampling - besterfield

7/25/2019 Acceptance Sampling - Besterfield

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Besterfield: Quality Control, 8thed.. 2009 Pearson Education, Upper addle !i"er, #$ 0%&'8.

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QualityQualityControlControl

Chapter 9- Lot-by-LotChapter 9- Lot-by-Lot

Acceptance SamplingAcceptance SamplingBy AttributesBy AttributesPowerPoint presentation to accompanyPowerPoint presentation to accompany

BesterfeldBesterfeldQuality Control, eQuality Control, e

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"utline"utline

Fundamental Aspects Statistical Aspects

Sampling Plan Design


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Learning "b#ecti$esLearning "b#ecti$es

When you have completed this chapter youshould be able to:

Know the advantages and disadvantages of

sampling; the types of sampling plans and

selection factors; criteria for formation of lots;

criteria for sampling selection; and decisions

regarding reected lots!

Determine the "# #urve for a single sampling

plan!


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Learning "b#ecti$es-cont%d&Learning "b#ecti$es-cont%d&


Determine the e$uations needed to graph the

"# #urve for a double sampling plan!Know the properties of "# #urves!

Know the consumer%producer relationships of

ris&' A()' and )(!


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Learning "b#ecti$es-cont%d&Learning "b#ecti$es-cont%d&


Determine the A"( curve and the A"() for a

single sampling plan!Determine single sampling plans for stipulated

producers ris& and for stipulated consumers

ris&!


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'undamental Aspects'undamental Aspects

Acceptance Sampling is a form of

inspection applied to lots or

batches of items before or after aprocess to udge conformance to

predetermined standards!


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Acceptance SamplingAcceptance Sampling

Acceptance Sampling is very useful when: )arge numbers of items must be)arge numbers of items must be

processed in a short amount of time!processed in a short amount of time!

*he cost of +passing defectives, is low!*he cost of +passing defectives, is low! Fatigue-boredom is caused by inspectingFatigue-boredom is caused by inspecting

large numbers of items!large numbers of items!


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Acceptance SamplingAcceptance Sampling

Acceptance Sampling is very useful when:Destructive testing is re$uired


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Acceptance SamplingAcceptance Sampling*hree important aspects of sampling:

.nvolves random sampling of theentire lot

Accept and /eect )ots 0does not

improve the $uality1 +)otSentencing,

Audit *ool

*hree approaches to +lot sentencing,:Accept with no inspection

2334 inspection

Acceptance Sampling


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Acceptance SamplingAcceptance SamplingAdvantages

)ess e5pensive/educed damage

/educes the amount of inspection

errorDisadvantages

/is& of accepting +bad, lots and

reecting +good, lots)ess information generated

/e$uires planning and

documentation


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Sampling PlansSampling Plans

Sampling Plans specify the lot si6e' samplesi6e' number of samples and

acceptance-reection criteria!

Sampling plans involve: Single sampling Double sampling 7ultiple sampling

Randomsample

Lot


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Sampling PlansSampling Plans

Single Sampling Plan

8 9 lot si6e

n 9 sample si6e

#9acceptance number.f c or less non%conforming units are found

in the sample' the lot is accepted' else it is

reected!


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Single Sampling PlanSingle Sampling Plan

A single sampling plan is one where:

A representative sample of n items isA representative sample of n items is

drawndrawn from a lot si6e of 8 itemsfrom a lot si6e of 8 items

ach item in the sample is e5amined

and classied as good-defective.f the number of defective e5ceeds a

specied reection number 0c1 the whole lot

is reected; otherwise the whole lot isaccepted


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(ouble Sampling Plan(ouble Sampling Plan

ADouble Sampling Plan allows to ta&e asecond sample if the results of the originalsample are inconclusive!Species the lot si6e' si6e of the initial sample'

the accept-reect-inconclusive criteria for theinitial sample 0N, n1, c1 (Ac), r1(Re)1Species the si6e of the second sample and theacceptance reection criteria based on the total

number of defective observed in both the rstand second sample 0n2,c2,r2)


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First Randomsample

Lot

C1 r1

First sample inconclusive,

take second sampleReject LotAccept Lot

Compare number of defective found in the first random sample toCompare number of defective found in the first random sample to C1C1

andand r1r1 and make appropriate decision.and make appropriate decision.



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C2

Reject LotAccept Lot

Compare the total number of defective in both lots toCompare the total number of defective in both lots to C2C2and makeand make

the appropriate decisionthe appropriate decision

Lot First Random sample

Second Random sample



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(ouble Sampling Plan(ouble Sampling PlanAMultiple Sampling Plan is similar to the

double sampling plan in that successivetrials are made' each of which hasacceptance' reection and inconclusiveoptions!

Which Plan you choose depends on:#ost and time8umber of samples needed and

number of items in each sample


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Lot 'ormationLot 'ormation

#onsiderations before inspection:)ots should be homogeneous

)arger lots are more preferable thansmaller lots

)ots should be conformable to thematerials%handling systems used inboth the vendor and consumerfacilities


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!andom Sampling!andom Sampling


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Statistical AspectsStatistical Aspects*he "perating #haracteristic

#urve:7easures the performance of an

acceptance sampling plan

Plots the probability of accepting thelot versus the lot fraction defective

Shows the probability that a lotsubmitted with a certain fraction

defective will be either accepted orreected

A t bl Q lit L lA t bl Q lit L l


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Acceptable Quality Le$elAcceptable Quality Le$el

)AQL*)AQL*

*he A() is a percent defective that isthe base line re$uirement for the$uality of the producer=s product! *heproducer would li&e to design a

sampling plan such that there is ahigh probability o acceptinga lotthat has a defect level less than ore$ual to the A()!

L t + l P tL t + l P t


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Lot +olerance PercentLot +olerance Percent

(eecti$e(eecti$e

*he )ot *olerance Percent Defective*he )ot *olerance Percent Defective)*PD or )( is a designated high)*PD or )( is a designated high

defect level that would bedefect level that would be

unacceptable to the consumer! *heunacceptable to the consumer! *he

consumer would li&e the samplingconsumer would li&e the samplingplan to have aplan to have alo! probability olo! probability o

acceptingacceptinga lot with a defect level asa lot with a defect level as

high as the )*PD!high as the )*PD!


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+ype .rror )Producer%s !is/*+ype .rror )Producer%s !is/*

*his is the probability' for a given

0n,c1 sampling plan' of reecting a lotthat has a defect level e$ual to theA()! *he producer su>ers when thisoccurs' because a lot with acceptable$uality was reected! *he symbol ? iscommonly used for the *ype . errorand typical values for range from 3!@

to 3!32!

+ . )C %+ . )C %


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+ype .rror )Consumer%s+ype .rror )Consumer%s

!is/*!is/**his is the probability' for a given0n,c1 sampling plan' of accepting alot with a defect level e$ual to the)*PD! *he consumer su>ers when

this occurs' because a lot withunacceptable $uality was accepted!*he symbol is commonly used forthe *ype .. error and typical values

range from 3!@ to 3!32!

" ti Ch t i ti"perating Characteristic


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"perating Characteristic"perating Characteristic

Cur$eCur$e*his curve plots the probability ofaccepting the lot 0B%a5is1 versus thelot fraction or percent defectives 0C%a5is1! "he #$ cur%e is the primary

tool or &isplaying an& in%estigatingthe properties o a 'ot AcceptanceSampling Plan!


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"C Cur$es"C Cur$es

*here are two types of "# curves:

*ype A

ives the probability ofacceptance of an individual lot

coming from nite production*ype E

ives the probability of

acceptance for lots coming froma continuous production

"CC Si l S li"CCs or Single Sampling


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An#perating $haracteristic $ur%e (#$$) is a

probability curve for a sampling plan that shows theprobabilities of accepting lots with various lot$uality levels 04 defectives1!

0

0.1

0.20.3

0.4

0.5

0.6

0.7

0.8

0.

1

0 .05 .10 .15 .20

!robabilit"

ofacceptin

#

lot

$ot %ualit" &' defective(

Under this sampling plan, if the lot has 3% defective

. the

probability of accepting the lot is 90% . theprobability of rejecting the lot is 10%

f the lot has 20% defective

. it has a small probability !"%# of being accepted

. the probability of rejecting the lot is 9"%

0.7

0.8

"CCs or Single Sampling"CCs or Single Sampling

PlansPlans


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0.2

0.3

0.40.5

0.6

0.7

0.8

0.

1

!

robabilit"

ofac

ceptin#

lot

00.1

0 .05 .10 .15 .20 $ot %ualit" &' defective(

$& ' percentage level of defects at(hich a c)stomer is (illing to accept

)$cceptable &ot*

*rod)cer+s is- probability acceptable lot is rejected

"CC, AQL and Producer%s !is/"CC, AQL and Producer%s !is/


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0.2

0.3

0.40.5

0.6

0.7

0.8

0.

1

!

robabilit"

ofac

ceptin#

lot

00.1

0 .05 .10 .15 .20 $ot %ualit" &' defective(

&/* ' )pper limit on the percentage&/* ' )pper limit on the percentage

of defectives that a c)stomer isof defectives that a c)stomer is

(illing to accept.(illing to accept.

Cons)mer+s is- probability )nacceptable is acceptedCons)mer+s is- probability )nacceptable is accepted

Unacceptable &ot

"CC, L+P( and Consumer%s !is/"CC, L+P( and Consumer%s !is/


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"CC or (ouble Sampling Plan"CC or (ouble Sampling Plan


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nspect a samplenspect a sample

o 012 rom loto 012 rom loto 3422o 3422

0 or less 0 or less

5onconorming5onconorming

units accept lots andunits accept lots andstopstop

4 or more 4 or more

5onconorming units5onconorming units

the lot is not acceptedthe lot is not acceptedand stopand stop

3 or 6 nonconorming 3 or 6 nonconormingunits, inspect a secondunits, inspect a second

sample o 322sample o 322

1 or less 1 or less5onconorming units5onconorming units

"n both samples,"n both samples,

Accept the lotAccept the lot

7 or more 7 or more5onconorming units5onconorming units

"n both samples"n both samples

+he lot is not accepted+he lot is not accepted

igure %G raphical description of the double sampling plan: 89@H33'n292G3'cr29H' n@9@33' c@9G' and r@9I


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"CC or a 8ultiple Sampling Plan"CC or a 8ultiple Sampling Plan

A$erage "utgoing QualityA$erage "utgoing Quality


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)A"Q*)A"Q*

A common procedure' whensampling and testing is non%destructive' is to 2334 inspectreected lots and replace all

defectives with good units! .n thiscase' all reected lots are madeperfect and the only defects left arethose in lots that were accepted&&


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*heA%erage #utgoing uality (A#)is theaverage of reected lots 02334 inspection1

and accepted lots 0 a sample of items

inspected))

ac

ac

N - nAOQ = P * p( ) where

N

P = Probability of accepting a lot

p = Fraction defective

n = saple si!e

N = "ot si!e



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A"Q and Acceptance SamplingA"Q and Acceptance Sampling

ProducerProducer5622256222

n9n9

c3c3ConsumerConsumer

01 lots3: nonconorming




Figure %2G Jow acceptance Sampling wor&s

A"Q and AcceptanceA"Q and Acceptance


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A"Q and AcceptanceA"Q and Acceptance

SamplingSampling+otal 5umber+otal 5umber 5umber5umber

5onconormi5onconormingng

00 lots-00 lots-

3:3:5onconorming5onconorming

00)6222*66,22200)6222*66,222 66,222)2&23*77266,222)2&23*772

4 lots-4 lots-

2:2:5onconorming5onconorming

4)6222*4)6222*)2&9*00,;72)2&9*00,;72

22

44,;7244,;72 772772

Percent 5onconorming )A"Q* Percent 5onconorming )A"Q* 772


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*ypically the term 08%n1-8 is very close to 2;

therefore' the e$uation most often used is:

AOQ = P *p where

P = Probability of accepting a lot

p = Fraction defective

ac

ac

A$erage Quality o nspectedA$erage Quality o nspectedLotsLots

" i Q li l


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A plot of theA#0B%a5is1 versus theincoming lotp0C%a5is1 will start at 3forp9 3' and return to 3 forp9 20where every lot is 2334 inspected

and rectied1! .n between' it willrise to a ma5imum! *his ma5imum'which is the worst possible longtermA#' is called the Average

"utgoing (uality )evelA#'!

A$erage "utgoing Quality Le$elA$erage "utgoing Quality Le$el

A$erage +otal nspection


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A$erage +otal nspection)A+*

When reected lots are 2334inspected' it is easy to calculate theA"if lots come consistently with adefect level ofp! For a )ASP 0n,c1

with a probabilitypaof accepting alot with defect levelp' we have:

A"9n * (2 + pa) (N + n)

where Nis the lot si6e!

A$erage Sample 5umberA$erage Sample 5umber


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)AS5*)AS5*

For a single sampling 0n,c1 we &now eachand every lot has a sample of si6e nta&en and inspected or tested! Fordouble' multiple and se$uential plans'the amount of sampling variesdepending on the number of defectsobserved!



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)AS5*)AS5*For any given double' multiple orse$uential plan' a long termASNcan be calculated assuming alllots come in with a defect level

ofp! A plot of theASN' versusthe incoming defect levelp'describes the samplingeLciency of a given plan

scheme!AS8 9 n2 M n@ 02 N P21 for a doublesampling plan!


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Sampling Plan (esignSampling Plan (esign

Suppose ? is &nown and the A() isalso &nown then :Sampling plan with stipulated

producers ris&

Sampling plan with stipulatedconsumers ris&

Sampling plan with stipulated

producers and consumers ris&can be designed!


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Stipulated Producers /is&? 9 3!3G A() 9 2!@4

Pa93!G P3!G9 3!32@

Assume values for #' nd np3!G forthis c value' calculate n


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Stipulated #onsumers /is& 9 3!23 )( 9 I!34

Pa93!23 P3!239 3!3I3

Assume values for #' nd np3!G forthis c value' calculate n


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Jave H plans! Select plan based on: )owest sampling si6ereatest sampling si6e

Plan e5actly meets consumersstipulation and is as close aspossible to producers stipulation

Plan e5actly meets producersstipulation and is as close aspossible to consumers stipulation

acceptance sampling - besterfield

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