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7/25/2019 Acceptance Sampling - Besterfield
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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
PowerPoints created by !osidaPowerPoints created by !osidaCoowarCoowar
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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&
When you have completed this chapter youshould be able to:
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$es-cont%d&
When you have completed this chapter youshould be able to:
Determine the A"( curve and the A"() for a
single sampling plan!Determine single sampling plans for stipulated
producers ris& and for stipulated consumers
ris&!
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'undamental Aspects'undamental Aspects
Acceptance Sampling is a form of
inspection applied to lots or
batches of items before or after aprocess to udge conformance to
predetermined standards!
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Acceptance SamplingAcceptance Sampling
Acceptance Sampling is very useful when: )arge numbers of items must be)arge numbers of items must be
processed in a short amount of time!processed in a short amount of time!
*he cost of +passing defectives, is low!*he cost of +passing defectives, is low! Fatigue-boredom is caused by inspectingFatigue-boredom is caused by inspecting
large numbers of items!large numbers of items!
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Acceptance SamplingAcceptance Sampling
Acceptance Sampling is very useful when:Destructive testing is re$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.
(ouble Sampling Plan(ouble Sampling Plan
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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
(ouble Sampling Plan(ouble Sampling Plan
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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 $ot %ualit" &' defective(
&/* ' )pper limit on the percentage&/* ' )pper limit on the percentage
of defectives that a c)stomer isof defectives that a c)stomer is
(illing to accept.(illing to accept.
Cons)mer+s is- probability )nacceptable is acceptedCons)mer+s is- probability )nacceptable is accepted
Unacceptable &ot
"CC, L+P( and Consumer%s !is/"CC, L+P( and Consumer%s !is/
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"CC or (ouble Sampling Plan"CC or (ouble Sampling Plan
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(ouble Sampling Plan(ouble Sampling Plan
nspect a samplenspect a sample
o 012 rom loto 012 rom loto 3422o 3422
0 or less 0 or less
5onconorming5onconorming
units accept lots andunits accept lots andstopstop
4 or more 4 or more
5onconorming units5onconorming units
the lot is not acceptedthe lot is not acceptedand stopand stop
3 or 6 nonconorming 3 or 6 nonconormingunits, inspect a secondunits, inspect a second
sample o 322sample o 322
1 or less 1 or less5onconorming units5onconorming units
"n both samples,"n both samples,
Accept the lotAccept the lot
7 or more 7 or more5onconorming units5onconorming units
"n both samples"n both samples
+he lot is not accepted+he lot is not accepted
igure %G raphical description of the double sampling plan: 89@H33'n292G3'cr29H' n@9@33' c@9G' and r@9I
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"CC or a 8ultiple Sampling Plan"CC or a 8ultiple Sampling Plan
A$erage "utgoing QualityA$erage "utgoing Quality
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A$erage "utgoing QualityA$erage "utgoing Quality
)A"Q*)A"Q*
A common procedure' whensampling and testing is non%destructive' is to 2334 inspectreected lots and replace all
defectives with good units! .n thiscase' all reected lots are madeperfect and the only defects left arethose in lots that were accepted&&
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*heA%erage #utgoing uality (A#)is theaverage of reected lots 02334 inspection1
and accepted lots 0 a sample of items
inspected))
ac
ac
N - nAOQ = P * p( ) where
N
P = Probability of accepting a lot
p = Fraction defective
n = saple si!e
N = "ot si!e
A$erage "utgoing QualityA$erage "utgoing Quality
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A"Q and Acceptance SamplingA"Q and Acceptance Sampling
ProducerProducer5622256222
n9n9
c3c3ConsumerConsumer
01 lots3: nonconorming
00 lots3: nonconorming
4 lots3: nonconorming
4 lots2: nonconorming
Figure %2G Jow acceptance Sampling wor&s
A"Q and AcceptanceA"Q and Acceptance
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A"Q and AcceptanceA"Q and Acceptance
SamplingSampling+otal 5umber+otal 5umber 5umber5umber
5onconormi5onconormingng
00 lots-00 lots-
3:3:5onconorming5onconorming
00)6222*66,22200)6222*66,222 66,222)2&23*77266,222)2&23*772
4 lots-4 lots-
2:2:5onconorming5onconorming
4)6222*4)6222*)2&9*00,;72)2&9*00,;72
22
44,;7244,;72 772772
Percent 5onconorming )A"Q* Percent 5onconorming )A"Q* 772
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*ypically the term 08%n1-8 is very close to 2;
therefore' the e$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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A$erage Sample 5umberA$erage Sample 5umber
)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$uential plans'the amount of sampling variesdepending on the number of defectsobserved!
A$erage Sample 5umberA$erage Sample 5umber
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A$erage Sample 5umberA$erage Sample 5umber
)AS5*)AS5*For any given double' multiple orse$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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Sampling Plan (esignSampling Plan (esign
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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Sampling Plan (esignSampling Plan (esign
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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Sampling Plan (esignSampling Plan (esign
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