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8/18/2019 4.1 Quality Control
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Quality Control
1
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Overview
• Inspection and quality control
-Types of Inspection, Control Charts -Introduction, Defnition, Classifcation, Types,Attributes, Variables
• Total Quality Management- Concept, Features, Kaizen model and 7 QualityControl Tools - Procedures, Variables, Quality level
• ecent concepts in Quality Control
- Introduction to !i" sigma, #pproaches,$ene%ts and Types& - DAIC, DADV, !reen belt,"lac# belt, aster blac# belts$
• Tutorial
- 'ro(lems in control charts&%
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Introduction
• Quality control &QC' includes t(e activities )ro*t(e suppliers, t(rou+( production, and to t(ecusto*ers$
• Inco*in+ *aterials are ea*ined to *a#e sure
t(ey *eet t(e appropriate specifcations$• T(e uality o) partially co*pleted products are
analy.ed to deter*ine i) production processes are)unctionin+ properly$
•
/inis(ed +oods and services are studied todeter*ine i) t(ey *eet custo*er epectations$
0
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QC T(rou+(out Production yste*s
2
3aw aterials,Parts, andupplies
ProductionProcesses
Products andervices
Inputs Con)ersion *utputs
Control C(artsand
Acceptance Tests
Control C(artsand
Acceptance TestsControl C(arts
Quality o) Inputs
Quality o) Outputs
Quality o) Partially Co*pleted
Products
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ervices and T(eir Custo*er4pectations
• 5ospital
• Patient receive t(e correct treat*ents6
• Patient treated courteously by all personnel6
• 5ospital environ*ent support patient recovery6
• "an#• Custo*er7s transactions co*pleted wit( precision6
• "an# co*ply wit( +overn*ent re+ulations6
• Custo*er7s state*ents accurate6
8
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Products and T(eir Custo*er4pectations
• Auto*a#er
• Auto (ave t(e intended durability6
• Parts wit(in t(e *anu)acturin+ tolerances6
• Auto7s appearance pleasin+6
9
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a*plin+
• T(e :ow o) products is bro#en into discretebatc(es called lots$
• 3ando* sa*ples are re*oved )ro* t(ese lots and*easured a+ainst certain standards$
• A rando* sa*ple is one in w(ic( eac( unit in t(elot (as an eual c(ance o) bein+ included in t(esa*ple$
• I) a sa*ple is rando*, it is li#ely to be
representative o) t(e lot$
;
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a*plin+
• 4it(er attributes or variables can be *easuredand co*pared to standards$
• Attributes are c(aracteristics t(at are classifedinto one o) two cate+ories, usually de)ective ¬
*eetin+ specifcations' or nonde)ective &*eetin+specifcations'$
• Variables are c(aracteristics t(at can be*easured on a continuous scale &wei+(t, len+t(,etc$'$
<
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i.e and /reuency o)a*ples• As t(e percenta+e o) lots in sa*ples is increased=
• t(e sa*plin+ and sa*plin+ costs increase, and
• t(e uality o) products +oin+ to custo*ers increases$
• Typically, very lar+e sa*ples are too costly$
• 4tre*ely s*all sa*ples *i+(t su>er )ro*statistical i*precision$
• ?ar+er sa*ples are ordinarily used w(en sa*plin+)or attributes t(an )or variables$
@
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en o nspecDurin+ t(e Production
Process• Inspect be)ore costly operations$• Inspect be)ore operations t(at are li#ely to
produce )aulty ite*s$
• Inspect be)ore operations t(at cover up de)ects$
• Inspect be)ore asse*bly operations t(at cannotbe undone$
• On auto*atic *ac(ines, inspect frst and lastpieces o) production runs, but )ew in-between
pieces$• Inspect fnis(ed products$
1B
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Central ?i*it T(eore*
• T(e central li*it t(eore* is= Samplingdistributions can be assumed to be normallydistributed even though the population (lot)distributions are not normal$
• T(e t(eore* allows use o) t(e nor*al distributionto easily set li*its )or control c(arts andacceptance plans )or bot( attributes andvariables$
11
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a*plin+ Distributions•
T(e sa*plin+ distribution can be assu*ed to benor*ally distributed unless sa*ple si.e &n' isetre*ely s*all$
• T(e *ean o) t(e sa*plin+ distribution & ' is eual tot(e population *ean &µ'$
• T(e standard error o) t(e sa*plin+ distribution &σ ' is
s*aller t(an t(e population standard deviation &σ ' by
a )actor o) 1
1%
-
n
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Population and a*plin+Distributions
10
f(x)f(x) Population Distribution
Sampling Distribution
of Sample Means
Mean = µ
Std. Dev. = σx
Mean = x = µStd. Error =
=
x
x
xx
σσ =
n
f(x)
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Control C(arts
• Pri*ary purpose o) control c(arts is to indicate ata +lance w(en production processes *i+(t (avec(an+ed suEciently to a>ect product uality$
• I) t(e indication is t(at product uality (as
deteriorated, or is li#ely to, t(en corrective ista#en$
• I) t(e indication is t(at product uality is bettert(an epected, t(en it is i*portant to fnd out w(yso t(at it can be *aintained$
• Fse o) control c(arts is o)ten re)erred to asstatistical process control &PC'$
12
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Constructin+ ControlC(arts• Vertical ais provides t(e scale )or t(e sa*ple
in)or*ation t(at is plotted on t(e c(art$
• 5ori.ontal ais is t(e ti*e scale$
• 5ori.ontal center line is ideally deter*ined )ro*
observin+ t(e capability o) t(e process$• Two additional (ori.ontal lines, t(e lower and
upper control li*its, typically are 0 standarddeviations below and above, respectively, t(ecenter line$
18
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Constructin+ ControlC(arts• I) t(e sa*ple in)or*ation )alls wit(in t(e lower
and upper control li*its, t(e uality o) t(epopulation is considered to be in controlGot(erwise uality is Hud+ed to be out o) control
and corrective action s(ould be considered$• Two versions o) control c(arts will be ea*ined
• Control c(arts )or attributes
• Control c(arts )or variables
19
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Control C(arts )orAttributes• Inspection o) t(e units in t(e sa*ple is per)or*ed
on an attribute &de)ectivenon-de)ective' basis$
• In)or*ation provided )ro* inspectin+ a sa*ple o)si.e n is t(e percent de)ective in a sa*ple, p, or
t(e nu*ber o) units )ound to be de)ective in t(atsa*ple divided by n$
1;
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Control C(arts )orAttributes•
Alt(ou+( t(e distribution o) sa*ple in)or*ation )ollowsa bino*ial distribution, t(at distribution can beapproi*ated by a nor*al distribution wit( a• *ean o) p
• standard deviation o)
•
T(e 0σ control li*its are
1<
-
)/n p(100 p −
)/n p(100 p3 -/ p −+
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4a*ple= AttributeControl C(art
4very c(ec# cas(ed or deposited at ?incoln"an# *ust be encoded wit( t(e a*ount o) t(ec(ec# be)ore it can be+in t(e /ederal 3eserveclearin+ process$ T(e accuracy o) t(e c(ec#
encodin+ process is o) up*ost i*portance$ I)t(ere is any discrepancy between t(e a*ount ac(ec# is *ade out )or and t(e encoded a*ount,t(e c(ec# is de)ective$
1@
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4a*ple= AttributeControl C(art
Twenty sa*ples, eac( consistin+ o) %8Bc(ec#s, were selected and ea*ined$ T(enu*ber o) de)ective c(ec#s )ound in eac( sa*pleis s(own below$
%B
2 1 8 0 % ; 2 8 % 0
% < 8 0 9 2 % 8 0 9
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4a*ple= AttributeControl C(art
T(e *ana+er o) t(e c(ec# encodin+depart*ent #nows )ro* past eperience t(atw(en t(e encodin+ process is in control, anavera+e o) 1$9 o) t(e encoded c(ec#s are
de)ective$(e wants to construct a p c(art wit( 0-
standard deviation control li*its$
%1
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4a*ple= AttributeControl C(art
%%
σ
− −= = = =
&1 ' $B19&1 $B19' $B18;22$BB;@09
%8B %8B p
p p
n
UCL = 3 =.016+3(.00!36)= .03!"0" or 3.!"# p
p σ +
LCL = 3 =.016-3(.00!36)=-.00"0"= 0# p
p σ −
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4a*ple= AttributeControl C(art
%0
p Chart for Lincoln Bank
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0 5 10 15 20
Sample Number
S a m p l e P r o p o r t i o n p
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Control C(arts )orVariables• Inspection o) t(e units in t(e sa*ple is per)or*ed
on a variable basis$
• T(e in)or*ation provided )ro* inspectin+ asa*ple o) si.e n is=
• a*ple *ean, , or t(e su* o) *easure*ent o)eac( unit in t(e sa*ple divided by n
• 3an+e, 3, o) *easure*ents wit(in t(e sa*ple, ort(e (i+(est *easure*ent in t(e sa*ple *inus t(elowest *easure*ent in t(e sa*ple
%2
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Control C(arts )orVariables•
In t(is case two separate control c(arts are used to*onitor two di>erent aspects o) t(e process7s output=• Central tendency
• Variability
• Central tendency o) t(e output is *onitored usin+ t(e
-c(art$• Variability o) t(e output is *onitored usin+ t(e 3-
c(art$
%8
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-C(art•
T(e central line is , t(e su* o) a nu*ber o) sa*ple*eans collected w(ile t(e process was considered tobe Jin controlK divided by t(e nu*ber o) sa*ples$
• T(e 0σ lower control li*it is - A3
• T(e 0σ upper control li*it is L A3
• /actor A is based on sa*ple si.e$
%9
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3-C(art•
T(e central line is 3, t(e su* o) a nu*ber o) sa*pleran+es collected w(ile t(e process was considered tobe Jin controlK divided by t(e nu*ber o) sa*ples$
• T(e 0σ lower control li*it is D13$
• T(e 0σ upper control li*it is D%3$
• /actors D1and D% are based on sa*ple si.e$
%;
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0σ Control C(art /actors)or Variables
Control ?i*it /actor Control ?i*it /actora*ple )or a*ple ean )or a*ple3an+e
i.e n A D1 D%
% 1$
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4a*ple= VariableControl C(art
%@
x Chart for eo! Cho!
4".#
4".$
4"."
50.0
50.1
50.2
50.3
0 5 10 15 20Sample Number
S a m p l e
e a n
%CL
LCL
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4a*ple= VariableControl C(art
0B
& B C ' ( )* Chart for eo! Cho!
0.00
0.10
0.20
0.30
0.400.50
0.+0
0.#0
0.$0
0 5 10 15 20Sample Number
S a m p l e * a n , e *
LCL
%CL
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Acceptance Plans
• Trend today is toward developin+ testin+ *et(odst(at are so uic#, e>ective, and inepensive t(atproducts are sub*itted to 1BBinspectiontestin+
•
4very product s(ipped to custo*ers is inspectedand tested to deter*ine i) it *eets custo*erepectations
• "ut t(ere are situations w(ere t(is is eit(eri*practical, i*possible or unecono*ical
• Destructive tests, w(ere no products survive test
• In t(ese situations, acceptance plans are sensible
01
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Acceptance Plans
• An acceptance plan is t(e overall sc(e*e )oreit(er acceptin+ or reHectin+ a lot based onin)or*ation +ained )ro* sa*ples$
• T(e acceptance plan identifes t(e=•
i.e o) sa*ples, n• Type o) sa*ples• Decision criterion, c, used to eit(er accept or reHect
t(e lot
• a*ples *ay be eit(er sin+le, double, or
seuential$
0%
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in+le-a*plin+ Plan
• Acceptance or reHection decision is *ade a)terdrawin+ only one sa*ple )ro* t(e lot$
• I) t(e nu*ber o) de)ectives, c7, does not eceedt(e acceptance criteria, c, t(e lot is accepted$
00
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in+le-a*plin+ Plan
02
Lot of % &te'
ando'
Sa'p*e of
n &te' % - n &te'
&npet n &te'
, , ep*ae
Defet/ve
n %ondefet/ve
, Defet/ve
ond /n Sa'p*e
e2et Lot ept Lot
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Double-a*plin+ Plan
• One s*all sa*ple is drawn initially$
• I) t(e nu*ber o) de)ectives is less t(an or eual toso*e lower li*it, t(e lot is accepted$
• I) t(e nu*ber o) de)ectives is +reater t(an so*e
upper li*it, t(e lot is reHected$• I) t(e nu*ber o) de)ectives is neit(er, a second
lar+er sa*ple is drawn$
• ?ot is eit(er accepted or reHected on t(e basis o)
t(e in)or*ation )ro* bot( o) t(e sa*ples$
08
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Double-a*plin+ Plan
09
Lot of % &te'
ando'
Sa'p*e of
n1 &te' % 4 n1 &te'
&npet n1 &te'
1, 5 1, 1
ep*ae
Defet/ve
n1 %ondefet/ve
1, Defet/ve
ond /n Sa'p*e
e2et Lot
ept Lot
Cont/ne
1 1, 5
(to next */de)
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(1, + 5,) 5
Double-a*plin+ Plan
0;
% 4 n1 &te'
ando'
Sa'p*e of n5 &te'
% 4 (n1 + n5)&te'
&npet n5 &te'
ep*ae
Defet/ve
n5 %ondefet/ve
5, Defet/ve
ond /n Sa'p*e
e2et Lot
ept Lot
Cont/ne
(1, + 5,) 5
(fro' prev/o */de)
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euential-a*plin+ Plan
• Fnits are rando*ly selected )ro* t(e lot andtested one by one$
• A)ter eac( one (as been tested, a reHect, accept,or continue-sa*plin+ decision is *ade$
• a*plin+ process continues until t(e lot isaccepted or reHected$
0<
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euential-a*plin+ Plan
0@0 10 50 30 0 $0 60 0 "0 !0 100 110 150 130
3
1
5
Un/t Sa'p*ed (n)
6
%'7er of Defet/ve
$
0
e2et Lot
ept Lot
Cont/ne Sa'p*/n8
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Defnitions
• Acceptance plan - a*ple si.e &n' and *ai*u*nu*ber o) de)ectives &c' t(at can be )ound in asa*ple to accept a lot
• Acceptable uality level &AQ?' - I) a lot (as no
*ore t(an AQ? percent de)ectives, it is considereda +ood lot
• ?ot tolerance percent de)ective &?TPD' - I) a lot(as +reater t(an ?TPD, it is considered a bad lot
2B
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Defnitions
• Avera+e out+oin+ uality &AOQ' M !iven t(e actual o) de)ectives in lots and a particular sa*plin+plan, t(e AOQ is t(e avera+e de)ectives in lotsleavin+ an inspection station
•
Avera+e out+oin+ uality li*it &AOQ?' M !iven aparticular sa*plin+ plan, t(e AOQ? is t(e*ai*u* AOQ t(at can occur as t(e actual de)ectives in lots varies
21
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Defnitions
• Type I error - "ased on sa*ple in)or*ation, a +ood&uality' population is reHected
• Type II error - "ased on sa*ple in)or*ation, a bad&uality' population is accepted
• Producer7s ris# &α' - /or a particular sa*plin+ plan,t(e probability t(at a Type I error will beco**itted
• Consu*er7s ris# &β' - /or a particular sa*plin+plan, t(e probability t(at a Type II error will beco**itted
2%
C id ti i
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Considerations inelectin+ a a*plin+ Plan• Operatin+ c(aracteristics &OC' curve
• Avera+e out+oin+ uality &AOQ' curve
20
O ti C( t i ti
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Operatin+ C(aracteristic&OC' Curve• An OC curve s(ows (ow well a particular sa*plin+
plan &n,c' discri*inates between +ood and badlots$
• T(e vertical ais is t(e probability o) acceptin+ a
lot )or a plan$• T(e (ori.ontal ais is t(e actual percent de)ective
in an inco*in+ lot$
• /or a +iven sa*plin+ plan, points )or t(e OC curvecan be developed usin+ t(e Poisson probability
distribution
22
O ti C( t i ti
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Operatin+ C(aracteristic&OC' Curve
28
$1B$1B
$%B$%B
$0B$0B
$2B$2B
$8B$8B$9B$9B
$;B$;B
$
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OC Curve &continued'• ana+e*ent *ay want to=
• peci)y t(e per)or*ance o) t(e sa*plin+ procedure byidenti)yin+ two points on t(e +rap(=• AQ? and α
• ?TPD and β
• T(en fnd t(e co*bination o) n and c t(at provides a
curve t(at passes t(rou+( bot( points
29
A O t i Q lit
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Avera+e Out+oin+ Quality&AOQ' Curve• AOQ curve s(ows in)or*ation depicted on t(e OC
curve in a di>erent )or*$
• 5ori.ontal ais is t(e sa*e as t(e (ori.ontal ais)or t(e OC curve &percent de)ective in a lot'$
•Vertical ais is t(e avera+e uality t(at will leavet(e uality control procedure )or a particularsa*plin+ plan$
• Avera+e uality is calculated based on t(eassu*ption t(at lots t(at are reHected are 1BB
inspected be)ore enterin+ t(e production syste*$
2;
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AOQ Curve
• Fnder t(is assu*ption,
AOQ πNP&A'1w(ere= π percent de)ective in an inco*in+ lot
P&A' probability o) acceptin+ a lot is
obtained )ro* t(e plan7s OC curve
• As t(e percent de)ective in a lot increases, AOQwill increase to a point and t(en decrease$
2<
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AOQ Curve
• AOQ value w(ere t(e *ai*u* is attained isre)erred to as t(e avera+e out+oin+ uality level&AOQ?'$
• AOQ? is t(e worst avera+e uality t(at will eit
t(e uality control procedure usin+ t(e sa*plin+plan n and c$
2@
Co*puters in Qualit
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Co*puters in QualityControl• 3ecords about uality testin+ and results li*it a
fr*7s eposure in t(e event o) a product liabilitysuit$
• 3ecall pro+ra*s reuire t(at *anu)acturers
•
now t(e lot nu*ber o) t(e parts t(at areresponsible )or t(e potential de)ects
• 5ave an in)or*ation stora+e syste* t(at can tie t(elot nu*bers o) t(e suspected parts to t(e fnalproduct *odel nu*bers
•5ave an in)or*ation syste* t(at can trac# t(e*odel nu*bers o) fnal products to custo*ers
8B
Co*puters in Quality
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Co*puters in QualityControl• it( auto*ation, inspection and testin+ can be so
inepensive and uic# t(at co*panies *ay beable to increase sa*ple si.es and t(e )reuencyo) sa*ples, t(us attainin+ *ore precision in bot(
control c(arts and acceptance plans
81
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Quality Control in ervices
• In all services t(ere is a continuin+ need to*onitor uality
• Control c(arts are used etensively in services to*onitor and control t(eir uality levels
8%
rap Fp= orld Class
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rap-Fp= orld-ClassPractice• Quality cannot be inspected into products$
Processes *ust be operated to ac(ieve ualitycon)or*anceG uality control is used to ac(ievet(is$
•
tatistical control c(arts are used etensively toprovide )eedbac# to everyone about ualityper)or*ance
• $ $ $ *ore
80
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9:%;