quality control full chap

8/7/2019 quality control full chap

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1 2002 South-Western/Thomson Learning2002 South-Western/Thomson Learning TMTM

Slides preparedSlides prepared

by John Loucksby John Loucks


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Chapter 17Chapter 17

Quality Control


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OverviewOverview

q

Introductionq Statistical Concepts in Quality Control

q Control Charts

q Acceptance Plans

q Computers in Quality Control

q Quality Control in Services

q Wrap-Up: What World-Class Companies Do


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IntroductionIntroduction

q

Quality control (QC) includes the activities from thesuppliers, through production, and to thecustomers.

q Incoming materials are examined to make sure they

meet the appropriate specifications.q The quality of partially completed products are

analyzed to determine if production processes arefunctioning properly.

q Finished goods and services are studied to determineif they meet customer expectations.


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QC Throughout Production SystemsQC Throughout Production Systems

Raw Materials,Raw Materials,

Parts, andParts, and

SuppliesSupplies

ProductionProduction

ProcessesProcessesProducts andProducts and

ServicesServices

InputsInputs

ConversionConversion OutputsOutputs

Control ChartsControl Charts

andand

Acceptance TestsAcceptance Tests


andand

Acceptance TestsAcceptance TestsControl ChartsControl Charts

Quality ofQuality of

InputsInputsQuality ofQuality of

OutputsOutputsQuality ofQuality of

Partially CompletedPartially Completed

ProductsProducts


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Services and Their Customer ExpectationsServices and Their Customer Expectations

q

Hospitalq Patient receive the correct treatments?

q Patient treated courteously by all personnel?

q Hospital environment support patient recovery?

q Bank

q Customers transactions completed withprecision?

q Bank comply with government regulations?q Customers statements accurate?


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Products and Their Customer ExpectationsProducts and Their Customer Expectations

q

Automakerq Auto have the intended durability?

q Parts within the manufacturing tolerances?

q Autos appearance pleasing?

q Lumber mill

q Lumber within moisture content tolerances?

q Lumber properly graded?

q Knotholes, splits, and other defects excessive?


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SamplingSampling

q

The flow of products is broken into discrete batchescalled lots.

q Random samples are removed from these lots andmeasured against certain standards.

q A random sample is one in which each unit in the lothas an equal chance of being included in thesample.

q If a sample is random, it is likely to be representative

of the lot.

q


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SamplingSampling

q

Either attributes or variables can be measured andcompared to standards.

q Attributes are characteristics that are classified intoone of two categories, usually defective (not

meeting specifications) or nondefective (meetingspecifications).

q Variables are characteristics that can be measured ona continuous scale (weight, length, etc.).


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Size and Frequency of SamplesSize and Frequency of Samples

q

As the percentage of lots in samples is increased:q the sampling and sampling costs increase, andq the quality of products going to customers

increases.

q Typically, very large samples are too costly.q Extremely small samples might suffer from statistical

imprecision.

q Larger samples are ordinarily used when sampling forattributes than for variables.

q


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When to InspectWhen to Inspect

During the Production ProcessDuring the Production Process

q

Inspect before costly operations.q Inspect before operations that are likely to produce

faulty items.

q Inspect before operations that cover up defects.

q Inspect before assembly operations that cannot beundone.

q On automatic machines, inspect first and last piecesof production runs, but few in-between pieces.

q Inspect finished products.


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Central Limit TheoremCentral Limit Theorem

q

The central limit theorem is: Sampling distributionscan be assumed to be normally distributed eventhough the population (lot) distributions are notnormal.

q The theorem allows use of the normal distribution toeasily set limits for control charts and acceptanceplans for both attributes and variables.


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Sampling DistributionsSampling Distributions

q

The sampling distribution can be assumed to benormally distributed unless sample size (n) isextremely small.

q The mean of the sampling distribution ( x ) is equal to

the population mean ( ).q The standard error of the sampling distribution ( x )

is smaller than the population standard deviation( x ) by a factor of 1/

q

q

==

--

n


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Population and Sampling DistributionsPopulation and Sampling Distributions

f(x)f(x)

x

Population DistributionPopulation Distribution

Sampling DistributionSampling Distribution

of Sample Meansof Sample Means

Mean =Mean =

Std. Dev. =Std. Dev. = xx

Mean = x =Mean = x = Std. Error =Std. Error = x

x

=

n

f(x)

==

xx


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q

Primary purpose of control charts is to indicate at aglance when production processes might havechanged sufficiently to affect product quality.

q If the indication is that product quality has

deteriorated, or is likely to, then corrective is taken.q If the indication is that product quality is better than

expected, then it is important to find out why sothat it can be maintained.

q Use of control charts is often referred to as statisticalprocess control (SPC).


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Constructing Control ChartsConstructing Control Charts

q

Vertical axis provides the scale for the sampleinformation that is plotted on the chart.

q Horizontal axis is the time scale.

q Horizontal center line is ideally determined from

observing the capability of the process.q Two additional horizontal lines, the lower and upper

control limits, typically are 3 standard deviationsbelow and above, respectively, the center line.


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Constructing Control ChartsConstructing Control Charts

q

If the sample information falls within the lower andupper control limits, the quality of the population isconsidered to be in control; otherwise quality isjudged to be out of control and corrective action

should be considered.q Two versions of control charts will be examined

q Control charts for attributesq Control charts for variables


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Control Charts for AttributesControl Charts for Attributes

q

Inspection of the units in the sample is performed onan attribute (defective/non-defective) basis.

q Information provided from inspecting a sample ofsize n is the percent defective in a sample, p, or the

number of units found to be defective in thatsample divided by n.

q


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q

Although the distribution of sample informationfollows a binomial distribution, that distributioncan be approximated by a normal distribution witha

q mean of pq standard deviation of

q The 3 control limits are

)/np(100p

)/np(100p3-/p+

Control Charts for AttributesControl Charts for Attributes

--


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Example: Attribute Control ChartExample: Attribute Control Chart

Every check cashed or deposited at LincolnBank must be encoded with the amount of the checkbefore it can begin the Federal Reserve clearingprocess. The accuracy of the check encoding process

is of upmost importance. If there is any discrepancybetween the amount a check is made out for and theencoded amount, the check is defective.


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Twenty samples, each consisting of 250checks, were selected and examined. The number ofdefective checks found in each sample is shownbelow.

4 1 5 3 2 7 4 5 2 3

2 8 5 3 6 4 2 5 3 6


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The manager of the check encoding departmentknows from past experience that when the encodingprocess is in control, an average of 1.6% of theencoded checks are defective.

She wants to construct a p chart with 3-standard deviation control limits.


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= = = =

(1 ) .016(1 .016) .015744.007936

250 250p

p p

n

UCL = 3 =.016+3(.007936)= .039808 or 3.98%p

p +

LCL = 3 =.016-3(.007936)=-.007808= 0%p

p


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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

SampleProport

ionp


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q

Inspection of the units in the sample is performed ona variable basis.

q The information provided from inspecting a sampleof size n is:

q Sample mean, x, or the sum of measurement ofeach unit in the sample divided by n

q Range, R, of measurements within the sample,or the highest measurement in the sample

minus the lowest measurement in the sample

Control Charts for VariablesControl Charts for Variables


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q

In this case two separate control charts are used tomonitor two different aspects of the processsoutput:

q Central tendencyq

Variabilityq Central tendency of the output is monitored using the

x-chart.

q Variability of the output is monitored using the R-

chart.

Control Charts for VariablesControl Charts for Variables


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x-Chartx-Chart

q

The central line is x, the sum of a number of samplemeans collected while the process was consideredto be in control divided by the number ofsamples.

q

The 3 lower control limit is x - ARq The 3 upper control limit is x + ARq Factor A is based on sample size.

==

==

==


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R-ChartR-Chart

q

The central line is R, the sum of a number of sampleranges collected while the process was consideredto be in control divided by the number ofsamples.

q The 3 lower control limit is D1R.q The 3 upper control limit is D2R.

q Factors D1and D2 are based on sample size.


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33 Control Chart Factors for VariablesControl Chart Factors for Variables

Control Limit Factor ControlLimit Factor Sample for Sample Mean for

Sample Range Size n A D1 D2

2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.116

10 0.308 0.223 1.777 15 0.223 0.348 1.652 20 0.180 0.414 1.586 25 0.153 0.459 1.541 Over 25 0.45+.001n

1.55-.0015n

0.75(1/ )n


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Example: Variable Control ChartExample: Variable Control Chart

Harry Coates wants to construct x and R chartsat the bag-filling operation for Meow Chow cat food.He has determined that when the filling operation isfunctioning correctly, bags of cat food average 50.01

pounds and regularly-taken 5-bag samples have anaverage range of .322 pounds.


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q

Sample Mean Chart x = 50.01, R = .322, n = 5

UCL = x + AR = 50.01 + .577(.322) =

50.196 LCL = x- AR= 50.01 - .577(.322) = 49.824

==

==

==


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x Chart for Meow Cho

49.7

49.8

49.9

50.0

50.1

50.2

50.3

0 5 10 15 20Sample Numbe

Sample

Mean

UCL

LCL


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q

Sample Range Chart x = 50.01, R = .322, n = 5

UCL = RD2 = .322(2.116) = .681

LCL = RD1= .322(0) = 0

==


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A B C D E FR Chart for Meow Chow

0.00

0.10

0.20

0.30

0.400.50

0.60

0.70

0.80

0 5 10 15 20Sample Number

SampleRan

geR

LCL

UCL


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Acceptance PlansAcceptance Plans

q

Trend today is toward developing testing methodsthat are so quick, effective, and inexpensive thatproducts are submitted to 100% inspection/testing

q Every product shipped to customers is inspected and

tested to determine if it meets customerexpectations

q But there are situations where this is eitherimpractical, impossible or uneconomical

q Destructive tests, where no products survivetest

q In these situations, acceptance plans are sensible


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Acceptance PlansAcceptance Plans

q

An acceptance plan is the overall scheme for eitheraccepting or rejecting a lot based on informationgained from samples.

q The acceptance plan identifies the:q

Size of samples, nq Type of samplesq Decision criterion, c, used to either accept or

reject the lot

q

Samples may be either single, double, or sequential.


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Single-Sampling PlanSingle-Sampling Plan

q

Acceptance or rejection decision is made afterdrawing only one sample from the lot.

q If the number of defectives, c, does not exceed theacceptance criteria, c, the lot is accepted.


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Single-Sampling PlanSingle-Sampling Plan

Lot of N ItemsLot of N ItemsRandoRando

mm

SampleSample

ofof

n Itemsn Items

N - n ItemsN - n Items

Inspect n ItemsInspect n Items

c > cc > c cc


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Double-Sampling PlanDouble-Sampling Plan

q

One small sample is drawn initially.q If the number of defectives is less than or equal to

some lower limit, the lot is accepted.

q If the number of defectives is greater than some upper

limit, the lot is rejected.q If the number of defectives is neither, a second larger

sample is drawn.

q Lot is either accepted or rejected on the basis of theinformation from both of the samples.

q


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Lot of N ItemsLot of N Items RandoRandomm

SampleSample

ofof

nn11

ItemsItems

N nN n11 ItemsItems

Inspect nInspect n11

ItemsItems

cc11 > c > c22 cc11


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(c(c11 + c + c22) > c) > c22


N nN n11 ItemsItems RandoRando

mm

SampleSample

ofof

nn22

ItemsItems

N (nN (n11 + n+ n22))ItemsItems

Inspect nInspect n22

ItemsItems

ReplaceReplace

DefectivesDefectives

nn22 NondefectivesNondefectives

cc22 Defectives Defectives

Found in SampleFound in SampleReject LotReject Lot

Accept LotAccept Lot

ContinueContinue

(c(c11 + c + c22))


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Sequential-Sampling PlanSequential-Sampling Plan

q

Units are randomly selected from the lot and testedone by one.

q After each one has been tested, a reject, accept, orcontinue-sampling decision is made.

q Sampling process continues until the lot is acceptedor rejected.


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Sequential-Sampling PlanSequential-Sampling Plan

0 100 10 20 30 40 5020 30 40 50 60 70 8060 70 80 90 100 11090 100 110120 130120 130

33

11

22

Units Sampled (n)Units Sampled (n)

66

Number of DefectivesNumber of Defectives

44

55

77

00

Reject LotReject Lot

Accept LotAccept Lot

Continue SamplingContinue Sampling


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DefinitionsDefinitions

q

Acceptance plan - Sample size (n) and maximumnumber of defectives (c) that can be found in asample to accept a lot

q Acceptable quality level (AQL) - If a lot has no more

than AQL percent defectives, it is considered agood lot

q Lot tolerance percent defective (LTPD) - If a lot hasgreater than LTPD, it is considered a bad lot

q


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q

Average outgoing quality (AOQ) Given the actual% of defectives in lots and a particular samplingplan, the AOQ is the average % defectives in lotsleaving an inspection station

q

Average outgoing quality limit (AOQL) Given aparticular sampling plan, the AOQL is themaximum AOQ that can occur as the actual %defectives in lots varies


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q

Type I error - Based on sample information, a good(quality) population is rejected

q Type II error - Based on sample information, a bad(quality) population is accepted

q Producers risk ( ) - For a particular sampling plan,the probability that a Type I error will becommitted

q Consumers risk ( ) - For a particular sampling plan,

the probability that a Type II error will becommitted

Considerations inConsiderations in


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Considerations inConsiderations in

Selecting a Sampling PlanSelecting a Sampling Plan

q

Operating characteristics (OC) curveq Average outgoing quality (AOQ) curve


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Operating Characteristic (OC) CurveOperating Characteristic (OC) Curve

q

An OC curve shows how well a particular samplingplan (n,c) discriminates between good and bad lots.

q The vertical axis is the probability of accepting a lotfor a plan.

q The horizontal axis is the actual percent defective inan incoming lot.

q For a given sampling plan, points for the OC curvecan be developed using the Poisson probability

distribution


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Operating Characteristic (OC) CurveOperating Characteristic (OC) Curve

.10.10

.20.20

.30.30

.40.40

.50.50

.60.60

.70.70

.80.80

.90.90

Probab

ilityof

Acc

ept i

ng

theLo t

ProbabilityofAcceptingtheLot

0 5 10 15 20 25 0 5 10 15 20 25

1.001.00

% Defectivesin Lots

AQL = 3%AQL = 3%

LTPD = 15%LTPD = 15%

Consumers Risk (Consumers Risk ( ) = 8.74%) = 8.74%Producers Risk (Producers Risk ( ) = 3.67%) = 3.67%

n = 15, c = 0n = 15, c = 0


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OC Curve (continued)OC Curve (continued)

q

Management may want to:q Specify the performance of the sampling

procedure by identifying two points on thegraph:

q

AQL and q LTPD and q Then find the combination of n and c that

provides a curve that passes through bothpoints

A O i Q i (AOQ) C


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Average Outgoing Quality (AOQ) CurveAverage Outgoing Quality (AOQ) Curve

q

AOQ curve shows information depicted on the OCcurve in a different form.

q Horizontal axis is the same as the horizontal axis forthe OC curve (percent defective in a lot).

q Vertical axis is the average quality that will leave thequality control procedure for a particular samplingplan.

q Average quality is calculated based on the

assumption that lots that are rejected are 100%inspected before entering the production system.

q

AOQ C


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AOQ CurveAOQ Curve

q

Under this assumption, AOQ = [P(A)]/1

where: = percent defective in an incominglot

P(A) = probability of accepting a lot is obtained from the plans OC curve

q As the percent defective in a lot increases, AOQ willincrease to a point and then decrease.


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C i Q li C lC t i Q lit C t l


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Computers in Quality ControlComputers in Quality Control

q

Records about quality testing and results limit afirms exposure in the event of a product liabilitysuit.

q Recall programs require that manufacturers

q Know the lot number of the parts that areresponsible for the potential defects

q Have an information storage system that can tiethe lot numbers of the suspected parts to the

final product model numbersq Have an information system that can track the

model numbers of final products to customers

q

C i Q li C lC t i Q lit C t l


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Computers in Quality ControlComputers in Quality Control

q

With automation, inspection and testing can be soinexpensive and quick that companies may be ableto increase sample sizes and the frequency ofsamples, thus attaining more precision in bothcontrol charts and acceptance plans

Q lit C t l i S iQ lit C t l i S i


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Quality Control in ServicesQuality Control in Services

q

In all services there is a continuing need to monitorquality

q Control charts are used extensively in services tomonitor and control their quality levels

W U W ld Cl P tiW U W ld Cl P ti


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Wrap-Up: World-Class PracticeWrap-Up: World-Class Practice

q

Quality cannot be inspected into products. Processesmust be operated to achieve quality conformance;quality control is used to achieve this.

q Statistical control charts are used extensively to

provide feedback to everyone about qualityperformance

q . . . more

W U W ld Cl P tiW U W ld Cl P ti


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Wrap-Up: World-Class PracticeWrap-Up: World-Class Practice

q

Where 100% inspection and testing are impractical,uneconomical, or impossible, acceptance plansmay be used to determine if lots of products arelikely to meet customer expectations.

q

The trend is toward 100% inspection and testing;automated inspection and testing has made such anapproach effective and economical.

E d f Ch t 17


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End of Chapter 17End of Chapter 17

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