set 6 quality management spc sqc

8/9/2019 SET 6 Quality Management SPC SQC

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Set -6et -6

POM-2POM-2

Quality ManagementQuality Management(SPC & SQC)(SPC & SQC)


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- Total Quality Management Defined

- Quality Specifications and Costs

- Six Sigma Quality and Tools

- External Benchmarking

- ISO 9000

- Service Quality Measurement

OBJECTIVES


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Total Quality Management (TQM)

- Total quality management isdefined as managing the entireorganization so that it excels onall dimensions of products andservices that are important to thecustomer


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Quality Specifications

- Design quality: Inherent value of theproduct in the marketplace Dimensions include: Performance,

Features, Reliability/Durability,Serviceability, Aesthetics, andPerceived Quality.

- Conformance quality: Degree to whichthe product or service designspecifications are met


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Costs of Quality

External FailureCosts

Appraisal Costs

Prevention Costs

Internal FailureCosts

Costs ofQuality

Costs of failure ofControl

Costs of Control


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6

Six Sigma Quality

- A philosophy and set of

methods companies use

to eliminate defects in

their products and

processes

- Seeks to reduce variation inthe processes that lead

to product defects

- The name, six sigma

refers to the variationthat exists within plus or

minus three standard

deviations of the process

outputs


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Six Sigma Quality (Continued)

- Six Sigma allows managers to readily describe

process performance using a commonmetric: Defects Per Million Opportunities(DPMO)

1,000,000x

unitsofNo.xunit

pererrorforiesopportunitofNumber

defectsofNumber

=DPMO


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Six Sigma Quality (Continued)Example of Defects Per Million

Opportunities (DPMO) calculation.Suppose we observe 200 lettersdelivered incorrectly to the wrongaddresses in a small city during asingle day when a total of 200,000letters were delivered. What is the

DPMO in this situation?

[ ]

000,1== 1,000,000x

200,000x1

200DPMO

So, for every onemillion lettersdelivered thiscitys postalmanagers canexpect to have1,000 lettersincorrectly sent

to the wrongaddress.

So, for every onemillion letters

delivered thiscitys postalmanagers canexpect to have1,000 lettersincorrectly sent

to the wrongaddress.

Cost of Quality: What might that DPMO mean in termsof over-time employment to correct the errors?

Cost of Quality: What might that DPMO mean in termsof over-time employment to correct the errors?


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Six Sigma Quality: DMAIC Cycle

- Define, Measure, Analyze, Improve, and Control

(DMAIC)

- Developed by General Electric as a means of

focusing effort on quality using a

methodological approach- Overall focus of the methodology is to understand

and achieve what the customer wants

- A 6-sigma program seeks to reduce the variation

in the processes that lead to these defects

- DMAIC consists of five steps.


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Six Sigma Quality: DMAIC Cycle

(Continued)

1. Define (D)

2. Measure (M)

3. Analyze (A)

4. Improve (I)

5. Control (C)

Customers and their priorities

Process and its performance

Causes of defects

Remove causes of defects

Maintain quality


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Example to illustrate theprocess

- We are the maker of this cereal.

Consumer reports has justpublished an article that shows that

we frequently have less than 15

ounces of cereal in a box.- What should we do?


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Step 1 - Define

- What is the critical-to-qualitycharacteristic?

-

The CTQ (critical-to-quality)characteristic in this case is theweight of the cereal in the box.

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2 - Measure

- How would we measure to evaluatethe extent of the problem?

-

- What are acceptable limits on thismeasure?

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2 Measure (continued)

- Lets assume that the governmentsays that we must be within 5

percent of the weight advertised onthe box.- Upper Tolerance Limit = 16 + .05(16)

= 16.8 ounces

- Lower Tolerance Limit = 16 .05(16)= 15.2 ounces

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2. Measure (continued)

- We go out and buy 1,000 boxes ofcereal and find that they weight an

average of 15.875 ounces with astandard deviation of .529 ounces.

- What percentage of boxes are

outside the tolerance limits?

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16

Upper Tolerance= 16.8

Lower Tolerance

= 15.2

ProcessMean = 15.875

Std. Dev. = .529

What percentage of boxes are defective (i.e. less than 15.2 oz)?

Z = (x Mean)/Std. Dev. = (15.2 15.875)/.529 = -1.276

NORMSDIST(Z) = NORMSDIST(-1.276) = .100978

Approximately, 10 percent of the boxes have less than 15.2Ounces of cereal in them!

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Step 3 - Analyze - How can weimprove the capability of our cereal

box filling process?

Decrease Variation

Center Process

IncreaseSpecifications

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Step 4 Improve How good is good enough?Step 4 Improve How good is good enough?Motorolas Six SigmaMotorolas Six Sigma

6 minimum from processcenter to nearest spec

1 23 1 02 3

12

6

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Motorolas Six SigmaMotorolas Six Sigma

- Implies 2 ppB bad with no process shift

- With 1.5 shift in either direction from

center (process will move), implies 3.4ppm bad.

1 23 1 02 3

12

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Step 5 ControlStep 5 Control

-Statistical Process Control (SPC) Use data from the actual

process

Estimate distributions Look at capability - is good

quality possible

Statistically monitor the processover time-

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Analytical Tools for Six Sigma and Continuous

Improvement: Flow ChartNo,ContinueMaterialReceived

fromSupplier

InspectMaterial for

DefectsDefectsfound?

Return toSupplierfor Credit

Yes

Can be used tofind qualityproblems

Can be used tofind qualityproblems

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Analytical Tools for Six Sigma and ContinuousImprovement: Run Chart

Can be used to identifywhen equipment orprocesses are notbehaving according tospecifications

Can be used to identifywhen equipment orprocesses are notbehaving according tospecifications

0.440.460.48

0.50.520.540.560.58

1 2 3 4 5 6 7 8 9 10 11 12Time (Hours)

Dia

me

ter

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Analytical Tools for Six Sigma and ContinuousImprovement: Pareto Analysis

Can be usedto find when80% of the

problemsmay beattributed to20% of the

causes

Can be usedto find when80% of the

problemsmay beattributed to20% of thecauses

Assy.Instruct.

Frequ

ency

Design Purch. Training

80%


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Analytical Tools for Six Sigma andContinuous Improvement: Histogram

Num

be

ro

fLots

Data RangesDefects

in lot

0 1 2 3 4

Can be used to identify the frequency of qualitydefect occurrence and display qualityperformance

Can be used to identify the frequency of qualitydefect occurrence and display qualityperformance

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Analytical Tools for Six Sigma andContinuous Improvement: Cause & Effect

Diagram

Effect

ManMachine

MaterialMethod

Environment

Possible causes:Possible causes: The resultsor effect

The resultsor effect

Can be used to systematically track backwards tofind a possible cause of a quality problem (oreffect)

Can be used to systematically track backwards tofind a possible cause of a quality problem (oreffect)

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Analytical Tools for Six Sigma and ContinuousImprovement: Control Charts

Can be used to monitor ongoing production processquality and quality conformance to stated standards ofquality

Can be used to monitor ongoing production processquality and quality conformance to stated standards ofquality

970

980

990

1000

1010

1020

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCL

UCL

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Other Six Sigma Tools

- Failure Mode and Effect Analysis (DMEA)is a structured approach to identify,

estimate, prioritize, and evaluate risk of

possible failures at each stage in the

process

- Design of Experiments (DOE) a statistical

test to determine cause-and-effect

relationships between process variables

and output

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Six Sigma Roles andResponsibilities

1.Executive leaders must championthe process of improvement

2.Corporation-wide training in SixSigma concepts and tools

3.Setting stretch objectives forimprovement

4.Continuous reinforcement andrewards

-

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The Shingo System: Fail-Safe Design

- Shingos argument: SQC methods do not prevent defects Defects arise when people make errors

Defects can be prevented by providingworkers with feedback on errors

- Poka-Yoke includes: Checklists

Special tooling that prevents workersfrom making errors

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ISO 9000

-

Series of standards agreed upon by theInternational Organization forStandardization (ISO)

- Adopted in 1987-

More than 100 countries- A prerequisite for global competition?- ISO 9000 directs you to "document

what you do and then do as you

documented"

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Three Forms of ISO Certification

1. First party: A firm audits itself againstISO 9000 standards

2. Second party: A customer audits itssupplier

3. Third party: A "qualified" national orinternational standards or certifying

agency serves as auditor

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External Benchmarking Steps

1. Identify those processes needingimprovement

2. Identify a firm that is the world leader

in performing the process3. Contact the managers of that company

and make a personal visit to interviewmanagers and workers

4. Analyze data

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Service Quality Measurement:Servqual

- A perceived service qualityquestionnaire survey methodology

- Examines Dimensions of ServiceQuality including: Reliability,

Responsiveness, Assurance,

Empathy, and Tangibles (e.g.,appearance of physical facilities,

equipment, etc.)

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Service Quality Measurement:Servqual (Continued)

- New version of this methodology is called e-

Service Quality dealing service on the Internet

- Dimensions of Service Quality on the e-Service

methodology include: Reliability,

Responsiveness, Access, Flexibility, Ease of

Navigation, Efficiency, Assurance/Trust,

Security/Privacy, Price Knowledge, Site

Aesthetics, and Customization/Personalization

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Question Bowl

Which of the following areDimensions of Design Quality?

a.Performance

b.Durabilityc.Aesthetics

d.All of the above

e.None of the aboveAnswer: d. All of the above

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Question Bowl

Approximately what percentage ofevery sales dollar is allocated tothe cost of quality?

a.Less than 5%b.About 10%

c.Between 15 and 20 %

d.More than 30%e.None of the aboveAnswer: c. Between 15 and 20 % (for cost ofreworking, scrapping, repeated service, etc.)

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Question Bowl

Which of the following areclassifications of the cost ofquality?

a.Appraisal costsb.Prevention costs

c.Internal failure costs

d.External failure costse.All of the above

Answer: e. All of the above


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Question Bowl

Which of the following is a CriticalCustomer Requirement (CCR) in thecontext of a Six Sigma program?

a.DMAICb.DPMOc.PCDAd.DOEe.None of the above

Answer: e. None of theabove (The CCR is thecriteria that is used todefine desired quality.

Processing a loan in 10days is an example of aCCR.)

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Question Bowl

The DMAIC cycle of Six Sigma issimilar to which of the followingquality management topics?

a.Continuous improvementb.Servqual

c.ISO 9000

d.External benchmarking

e.None of the aboveAnswer: a. Continuous improvement


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Question Bowl

Which of the following analyticaltools depict trends in quality dataover time?

a.Flowcharts

b.Run charts

c.Pareto charts

d.Checksheets

e.Cause and effect diagramsAnswer: b. Run charts


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Technical Note 8

Process Capability and

Statistical Quality Control

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-

Process Variation- Process Capability

- Process Control Procedures

Variable data

Attribute data

- Acceptance Sampling

Operating Characteristic Curve

OBJECTIVES

ONLY

IF TIMEPERMITS

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Basic Forms of VariationAssignable variation

is caused byfactors that can beclearly identifiedand possibly

managed

Common variationisinherent in theproduction process

Example: A poorly trainedemployee that creates variationin finished product output.

Example: A poorly trainedemployee that creates variationin finished product output.

Example: A molding processthat always leaves burrs orflaws on a molded item.

Example: A molding processthat always leaves burrs orflaws on a molded item.

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Taguchis View of Variation


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Taguchis View of Variation

IncrementalCost ofVariability

High

Zero

LowerSpec

TargetSpec

UpperSpec

Traditional View

IncrementalCost ofVariability

High

Zero

LowerSpec

TargetSpec

UpperSpec

Taguchis View

ExhibitsTN8.1 &TN8.2

ExhibitsTN8.1 &TN8.2

Traditional view is that quality within the LS and US is good and that thecost of quality outside this range is constant, where Taguchi views costs as

increasing as variability increases, so seek to achieve zero defects and thatwill truly minimize quality costs.

Traditional view is that quality within the LS and US is good and that thecost of quality outside this range is constant, where Taguchi views costs asincreasing as variability increases, so seek to achieve zero defects and that

will truly minimize quality costs.


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Process Capability Index, Cpk

3X-UTLor

3LTLXmin=Cpk

Shifts in Process Mean

Capability Index shows how

well parts being produced fitinto design limit specifications.

Capability Index shows how

well parts being produced fitinto design limit specifications.

As a production processproduces items smallshifts in equipment orsystems can cause

differences inproductionperformance fromdiffering samples.

As a production processproduces items smallshifts in equipment orsystems can causedifferences inproductionperformance fromdiffering samples.

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C S f


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A simple ratio:

Specification Width _________________________________________________________

Actual Process Width

Generally, the bigger the better.

Process Capability A Standard Measure ofProcess Capability A Standard Measure ofHow Good a Process Is.How Good a Process Is.

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P C bilit


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Process CapabilityProcess Capability

This is a one-sided Capability IndexConcentration on the side which is closest to

the specification - closest to being bad

=

3;

3

XUTLLTLXMinCpk

53

Th C l B E l


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The Cereal Box Example

- We are the maker of this cereal. Consumer reports

has just published an article that shows that wefrequently have less than 15 ounces of cereal in a

box.

- Lets assume that the government says that we

must be within 5 percent of the weightadvertised on the box.

- Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces

- Lower Tolerance Limit = 16 .05(16) = 15.2 ounces

- We go out and buy 1,000 boxes of cereal and find

that they weight an average of 15.875 ounces with

a standard deviation of .529 ounces.

-

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C l B P C bilitC l B P C bilit


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Cereal Box Process CapabilityCereal Box Process Capability

- Specification orTolerance Limits

Upper Spec = 16.8 oz

Lower Spec = 15.2 oz

-

Observed Weight Mean = 15.875 oz Std Dev = .529 oz

= 3

;3

XUTLLTLXMinCpk

=)529(.3

875.158.16;

)529(.3

2.15875.15MinCpk

{ }5829.;4253.MinCpk =

4253.=pkC

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What does a Cpk of .4253 mean?

- An index that shows how well the unitsbeing produced fit within the

specification limits.- This is a process that will produce a

relatively high number of defects.

-

Many companies look for a Cpk of 1.3 orbetter 6-Sigma company wants 2.0!

-


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Statistical UCL


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ProcessControl

(SPC) Charts LCLSamplesover time

1 2 3 4 5 6

UCL

LCL

Samplesover time

1 2 3 4 5 6

UCL

LCL

Samples

over time

1 2 3 4 5 6

Normal BehaviorNormal Behavior

Possible problem, investigatePossible problem, investigate

Possible problem, investigatePossible problem, investigate

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Control Limits are based on the


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Control Limits are based on theNormal Curve

x

0 1 2 3-3 -2 -1z

Standarddeviation unitsor z units.

Standard

deviation unitsor z units.

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C t l Li it


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Control Limits

We establish the Upper Control Limits (UCL) and

the Lower Control Limits (LCL) with plus or minus3 standard deviations from some x-bar or mean

value. Based on this we can expect 99.7% of our

sample observations to fall within these limits.

xLCL UCL

99.7%

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Example of Constructing ap-Chart:Required Data

1 100 4

2 100 2

3 100 5

4 100 3

5 100 6

6 100 4

7 100 3

8 100 7

9 100 1

10 100 2

11 100 3

12 100 2

13 100 2

14 100 8

15 100 3

Sample

No.

No. of

Samples

Number ofdefects foundin each sample

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Statistical Process Control Formulas:Attribute Measurements (p-Chart)

p =Total Numb er of Defe ctives

Total Numb er of Obse rvations

n

s

)p-(1p=

p

p

p

z-p=LCL

z+p=UCL

s

s

Given:

Compute control limits:

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Example of Constructing a p chart:


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1. Calculate thesample proportions,p (these are whatcan be plotted onthep-chart) for eachsample

1. Calculate thesample proportions,p (these are whatcan be plotted on

thep-chart) for eachsample

Sample n Defectives p1 100 4 0.04

2 100 2 0.02

3 100 5 0.05

4 100 3 0.03

5 100 6 0.06

6 100 4 0.04

7 100 3 0.03

8 100 7 0.07

9 100 1 0.01

10 100 2 0.02

11 100 3 0.03

12 100 2 0.02

13 100 2 0.02

14 100 8 0.08

15 100 3 0.03

Example of Constructing ap-chart:Step 1

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2. Calculate the average of the sample proportions2. Calculate the average of the sample proportions

0.036=1500

55=p

3. Calculate the standard deviation of the

sample proportion

3. Calculate the standard deviation of the

sample proportion

.0188=100

.036)-.036(1=

)p-(1p=p

ns

Example of Constructing ap-chart:Steps 2&3

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4. Calculate the control limits4. Calculate the control limits

3(.0188).036

UCL = 0.0924LCL = -0.0204 (or 0)UCL = 0.0924LCL = -0.0204 (or 0)

p

p

z-p=LCL

z+p=UCL

s

s

Example of Constructing ap-chart:Step 4

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f C C S


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Example of Constructing ap-Chart: Step 5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

p

Observation

UCL

LCL

5. Plot the individual sample proportions, the averageof the proportions, and the control limits

5. Plot the individual sample proportions, the averageof the proportions, and the control limits

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E l f b d R Ch t


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Example of x-bar and R Charts:Required Data

Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5

1 10.68 10.689 10.776 10.798 10.714

2 10.79 10.86 10.601 10.746 10.779

3 10.78 10.667 10.838 10.785 10.723

4 10.59 10.727 10.812 10.775 10.73

5 10.69 10.708 10.79 10.758 10.6716 10.75 10.714 10.738 10.719 10.606

7 10.79 10.713 10.689 10.877 10.603

8 10.74 10.779 10.11 10.737 10.75

9 10.77 10.773 10.641 10.644 10.725

10 10.72 10.671 10.708 10.85 10.712

11 10.79 10.821 10.764 10.658 10.708

12 10.62 10.802 10.818 10.872 10.727

13 10.66 10.822 10.893 10.544 10.75

14 10.81 10.749 10.859 10.801 10.701

15 10.66 10.681 10.644 10.747 10.728

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E l f b d R h t St 1 C l l t


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Example of x-bar and R charts: Step 1. Calculatesample means, sample ranges, mean of means,

and mean of ranges.

Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Avg Range

1 10.68 10.689 10.776 10.798 10.714 10.732 0.116

2 10.79 10.86 10.601 10.746 10.779 10.755 0.259

3 10.78 10.667 10.838 10.785 10.723 10.759 0.171

4 10.59 10.727 10.812 10.775 10.73 10.727 0.221

5 10.69 10.708 10.79 10.758 10.671 10.724 0.1196 10.75 10.714 10.738 10.719 10.606 10.705 0.143

7 10.79 10.713 10.689 10.877 10.603 10.735 0.274

8 10.74 10.779 10.11 10.737 10.75 10.624 0.669

9 10.77 10.773 10.641 10.644 10.725 10.710 0.132

10 10.72 10.671 10.708 10.85 10.712 10.732 0.179

11 10.79 10.821 10.764 10.658 10.708 10.748 0.16312 10.62 10.802 10.818 10.872 10.727 10.768 0.250

13 10.66 10.822 10.893 10.544 10.75 10.733 0.349

14 10.81 10.749 10.859 10.801 10.701 10.783 0.158

15 10.66 10.681 10.644 10.747 10.728 10.692 0.103

Averages 10.728 0.220400

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Example of x-bar and R charts: Step 2. Determine ControlLimit Formulas and Necessary Tabled Values

x Chart Control Limits

UCL = x + A R

LCL = x - A R

2

2

R Chart Control Limits

UCL = D R

LCL = D R

4

3

From Exhibit TN8.7From Exhibit TN8.7

n A2 D3 D4

2 1.88 0 3.27

3 1.02 0 2.574 0.73 0 2.28

5 0.58 0 2.11

6 0.48 0 2.00

7 0.42 0.08 1.92

8 0.37 0.14 1.869 0.34 0.18 1.82

10 0.31 0.22 1.78

11 0.29 0.26 1.74

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Example of x-bar and R charts: Steps 3&4 Calculate


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Example of x bar and R charts: Steps 3&4. Calculatex-bar Chart and Plot Values

10.601

10.856

=).58(0.2204-10.728RA-x=LCL=).58(0.2204-10.728RA+x=UCL

2

2

==

10.550

10.600

10.650

10.700

10.750

10.800

10.850

10.900

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Sample

Means

UCL

LCL

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Example of x-bar and R charts: Steps 5&6. Calculate


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p pR-chart and Plot Values

0

0.46504

==

==

)2204.0)(0(RD=LCL

)2204.0)(11.2(RD=UCL

3

4

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Sample

R

UCL

LCL

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Basic Forms of Statistical Sampling forQuality Control

- Acceptance Sampling is samplingto accept or reject the immediate

lot ofproductat hand- Statistical Process Control is

sampling to determine if the

process is within acceptablelimits

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A t S li

ONLY


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Acceptance Sampling

- Purposes Determine quality level Ensure quality is within predetermined

level

- Advantages Economy Less handling damage Fewer inspectors Upgrading of the inspection job

Applicability to destructive testing Entire lot rejection (motivation for

improvement)

IF TIMEPERMITS

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Acceptance Sampling (Continued)

- Disadvantages Risks of accepting bad lots and

rejecting good lots Added planning and documentation

Sample provides less informationthan 100-percent inspection

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Acceptance Sampling:Single Sampling Plan

A simple goal

Determine (1) how many units, n,to sample from a lot, and (2) themaximum number of defectiveitems, c, that can be found in the

sample before the lot is rejected

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Risk


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Risk

- Acceptable Quality Level (AQL)

Max. acceptable percentage of defectivesdefined by producer

- The (Producers risk) The probability of rejecting a good lot

- Lot Tolerance Percent Defective (LTPD) Percentage of defectives that defines

consumers rejection point

- The (Consumers risk) The probability of accepting a bad lot

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Operating Characteristic Curve


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p g

n = 99c = 4

AQL LTPD

00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

1 2 3 4 5 6 7 8 9 10 11 12

Percent defective

P

robability

of

accept

ance

=.10(consumers risk)

= .05 (producers risk)

The OCC brings the concepts of producers risk, consumers risk, samplesize, and maximum defects allowed together

The OCC brings the concepts of producers risk, consumers risk, samplesize, and maximum defects allowed together

The shape orslope of thecurve isdependent on aparticular

combination ofthe fourparameters

The shape orslope of thecurve isdependent on a

particular

combination ofthe fourparameters

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Example: Acceptance Sampling Problem

Zypercom, a manufacturer of video interfaces,purchases printed wiring boards from an outsidevender, Procard. Procard has set an acceptablequality level of 1% and accepts a 5% risk of rejectinglots at or below this level. Zypercom considers lotswith 3% defectives to be unacceptable and will assumea 10% risk of accepting a defective lot.

Develop a sampling plan for Zypercom and determine

a rule to be followed by the receiving inspectionpersonnel.

Zypercom, a manufacturer of video interfaces,

purchases printed wiring boards from an outsidevender, Procard. Procard has set an acceptablequality level of 1% and accepts a 5% risk of rejectinglots at or below this level. Zypercom considers lots

with 3% defectives to be unacceptable and will assumea 10% risk of accepting a defective lot.

Develop a sampling plan for Zypercom and determine

a rule to be followed by the receiving inspectionpersonnel.

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Example:


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Example:

Step 1. What is given and what is not?

In this problem, AQL is given to be 0.01 and LTDPis given to be 0.03. We are also given an alpha of0.05 and a beta of 0.10.

In this problem, AQL is given to be 0.01 and LTDPis given to be 0.03. We are also given an alpha of0.05 and a beta of 0.10.

What you need to determine is your samplingplan is c and n.

What you need to determine is your samplingplan is c and n.

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Example: Step 2 Determine c


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Example: Step 2. Determine c

First divide LTPD by AQL.First divide LTPD by AQL.

LTPD

AQL

=.03

.01

= 3

Then find the value for c by selecting the value in theTN7.10 n(AQL)column that is equal to or just greater thanthe ratio above.

Then find the value for c by selecting the value in theTN7.10 n(AQL)column that is equal to or just greater thanthe ratio above.

Exhibit TN 8.10Exhibit TN 8.10

c LTPD/AQL n AQL c LTPD/AQL n AQL

0 44.890 0.052 5 3.549 2.6131 10.946 0.355 6 3.206 3.286

2 6.509 0.818 7 2.957 3.981

3 4.890 1.366 8 2.768 4.695

4 4.057 1.970 9 2.618 5.426

So, c = 6.So, c = 6.

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Example: Step 3 Determine Sample Size


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Example: Step 3. Determine Sample Size

c = 6, from Tablen (AQL) = 3.286, from Table

AQL = .01, given in problem

c = 6, from Tablen (AQL) = 3.286, from Table

AQL = .01, given in problem

Sampling Plan:Take a random sample of 329 units from a lot.Reject the lot ifmore than 6 units are defective.

Sampling Plan:Take a random sample of 329 units from a lot.Reject the lot ifmore than 6 units are defective.

Now given the information below, compute the sample size in

units to generate your sampling plan

Now given the information below, compute the sample size inunits to generate your sampling plan

n(AQL/AQL) = 3.286/.01 = 328.6, or 329 (always round up)n(AQL/AQL) = 3.286/.01 = 328.6, or 329 (always round up)

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Question Bowl


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Question BowlA methodology that is used to show how well parts

being produced fit into a range specified by

design limits is which of the following?

a. Capability index

b. Producers risk

c. Consumers risk

d. AQL

e. None of the above

Answer: a. Capability index

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On a quality control chart if one of the values plotted falls outside

a boundary it should signal to the production manager to do

which of the following?

a. System is out of control, should be stopped and fixed

b. System is out of control, but can still be operated without any

concern

c. System is only out of control if the number of observationsfalling outside the boundary exceeds statistical

expectations

d. System is OK as is

e. None of the aboveAnswer: c. System is only out ofcontrol if the number of observationsfalling outside the boundary exceedsstatistical expectations

(We expect with Six Sigma that 3 out of 1,000 observations will fall outsidethe boundaries normally and those deviations should not lead managers to

conclude the system is out of control.)

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Question BowlYou want to prepare apchart and you

observe 200 samples with 10 in each,and find 5 defective units. What is the

resulting fraction defective?

a.25

b.2.5

c.0.0025

d.0.00025

e.Can not be computed on data above

Answer: c. 0.0025 (5/(2000x10)=0.0025)

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Question Bowl

You want to prepare an x-bar chart. If the number of

observations in a subgroup is 10, what is theappropriate factor used in the computation of

the UCL and LCL?

a. 1.88

b. 0.31c. 0.22

d. 1.78


Answer: b. 0.31 (from Exhibit TN8.7)

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Question BowlYou want to prepare an Rchart. If the number of

observations in a subgroup is 5, what is theappropriate factor used in the computation

of the LCL?

a. 0

b. 0.88c. 1.88

d. 2.11


Answer: a. 0 (from Exhibit TN8.7)

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Question Bowl

You want to prepare an Rchart. If the

number of observations in a subgroupis 3, what is the appropriate factor

used in the computation of the UCL?

a.0.87

b.1.00c.1.88

d.2.11

e.None of the above

Answer: e. None of the above (from ExhibitTN8.7 the correct value is 2.57)

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Question Bowl

The maximum number of defectives that can be

found in a sample before the lot is rejected isdenoted in acceptance sampling as which of

the following?

a. Alpha

b. Betac. AQL

d. c


Answer: d. c

set 6 quality management spc sqc

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