I.2 Examples To Illustrate DOE Concepts 1. Optimally Feeding Fish Response Surfaces 2. Targeting A Process/Reducing Process Variation Sony USA.

I.2 Examples To Illustrate DOE I.2 Examples To Illustrate DOE ConceptsConcepts

1. Optimally Feeding Fish1. Optimally Feeding Fish Response SurfacesResponse Surfaces

2. Targeting A Process/Reducing 2. Targeting A Process/Reducing Process VariationProcess Variation Sony USA versus Sony JapanSony USA versus Sony Japan(Specs versus “Defects”)(Specs versus “Defects”)

3. Improving A Process3. Improving A Process 4. Weighing Two Objects4. Weighing Two Objects

I.2 Examples To Illustrate DOE I.2 Examples To Illustrate DOE ConceptsConcepts

5. Baking Bread5. Baking Bread 6. Mitigating Noise Factors6. Mitigating Noise Factors

Using Interactions Between Using Interactions Between Noise Factors and Control Noise Factors and Control Factors To Robustify A ProcessFactors To Robustify A Process

7. Comparing Tires7. Comparing Tires

Example 1Example 1Fitted Response Surface - With Fitted Response Surface - With

Design PointsDesign Points

Example 2Example 2Targeting a Process/Reducing VariationTargeting a Process/Reducing Variation

Example 2Example 2Accuracy versus PrecisionAccuracy versus Precision

xx

xxxxxx

Accurate and

Precise

Not Accurate but

Precise

x xx

x xxx xx

x xx

x xxx xx

Accurate but

Not Precise

x x

x

xxx

x

xx

x xxx

x

x

xx

xxx x

x

x x

x

xxx

x

xx

x xxx

x

x

x

xxx x

x

Not Accurate and

Not Precise

Example 2Example 2Sony USA vs Sony JAPANSony USA vs Sony JAPAN

Sony Japan Sony USA

LSL USL

Distribution of The Color Density in Television Sets Target Value is

Example 2Example 2What is the enemy?What is the enemy?

VARIATION (Nonuniformity of Product)VARIATION (Nonuniformity of Product) Why isn't it just defects?Why isn't it just defects?

– Well, for example,Well, for example,1. What was tolerable this week may not 1. What was tolerable this week may not be next week if your competitor has be next week if your competitor has reduced the variation of their process.reduced the variation of their process.

2. Oftentimes the definition of a defect 2. Oftentimes the definition of a defect is that it does not meet spec's. Since is that it does not meet spec's. Since spec's are manmade, they are subject to spec's are manmade, they are subject to the frailties therein. the frailties therein.

Example 2Example 2Statistical ThinkingStatistical Thinking

(Snee, 1990)(Snee, 1990)

Improvement Comes From Finding OutImprovement Comes From Finding Out 1. Where The Variation Is1. Where The Variation Is 2. What Kind Exists2. What Kind Exists 3. How Much There Is3. How Much There Is 4. How It Can Be Reduced4. How It Can Be Reduced

Deming - Reduce Variation to ImproveDeming - Reduce Variation to ImproveQuality and the ProcessQuality and the Process

Taguchi - Design Product to ReduceTaguchi - Design Product to ReduceFunctional VariationFunctional Variation

Example 3Example 3Improving a ProcessImproving a Process

Goal - Determine which factors affect the Goal - Determine which factors affect the mean of the process and which ones affect mean of the process and which ones affect the variation.the variation.

LOOK FOR (UNUSUAL) PATTERNS IN THE DATALOOK FOR (UNUSUAL) PATTERNS IN THE DATA

Example 3Example 3Improving a ProcessImproving a Process

1

2

Which Factors Which Factors AffectAffect– Accuracy?Accuracy?– Precision?Precision?

Example 4Example 4Weighing Two ObjectsWeighing Two Objects(Hotelling via Daniel)(Hotelling via Daniel)

M = A + EM = A + E M M Measured Weight Measured Weight E E Error Error

Example 4Example 4Weighing Two ObjectsWeighing Two Objects

Description Of The Problem:Description Of The Problem:– You Have Two Objects To Weigh On A You Have Two Objects To Weigh On A Counter Balance Scale.Counter Balance Scale.

– What Are Some Different Ways That You What Are Some Different Ways That You Weigh The Objects And Still Be Able To Weigh The Objects And Still Be Able To Calculate The Weights?Calculate The Weights?

– What Is The Best Way To Do It If You What Is The Best Way To Do It If You Are Only Allowed Two Weighings (Best So Are Only Allowed Two Weighings (Best So That The Error Of The Measured Weight That The Error Of The Measured Weight Is Made As Small As Possible)?Is Made As Small As Possible)?

Example 4Example 4Hidden ReplicationHidden Replication

With A Properly Designed With A Properly Designed Experiment You Can Make The Experiment You Can Make The Data Work Twice For You.Data Work Twice For You.

Example 5Example 5Baking BreadBaking Bread

Here We Use Design Principles To Here We Use Design Principles To Discover What Factors In A Bread Discover What Factors In A Bread Recipe Affect Some Responses Of Recipe Affect Some Responses Of Interest. Two Designs Are Interest. Two Designs Are Considered. The First Is When The Considered. The First Is When The Factors Are Changed One At A Time Factors Are Changed One At A Time (OAT). The Second Design Is A (OAT). The Second Design Is A Factorial Design.Factorial Design.

Example 5Example 5Factors and ResponsesFactors and Responses

FactorsFactors – A. Cake (-) or Dry (+) A. Cake (-) or Dry (+) Yeast Yeast

– B. Water TempB. Water Temp(Hi = +, Lo = -)(Hi = +, Lo = -)

– C. Amount of SugarC. Amount of Sugar(Two Levels -,+)(Two Levels -,+)

Example 5Example 5Factors and ResponsesFactors and Responses

Responses (Yes or No)Responses (Yes or No)– 1. How Well Did Yeast 1. How Well Did Yeast ProofProof (Froth Doubles Volume) (Froth Doubles Volume)

– 2. Rises Adequately2. Rises Adequately(Doubles Volume Within (Doubles Volume Within An Hour)An Hour)

– 3. Second Rising Is 3. Second Rising Is AdequateAdequate

Example 5Example 5OAT DesignOAT Design

B.

Water Temp.

- + -

- - +

- - - + - -A. YeastA B C

Example 5Example 5OAT Design ResponsesOAT Design Responses

What Factors What Factors AffectAffect– Response 1?Response 1?– Response 2?Response 2?– Response 3?Response 3?

B.

Water Temp.

- + -

- - +

- - - + - -A. YeastA B C

Y N N

N N N

N Y N

N N N

B.

Water Temp.

- + -

- - +

- - - + - -A. YeastA B C

- + +

+ - +

+ + -

+ + +

Baking Bread

Example 5Example 5Factorial DesignFactorial Design

B.

Water Temp.

- + -

- - +

- - - + - -A. Yeast

A B C

- + +

+ - +

+ + -

+ + +

Y Y N Y Y Y

Y N N Y N N

N N N

N Y N N Y Y

N N N

Example 5Example 5Factorial Design ResponsesFactorial Design Responses

What Factors AffectWhat Factors Affect– Response 1?Response 1?– Response 2?Response 2?– Response 3?Response 3?

Example 5Example 5Detecting InteractionsDetecting Interactions

From The First Design, We Discovered That From The First Design, We Discovered That Factor B Affected Response 1 And That Factor B Affected Response 1 And That Factor C Affected Response 2. But, Factor C Affected Response 2. But, Because It Was A OAT Design, We Could Not Because It Was A OAT Design, We Could Not Pick Up On The Interaction Between Factors Pick Up On The Interaction Between Factors A And C Which Affected Response 3. But It A And C Which Affected Response 3. But It Was Detected By The Factorial Design.Was Detected By The Factorial Design.

Example 6Example 6Mitigating Noise FactorsMitigating Noise Factors

FactorsFactors Machines 10 (+) and 16 (-)Machines 10 (+) and 16 (-) TreatmentTreatment

SiliconeSilicone OperatorsOperators

Estella (-)Estella (-) Donald (+)Donald (+)

ResponseResponse Number of picks (snags)Number of picks (snags)

Example 6Example 6Cube PlotCube Plot

What Can We Learn From This Plot?What Can We Learn From This Plot?

27 6

4 2

1 1

111

Silicone TreatmentNo Yes

Operator

Estella

Donald

Machine

10

16

Example 7Example 7Comparing TiresComparing Tires

Which of the two designs on Which of the two designs on the next slide is more the next slide is more appropriate for comparing appropriate for comparing four brands of tires?four brands of tires?

Why?Why?

Example 7Example 7Comparing TiresComparing Tires

DESIGN 1 Car

Tire Position 1 2 3 4I a b a bII b a b aIII c d c dIV d c d c

DESIGN 2

I a b c dII b a d cIII c d a bIV d c b a