purpose - courses.cecs.anu.edu.aucourses.cecs.anu.edu.au/courses/engn8101/lectures...parameter...

8/06/2007 ENGN8101 Modelling and Optimization 1

To provide direction in understanding the process and application of Parameter Design in the

development of robust products and processes

PurposePurpose


Parameter Design Course Objectives

Describe how Parameter Design relates to quality engineering.Apply the Engineered System model to the product/process of study.Identify the ideal function of the system.Identify control and noise factors affecting the system.


Parameter Design Course Objectives (continued)

Develop an experimental plan for both static and dynamic Parameter Design experiments.Use statistical concepts and tools from Experimental Design to analyze data from Parameter Design experiments.Make predictions and confirm improved robustness.Apply Parameter Design principles to teamwork to optimize project outcomes.

Introduction to Robustness

Introduction

to Robustness


Traditional Philosophy of Quality

No Good No GoodGood

No Loss Loss

LowerLimit

yTargetValue

Loss

ResponseUpperLimit


Either Side ofthe Specification Limit

Lower Limit

Target Value

Upper Limit

Just “in Spec”

Just“out of Spec”


Lower Limit

Target Value

Upper Limit

The Difference Between Targetand Specification Limit


Meeting the Target

The further away from target value, the lower the quality and the less satisfied the customer

Meet the TargetMeet the Target

The goal is to meet the target, not the specification

Lower Limit

Target Value

Upper Limit


Loss Function Philosophy

TargetPoor

ym

Loss

Poor

BestGood Good

FairFair

$

Response


How the Distribution Affects Quality Loss

Producing this distribution, we would experience some loss

Lower Limit

Target Value

Upper Limit

Loss Function


How the Distribution Affects Quality Loss

Producing this distribution, that has less variance from target, the loss would be lower

Lower Limit

Target Value

Upper Limit

Loss Function


Definition of Noise

NOISE FACTORS:Parameters which affect system response variability and are difficult, impossible or expensive to control.


Robustness

ROBUSTNESS: Low system response variability in the presence of noise.


For Example...

As consumers, we expect our automobiles to start every time, on the first turn of the key, regardless of:

Ambient temperatureAltitudeAge of the carHot or cold start, etc.


The Robust Product/Process

The robust product/process can operate within a wide range of conditions and still perform its intended function at a high quality level as perceived by the customer.


The Non-Robust Product/Process

The non-robust product/process will operate at a high quality level only within a limited range of conditions.

Parameter Design Introduction

Parameter

Design Intro


Dealing With Noise

Traditional– Eliminate or reduce– Compensate– Overlook

Parameter Design– Minimize the effect of noise


Parameter Designat the INA Tile Company

Kiln Wall

BurnersTiles

Initial Distribution

TargetAcceptable Deviation

TileDimension


The Traditional Approach

Upgrade technology– Build a new kiln– Add more burners

Feedback control– Control the temperature variation of the oven


Alternative Solutions

1. Redesign and build a new kiln» Cost = $1 million

2. Adjust the parameters that could be changed easily and inexpensively

» Cost = Unknown


Actions

$$ $$ $

INA Tile Company AlternativesCost Comparisons

Inspection and Scrap

Redesigned Kiln Increased Lime Content


Parameter Design at the INA Tile Company Summary

TargetAcceptable Deviation

Improved Distribution

Initial Distribution

Tile Dimension


What is the intent and how do we maximize it?

Shift from:

What is wrong and how do we fix it?

to:

Dr. Genichi Taguchi’s Approach


Making the system insensitive to usage variations

Shift from:

Controlling, compensating or eliminating usage variationsto:



Taguchi’s 3-Step Robust Engineering Process

1. Concept Design

2. Parameter Design

3. Tolerance Design


The Impact ofIgnoring Parameter Design

Concept DesignOften requires longer lead timesMay introduce unnecessarily high levels of technology

Tolerance DesignMakes products more expensive to manufacture


Parameter Design

2.Selecting optimum values for parameters that will reduce the variability of the response to noise

The best design is determined at the leastcost by:1. Running a designed experiment with

low cost components and processsettings


Parameter Design

4.Selecting the lowest cost setting for factors that have minimal effect onresponse

The best design is determined at the leastcost by:3. Selecting optimum values for control

factors that will shift the mean of theresponse toward target


Steps in Parameter Design

1. Identify Project and Team

2. Formulate Engineered System: Ideal Function

3. Formulate Engineered System: Parameters

4. Assign Control Factors to Inner Array

5. Assign Noise Factors to Outer Array

6. Conduct Experiment and Collect Data

7. Analyze Data and Select Optimal Design

8. Predict and Confirm

Parameter Design: Static

Parameter

Design: Static


Steps in Parameter Design: Static










Project Selection

Project selection should be based on the potential to:– Increase customer satisfaction– Increase reliability– Incorporate new technology– Reduce cost– Reduce warranty– Achieve Best-in-Class


Successful Project Requirements

A clear objective Cross-functional team Thorough planning Management support


Customer’s World

“Voice of the Customer”

INTENT:What the customer expects

PERCEIVED RESULT:What the

customer gets

Customer’s World


SYSTEM:Transforms intent into perceived

result

SIGNAL:Causes the system to fulfill the intent

RESPONSE (y):System output that determines the perceived result

Engineer’s World

Engineer’s World


Signal Energy

Transformations

Engineer’s World

Response (y)

Intended Result

Unintended Result

Maximizing energy which produces the intended result will minimize the unintended results (error states)

System:

Energy Transfer


The ideal function is the transfer of energy to the intended result

Ideal Function

Engineer’s World

Response (y)

Intended Result

SystemSignal


Measuring the transformation of energy

Shift from:

Measuring symptoms of poor quality

to:



Response

A response should:Be related to the Perceived ResultBe an engineering metricBe related to the Ideal Function of the systemQuantify the energy transfer


Composite View

“Voice of the Customer”

System Response (y)Signal

Customer Intent

PerceivedResult


Completing the Engineered System

Signal ResponseSystem

CONTROL FACTORS: parameters that are controllable by the engineer

NOISE FACTORS: parameters that affect the system and are difficult, impossible or expensive to control


Where to Look for Noise

environment

customer usage

neighboring systems

deterioration

manufacturing


Noise or Control?

Is material hardness (Rockwell) a noise or control factor?

ControlNoise


Experimental PlanSelect Control Factors

Filter control factor list based on:– Improvement potential– Change feasibility– Cost– Testing resources – Prioritize list

Control FactorsA B C …


Experimental PlanIdentify Levels

Keep in mind:– 2 or 3 levels is most

common– Level range should be

as wide as possible– One level may

represent baseline– More levels require

more testing

A1

A2

Leve

ls…



Experimental PlanSelect Orthogonal Array

Select based on:– Number of factors– Number of levels– Testing resources


Leve

ls

Orthogonal array L?This array is called the Inner Array


Inner and Outer Arrays

A B CControl Factors

...

Noise Factors

Outer Orthogonal Array

Response Data

Inner Orthogonal

Array


Noise

Noise Factors

Outer Array – Effect on energy transfer– Effect on response

variability– Engineering knowledge– Screening experiments– Customer usage profiles

• Prioritize noise factor list based on:


Preliminary Run

Dot plot

ResponseN1 N2


Experimental Layout

An experiment can be run in any order

Outer Array

Inner Array

A B C …...y11 y12

y21 y22 ...

............

123

Run N1 N2…


1900305000.0On

15

Level2

600456000.5Off

9

Ball-and-Ramp Analysis: Introduction

Response:Swirl Time (secs)

Control Factors (Inner Array):L : Run Length (mm)A : Ramp-to-Funnel Angle (deg)H : Run End Height (mm)C : Clamping (turns unscrewed)O : Operator Hat

Noise Factor (Outer Array)Ball Size (mm)


Experimental Plan

25

11

14

267 28 2

Run No. A

123 1

1

1

2

122

H

12

2

1

2

211

O

12

C

1

1

2

212

21

L

2

1

1

112

22

1

1

1

221

22

c6

2

1

2

121

21

c5NOISE

N1 N2


Calculating Averages

13.0 13.0 13.5

7.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

1 1 1 1 1 8.3 8.4 8.11

8.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

9.1 9.4 9.3 11.7 11.9 11.72 1 2 2 167 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 18 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2

Run No. A H O C L N1

NOISEN2

5.4 5.1 5.4 6.7 6.8 6.21 1 1 2 22

N1 N2 y

3 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

Avg 1Avg 2Effect Effect

Avg N2Avg N1


13.0 13.0 13.5

9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

10.71 1 1 1 1 8.3 8.4 8.11

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 167 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 22

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

Avg 1Avg 2Effect

Avg N2Avg N1Effect



13.0 13.0 13.5

9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.75

10.71 1 1 1 1 8.3 8.4 8.1 8.31

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.34

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.367 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.2


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.32

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5


Avg N2Avg N1



9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1


Avg N2Avg N1



Calculating Control Factor Effects

9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1


Avg N2Avg N1


10.7

9.710.512.6

9.2


7.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

1 1 1 1 1 8.3 8.4 8.1 13.0 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

9.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.38 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 10.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1

8.8Avg 1Avg 2Effect Effect

Avg N2Avg N1



9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1

10.58.8Avg 1

Avg 2Effect Effect

Avg N2Avg N1


8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1

9.7


7.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

-1.710.5


Avg N2Avg N1



9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1


9.2 9.6 10.5 10.910.1 9.7 8.9 8.4-0.9 -0.1 1.6 2.5

Avg N2Avg N1

-1.710.5

8.8


9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1

-1.710.5


9.2 9.6 10.5 10.910.1 9.7 8.9 8.4-0.9 -0.1 1.6 2.5

Avg N2Avg N1

Calculating the Noise Effect


10.7

11.5 11.6 12.0

13.0 13.0 13.5

11.4 11.5 11.4

11.7 11.9 11.715.5 15.4 15.110.8 10.6

6.7 6.8 6.211.0 11.2 11.2

11.5

9.77.6 7.8 7.62 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 8.3 13.21

9.98.5 8.3 8.21 2 2 2 1 8.3 11.44

10.59.1 9.4 9.32 1 2 2 1 9.3 11.867 9.8 10.0 10.02 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.41 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.51 2 2 1 2 6.5 11.1

-1.710.5


9.2 9.6 10.5 10.910.1 9.7 8.9 8.4-0.9 -0.1 1.6 2.5

Avg N2Avg N1




13.0

11.5

9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1

-1.710.5


9.2 9.6 10.5 10.910.1 9.7 8.9 8.4-0.9 -0.1 1.6 2.5

7.9Avg N2Avg N1



3.6

13.0

11.5

9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 2 7.7 11.75

10.71 1 1 1 1 8.3 8.4 8.1 13.0 13.5 8.3 13.21

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 1 8.3 11.44

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 1 9.3 11.867 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 9.9 15.3 12.68 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 7.7 9.210.7


NOISEN2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 2 5.3 6.62

N1 N2 y

8.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2 6.5 11.1

-1.710.5


9.2 9.6 10.5 10.910.1 9.7 8.9 8.4-0.9 -0.1 1.6 2.5

7.9Avg N2Avg N1


Avg 1Avg 2Effect

A H O C L N8.8 9.2 9.6 10.5 10.9 7.9

10.5 10.1 9.7 8.9 8.4 11.5− 1.6 − 0.9 − 0.1 1.6 2.5 3.6

Main Effects Plot

6789

10111213

A1 A2 H1 H2 O1 O2 C1 C2 L1 L2 N1 N2

Factors

Ave

rage

Tim

e (s

ecs)


1

2

11.48.3

7.7 10.7

7.7

8.3

9.39.9

5.36.5

11.7

13.2

11.815.3

6.611.1

Calculating Noise x Control Interaction Effects

N1 N2 N1 N2 N1 N2 N1 N2 N1 N2CF 1CF 2

Effect

N1 N2 yRun No. A H O C L N1 N212345678

DATA2 1 2 1 2

1 1 1 1 1

1 2 2 2 1

1 2 2 12 2 1 1 1

22 1 2 2

1 1 1 2 22 2 1 2

9.7

10.7

9.9

10.512.6

9.2

5.98.8


7.7

11.4

10.7

7.7 11.79.3 11.89.9 15.3

2222


8.3

7.1N1 N2 N1 N2 N1 N2 N1 N2 N1 N2

CF 1CF 2

Effect


DATA1 2 1 2

1 1 1 1 1

1 2 2 2 1

1 2 2 12 1 1 12 1 2 2

1 1 1 2 21 2 2 1 2

9.7

10.78.3 13.2

9.9

10.512.6

9.2

5.95.3 6.68.86.5 11.1


15.3

11.4

15.3

11.7

13.2

11.8

10.7

6.611.1

8.3


7.18.6

N1 N2 N1 N2 N1 N2 N1 N2 N1 N2CF 1CF 2

Effect


DATA2 1 2 1 2

1 1 1 1 1

1 2 2 2 1

2 1 2 2 12 2 1 1 1

22 1 2 2

1 1 1 2 22 2 1 2

9.77.7

10.78.3

9.9

10.59.39.9 12.67.7 9.2

5.98.86.5


11.411.16.5

7.715.310.7

8.3

10.67.18.6

N1 N2 N1 N2 N1 N2 N1 N2 N1 N2CF 1CF 2

Effect



DATA2 1 2 1 2

1 1 1 1 1

1 2 2 2 1

2 1 2 2 12 2 1 1 1

22 1 2 2

1 1 1 2 21 2 2 1 2

9.77.7 11.7

10.78.3 13.2

9.9

10.59.3 11.89.9 12.6

9.2

5.95.3 6.68.8


10.7

6.5

7.7

12.410.67.1

8.6


8.3

N1 N2 N1 N2 N1 N2 N1 N2 N1 N2CF 1CF 2

Effect


DATA2 1 2 1 2

1 1 1 1 1

1 2 2 2 1

2 1 2 2 12 2 1 1 1

22 1 2 2

1 1 1 2 21 2 2 1 2

9.77.7 11.7

10.78.3 13.2

9.911.4

10.59.3 11.89.9 15.3 12.6

9.2

5.95.3 6.68.811.1


Calculating Interaction Effects

+−

++

−− + −−+

A

B

(− −) = B(− +) −Interactioneffect

( − ) =2

A B

(+ +) − (+ −) = A


12.410.6


8.3

7.18.6

N1 N2 N1 N2 N1 N2 N1 N2 N1 N2CF 1CF 2

Effect


DATA2 1 2 1 2

1 1 1 1 1

1 2 2 2 1

2 1 2 2 12 2 1 1 1

22 1 2 2

1 1 1 2 21 2 2 1 2

9.77.7 11.7

10.78.3 13.2

9.911.4

10.59.3 11.89.9 15.3 12.67.7 9.210.7

5.95.3 6.68.86.5 11.1

0.1

Effect( ) ( )

2

+ + + − − + − −− −−=



8.3

N1 N2 N1 N2 N1 N2 N1 N2 N1 N2CF 1CF 2

Effect


DATA2 1 2 1 2

1 1 1 1 1

1 2 2 2 1

2 1 2 2 12 2 1 1 1

22 1 2 2

1 1 1 2 21 2 2 1 2

9.77.7 11.7

10.78.3 13.2

9.911.4

10.59.3 11.89.9 15.3 12.67.7 9.210.7

5.95.3 6.68.86.5 11.1

0.1 0.4 0.0 -1.1 -0.4

7.6 10.8 7.8 11.4 8.1 12.8 9.0 12.98.1 12.2 7.9 11.5 7.6 10.1 6.8 10.012.4

10.67.18.6 Effect

( ) ( )2

+ + + − − + − −− −−=


Noise x Control Interaction Plot

4

6

8

10

12

14

N1 N2

Ave

rage

Tim

e

CF Level 1CF Level 2

A H O C LN1 N2

CF 1 7.1 10.6 7.6 10.8 7.8 11.4 8.1 12.8 9.0 12.9CF 2 8.6 12.4 8.1 12.2 7.9 11.5 7.6 10.1 6.8 10.0Effect 0.1 0.4 0.0 -1.1 -0.4

N1 N2 N1 N2N1 N2 N1 N2

N1 N2N1 N2 N1 N2 N1 N2


Average Effects Daniel PlotN

xO

O NxA

Nxc

5

Nxc

6

c5 NxL

c6 NxH

H NxC

C A L N

Absolute Effect

Half-NormalScores

NxC

N

L

AC

H

0.0

1.0

2.0

3.0

4.0

0.00 0.50 1.00 1.50 2.00

Half-Normal Scores

Abs

olut

e Ef

fect

s

0.0 0.1 0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.9 1.1 1.6 1.7 2.5 3.6.04 .12 .21 .29 .38 .47 .57 .67 .77 .89 1.02 1.17 1.36 1.61 2.10


1. Reduce variabilityIdentify factors which interact with noise -- use these to reduce variability.

2. Adjust to mean to targetIdentify factors with location effects, that do not interact with noise -- use these to adjust the mean.

2-Step Optimization


=Energy producing the intended resultEnergy wasted on unintended results

SN

Signal-to-Noise Ratio


y

Intended vs. Unintended Results

measured in σ’s


SN = 10 log10( )

2yσ

Robustness Metric

Always maximize S/N to improve robustness


Calculating Signal-to-Noise Ratio

Run No. N1 N2 σ S/Ny

Avg 1Avg 2Effect

9.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

13.0 13.0 13.5 10.71 1 1 1 1 8.3 8.4 8.11

9.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

10.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

8 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

5.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 228.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6

A H O C L


13.5 2.7

Run No. N1 N2 σ S/N


y

Effect

2.29.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

13.0 13.0 10.71 1 1 1 1 8.3 8.4 8.11

1.79.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

1.410.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

1.78 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

0.75.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 222.58.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6 3.0

Avg 1Avg 2

A H O C L


12.0

S


N = 10 log10 ( )2y

σ


Effect

2.2 12.89.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

2.713.0 13.0 13.5 10.71 1 1 1 1 8.3 8.4 8.11

1.7 15.39.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

1.4 17.710.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

1.7 14.88 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

0.7 18.25.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 222.5 10.88.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6 12.63.0

Avg 1Avg 2

A H O C L


Calculating Signal-to-Noise Effects


Effect

2.2 12.89.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

2.7 12.013.0 13.0 13.5 10.71 1 1 1 1 8.3 8.4 8.11

1.7 15.39.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

1.4 17.710.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

1.7 14.88 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

0.7 18.25.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 222.5 10.88.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6 12.63.0

Avg 1Avg 2

A H O C L


14.1


Run No. A H O C L N1 N2 σ S/Ny

Effect

2.2 12.89.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

2.7 12.013.0 13.0 13.5 10.71 1 1 1 1 8.3 8.4 8.11

1.7 15.39.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

1.4 17.710.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

1.7 14.88 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

0.7 18.25.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 222.5 10.88.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6 12.63.0

Avg 1Avg 2



15.3

14.1


Effect

2.2 12.89.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

2.7 12.013.0 13.0 13.5 10.71 1 1 1 1 8.3 8.4 8.11

1.79.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

1.4 17.710.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

1.7 14.88 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

0.7 18.25.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 222.5 10.88.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6 12.63.0

Avg 1Avg 2 14.5



15.3

14.1


Effect

2.2 12.89.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

2.7 12.013.0 13.0 13.5 10.71 1 1 1 1 8.3 8.4 8.11

1.79.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

1.4 17.710.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

1.7 14.88 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

0.7 18.25.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 222.5 10.88.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6 12.63.0

Avg 1Avg 2 14.5

-0.4


15.3

14.1

Run No. A H O C L N1 N2 σ S/N


y

Effect

2.2 12.89.77.6 7.8 7.6 11.5 11.6 12.02 1 2 1 25

2.7 12.013.0 13.0 13.5 10.71 1 1 1 1 8.3 8.4 8.11

1.79.98.5 8.3 8.2 11.4 11.5 11.41 2 2 2 14

1.4 17.710.59.1 9.4 9.3 11.7 11.9 11.72 1 2 2 16

1.7 14.88 2 7.4 7.9 7.7 10.8 10.6 10.72 1 2 2 9.2

0.7 18.25.95.4 5.1 5.4 6.7 6.8 6.21 1 1 2 222.5 10.88.83 6.5 6.5 6.5 11.0 11.2 11.21 2 2 1 2

7 9.8 10.0 10.0 15.5 15.4 15.12 2 1 1 1 12.6 12.63.0

Avg 1Avg 2 14.5

-0.4 1.8

15.213.4

0.3

14.414.1

-4.4

12.116.5

0.2

14.414.2


S/N Ratio Effects Plot

A H O C L14.1 15.2 14.4 12.1 14.414.5 13.4 14.1 16.5 14.2- 0.4 1.8 0.3 - 4.4 0.2

101112131415161718

A1 A2 H1 H2 O1 O2 C1 C2 L1 L2Factors

Ave

rage

S/N

Avg 1Avg 2Effect


S/N Daniel Plot

L O A c5 c6 H CAbsolute Effect 0.2 0.3 0.4 0.9 1.1 1.8 4.4

Half-Normal Score 0.09 0.27 0.45 0.66 0.90 1.20 1.71

C

0.0

1.0

2.0

3.0

4.0

5.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80Half-Normal Score

Abs

olut

e Ef

fect


2-Step Optimization

1. Reduce variabilityIdentify factors with large S/N effects--use these to reduce variability.

2. Adjust mean to targetIdentify factors with location effects--use these to adjust the mean.


2-Step Optimization Example

A1 A2 H1 H2 O1 O2 C1 C2 L1 L210

12

14

16

18

Ave

rage

S/N

6

8

10

12

Ave

rage

Tim

e

A1 A2 H1 H2 O1 O2 C1 C2 L1 L2

purpose - courses.cecs.anu.edu.aucourses.cecs.anu.edu.au/courses/engn8101/lectures...parameter...

Documents