Design of Engineering Experiments

Hussam Alshraideh

Chapter 1: Introduction to Designed Experiments

October 4, 2015

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Introduction

Statistical Studies

How can we evaluate evidenceagainst global warming?

Are cell phones dangerous?

How likely are we to win thelottery?

Is there bias against women inappointing managers?

Can Champix help smokers inquitting?

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Introduction

Data

Data is information we gatherthrough experiments or observation.

Experiment on low carb diet

Data: weight of subjectsbefore and after

Survey on effectiveness of a TVad

Data: percentage who wentto Starbucks since ad aired

- The ultimate goal is to translate data into knowledge andunderstanding.

- Statistics is the art and science of learning from data.

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Introduction

Three Aspects of a Study

Design: Planning how to obtaindata

Description: Summarizing thedata

Inference: Making decisions andpredictions

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Introduction

Methods of Data Collection

Observational: used to assess association

Retrospective studies: historical dataProspective studies: current observation

Designed Experiments: used to obtain cause-and-effect relationships

Study ”Subjects” are controlled.

Subjects: The entities that we measure in a studyMeasurements may vary from subject to subject. ⇒ Variability

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Introduction to DOX

Introduction to DOX

An experiment is a test or a series of tests to identify reasons ofchange in some response variable.

Experiments are used widely in the engineering world

Process characterization & optimizationEvaluation of material propertiesProduct design & developmentComponent & system tolerance determination

”All experiments are designed experiments, some are poorly designed,some are well-designed”

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Introduction to DOX

Introduction to DOX

Example: study the effect of two hardening processes on an aluminumalloy.

Oil quenching vs. Saltwater quenching.

Objective: to determine which quenching solution produces themaximum hardness.

Run tests for each solution and compare averages.⇒ poor design

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Introduction to DOX

Introduction to DOX

Before running the experiment need to know:

Other quenching media: air

Other factors: temperature of media

# of runs at each combination: 2, 3, 5?

Order of runs

Method of data analysis

Significant difference in the average

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Introduction to DOX

Engineering Experiments

What variables are mostinfluential?

Screening experiments

Settings of x’s for optimal y?

Response surface methods

Settings of x’s to minimizevariability of y?

Robust parameter designs

Setting of x’s for minimumeffect of z’s on y?

Robust parameter designs

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History of DOE

Four Eras in the History of DOX

The agricultural origins, 1908 1940s

W.S. Gossett and the t-test (1908)R. A. Fisher & his co-workersProfound impact on agricultural scienceFactorial designs, ANOVA

The first industrial era, 1951 late 1970s

Box & Wilson (1951), response surfacesApplications in the chemical & process industries

The second industrial era, late 1970s 1990

Quality improvement initiatives in many companiesTaguchi and robust parameter design, process robustness

The modern era, beginning circa 1990

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History of DOE

William Sealy Gosset (1876-1937)

Gosset’s interest in barley cultivationled him to speculate that design ofexperiments should aim, not only atimproving the average yield, but also atbreeding varieties whose yield wasinsensitive (robust) to variation in soiland climate. Gosset was a friend ofboth Karl Pearson and R.A. Fisher, anachievement, for each had amonumental ego and a loathing for theother. Gosset was a modest man whocut short an admirer with the commentthat Fisher would have discovered it allanyway.”

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History of DOE

R. A. Fisher (1890 1962) George E. P. Box

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The Basic Principles of DOX

The Basic Principles of DOX

Randomization

Running the trials in an experiment in random orderNotion of balancing out effects of lurking variables

Replication

Sample size (improving precision of effect estimation, estimation oferror or background noise)Replication versus repeat measurements? (see pages 12, 13)

Blocking

Dealing with nuisance factors

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Strategy of Experimentation

Strategy of Experimentation

”Best-guess” experiments

Used a lotMore successful than you might suspect, but there aredisadvantages(needs good first guess, no guarantee of optimality)

One-factor-at-a-time (OFAT) experiments

Sometimes associated with the scientific or engineering methodDevastated by interaction, also very inefficient

Statistically designed experiments

Based on Fishers factorial concept

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Factorial Designs

Factorial Designs

In a factorial experiment, all possiblecombinations of factor levels are tested

The golf experiment:

Type of driver (Oversized, Regular sized)Type of ball (Balata, Three piece)Walking vs. RidingType of beverage (Water, Something Else)Time of round (morning, afternoon)Weather (cool, hot)Type of golf shoe spike (metal, plastic)Windy vs. calm days

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Factorial Designs

Factorial Designs

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Factorial Designs

No Title

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Factorial Designs

Factorial Designs with Several Factors

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Factorial Designs

Factorial Designs with Several Factors: A FractionalFactorial

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Planning, Conducting and Analyzing an Experiment

Planning, Conducting & Analyzing an Experiment

1 Recognition of and statement of problem

2 Choice of factors, levels, and ranges

3 Selection of the response variable(s)

4 Choice of design

5 Conducting the experiment

6 Statistical analysis

7 Drawing conclusions, recommendations

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Planning, Conducting and Analyzing an Experiment

Planning, Conducting & Analyzing an Experiment

Get statistical thinking involved early

Your non-statistical knowledge is crucial to success

Pre-experimental planning (steps 1-3) vital

Think and experiment sequentially (use the KISS principle)

See Coleman & Montgomery (1993) Technometrics paper +supplemental text material

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