Fundamental Concepts in the Design of Experiments

by Hicks, Charles R.

• ISBN13: 9780195105810
• ISBN10: 0195105818
• Edition: 4th
• Format: Hardcover
• Copyright: 1994-01-01
• Publisher: Oxford University Press

Summary

This brief, yet comprehensive text covers the essentials of experimental design used by applied researchers in solving problems in the field. It is appropriate for a variety of experimental methods courses found in engineering and statistics departments. Students learn to use applied statistics for planning, running, and analyzing an experiment. The text includes 350+ problems taken from the author's actual industrial consulting experiences to give students valuable practice with real data and problem solving. The use of the computer is promoted and SAS (Statistical Analysis System) computer programs are incorporated to facilitate analysis. Coverage of the analysis of residuals, the concepts of resolution in fractional replications, the Plackett-Burman designs, and Taguchi techniques isnew to this edition.

Table of Contents

Preface

The Experiment, the Design, and the Analysis

Introduction to Experimental Design

The Experiment

The Design

The Analysis

Examples

Summary in Outline

Further ReadingProblems

Review of Statistical Inference

Introduction

Estimation

Tests of Hypothesis

The Operating Characteristic Curve

How Large a Sample?

Application to Tests on Variances

Application to Tests on Means

Assessing Normality

Applications to Tests on Proportions

Analysis of Experiments with SAS

Further ReadingProblems

Single-Factor Experiments with No Restrictions on Randomization

Introduction

Analysis of Variance Rationale

After ANOVA--What?

Tests on Means

Confidence Limits on Means

Components of Variance

Checking the Model

SAS Programs for ANOVA and Tests after ANOVA

Summary

Further ReadingProblems

Single-Factor Experiments: Randomized Block and Latin Square Designs

Introduction

Randomized Complete Block Design

ANOVA Rationale

Missing Values

Latin Squares

Interpretations

Assessing the Model

Graeco-Latin Squares

Extensions

SAS Programs for Randomized Blocks and Latin Squares

Summary

Further ReadingProblems

Factorial Experiments

Introduction

Factorial Experiments: An Example

Interpretations

The Model and Its Assessment

ANOVA Rationale

One Observation Per Treatment

SAS Programs for Factorial Experiments

Summary

Further ReadingProblems

Fixed, Random, and Mixed Models

Introduction

Single-Factor Models

Two-Factor Models

EMS Rules

EMS Derivations

The Pseudo-F Test

Expected Mean Squares Via Statistical Computing Packages

Remarks

Repeatability and Reproducibility for a Measurement System

SAS Problems for Random and Mixed Models

Further ReadingProblems

Nested and Nested-Factorial Experiments

Introduction

Nested Experiments

ANOVA Rationale

Nested-Factorial Experiments

Repeated-Measures Design and Nested-Factorial Experiments

SAS Programs for Nested and Nested-Factorial Experiments

SummaryFurther ReadingProblems

Experiments of Two or More Factors: Restrictions on Randomization

Introduction

Factorial Experiment in a Randomized Block Design

Factorial Experiment in a Latin Square Design

Remarks

SAS Programs

SummaryProblems

2f Factorial Experiments

Introduction

2 Squared Factorial

2 Cubed Factorial

2f Remarks

The Yates Method

Analysis of 2f Factorials When n=1

Some Commments about Computer Use

Summary

Further ReadingProblems

3f Factorial Experiments

Introduction

3 Squared Factorial

3 Cubed Factorial

Computer Programs

SummaryProblems

Factorial Experiment: Split-Plot Design

Introduction

A Split-Plot Design

A Split-Split-Plot Design

Using SAS to Analyze a Split-Plot Experiment

Summary

Further ReadingProblems

Factorial Experiment: Confounding in Blocks

Introduction

Confounding Systems

Block Confounding, No Replication

Block Confounding with Replication

Confounding in 3F Factorials

SAS Progrms

Summary

Further ReadingProblems

Fractional Replication

Introduction

Aliases

2f Fractional Replications

Plackett-Burman Designs

Design Resolution

3f-k Fractional Factorials

SAS Programs

Summary

Further ReadingProblems

The Taguchi Approach to the Design of Experiments

Introduction

The L4 (2 Cubed) Orthogonal Array

Outer Arrays

Signal-To-Noise Ratio

The L8 (2 7) Orthogonal Array

The L16 (2 15) Orthogonal Array

The L9 (3 4) Orthogonal Array

Some Other Taguchi Designs

Summary

Further ReadingProblems

Regression

Introduction

Linear Regression

Curvilinear Regression

Orthogonal Polynomials

Multiple Regression

Summa

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