Design and Analysis of Experiments Seventh Edition by Douglas Montgomery ISBN 978-0470128664 0470128666
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ISBN 10: 0470128666
ISBN 13: 978-0470128664
Author: Douglas C. Montgomery
This bestselling professional reference has helped over 100,000 engineers and scientists with the success of their experiments. The new edition includes more software examples taken from the three most dominant programs in the field: Minitab, JMP, and SAS. Additional material has also been added in several chapters, including new developments in robust design and factorial designs. New examples and exercises are also presented to illustrate the use of designed experiments in service and transactional organizations. Engineers will be able to apply this information to improve the quality and efficiency of working systems.
Table of contents:
1 Introduction
1.1 Strategy of Experimentation
1.2 Some Typical Applications of Experimental Design
1.3 Basic Principles
1.4 Guidelines for Designing Experiments
1.5 A Brief History of Statistical Design
1.6 Summary: Using Statistical Techniques in Experimentation
1.7 Problems
2 Simple Comparative Experiments
2.1 Introduction
22 Basic Statistical Concepts
2.3 Sampling and Sampling Distributions
2.4 Inferences About the Differences in Mears, Randomized Designs
2.4.1 Hypothesis Testing
2.4.2 Choice of Sample Size
2.4.3 Confidence Intervals
2.4.4 The Case Where of
24.5 The Case Where of and or Are Knowa
2.4.6 Comparing a Single Mean to a Specified Value
2.4.7 Summary
2.5 Inferences About the Differences in Means, Paired Comparison Designs
2.5.1 The Paired Comparison Problem
2.5.2 Advantages of the Paired Comparison Design
2.6 Inferences About the Variances of Normal Distributions
2.7 Problems
3 Experiments with a Single Factor: The Analysis of Variance
3.1 An Example
3.2 The Analysis of Variance
3.3 Analysis of the Fixed Effects Model
3.3.1 Decomposition of the Total Sam of Squares
3.3.2 Sutistical Analysis
3.3.3 Estimation of the Model Parameters
3.3.4 Unbalanced Data
3.4 Model Adequacy Checking
3.4.1 The Normality Assumption
3.4.2 Plot of Residuals in Time Sequence
3.4.3 Plot of Residuals Versus Fitted Values
3.4.4 Plots of Residuals Versus Other Variables
3.5 Practical Interpretation of Results
3.5.1 A Regression Model
3.5.2 Comparisons Among Treatment Means
3.5.3 Graphical Comparisons of Means
3.5.4 Contrasts
3.5.5 Orthogonal Contrasts
3.5.6 Scheffe’s Method for Comparing All Contrasts
3.5.7 Comparing Pairs of Treatment Means
3.5.8 Comparing Treatment Means with a Control
3.6 Sample Computer Output
3.7 Determining Sample Size
3.7.1 Operating Characteristic Curves
3.7.2 Specifying a Standard Deviation Increase
3.7.3 Confidence Interval Estimation Method
3.8 A Real Economy Application of a Designed Experiment
3.9 Discovering Dispersion Effects
3.10 The Regression Approach to the Analysis of Variance
3.10.1 Least Squares Estimation of the Model Parameters
3.10.2 The General Regression Significance Test
3.11 Nonparametric Methods in the Analysis of Variance
3.11.1 The Kruskal-Wallis Test
3.11.2 General Comments on the Rank Transformaion
3.12 Problems
4 Randomized Blocks, Latin Squares, and Related Designs
4.1. The Randomized Complete Block Design
4.1.1 Statistical Analysis of the RCBD
4.1.2 Model Adequacy Checking
4.1.3 Sone Other Aspects of the Randomized Complete Block Design
4.1.4 Estimating Model Parameters and the General Regression
Significance Test
4.2 The Latin Square Design
4.3 The Graeco-Latin Square Design
4.4 Balanced Incomplete Block Designs
4.4.1 Statistical Analysis of the BIBD
4.4.2 Least Squares Estimation of the Parameters
4.4.3 Recovery of Interblock Information in the BIBD
4.5 Problems
5 Introduction to Factorial Designs
5.1 Basic Definitions and Principles
5.2 The Advantage of Factorials
5.3 The Two-Factor Factorial Design
5.3.1 An Example
5.3.2 Sturistical Analysis of the Fixed Effects Model
5.3.3 Model Adequacy Checking
5.3.4 Estimating the Model Parameters
5.3.5 Choice of Sample Size
5.3.6 The Assumption of No Interaction in a Two-Factor Model
5.3.7 One Observation per Cell
5.4 The General Factorial Design
5.5 Fitting Response Curves and Surfaces
5.6 Blocking in a Factorial Design
5.7 Problems
6 The 2 Factorial Design
6.1 Introduction
6.2 The 2 Design
6.3 The 2 Design
6.4 The General 2 Design
6.5 A Single Replicate of the 2 Design
6.6 Additional Examples of Unreplicated 2 Design
6.7 2 Designs are Optimal Designs
6.8 The Addition of Center Points to the 2 Design
6.9 Why We Work with Coded Design Variables
6.10 Problems
7 Blocking and Confounding in the 2 Factorial Design
7.1 Introduction
7.2 Blocking a Replicated 2 Factorial Design
7.3 Confounding in the 2ª Factorial Design
7.4 Confounding the 2′ Factorial Design in Two Blocks
7.5 Another illustration of Why Blocking Is Important
7.6 Confounding the 2ª Factorial Design in Four Blocks
7.7 Confounding the 2ª Factorial Design in 2 Blocks
7.8 Partial Confounding
7.9 Problems
8 Two-Level Fractional Factorial Designs
8.1 Introduction
8.2 The One-Half Fraction of the 2 Design
8.2.1 Definitions and Basic Principles
8.2.2 Design Resolution
823 Construction and Analysis of the One-Half Fraction
8.3 The One-Quarter Fraction of the 2* Design
8.4 The General 2 Fractional Factorial Design
8.4.1 Choosing a Design
8.4.2 Analysis of 2 Fractional Factorials
8.4.3 Blocking Fractional Factorials
8.5 Alias Structures in Fractional Factorials and other Designs
8.6 Resolution III Designs
8.6.1 Constructing Resolution III Designs
8.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects
8.6.3 Placket-Burman Designs
8.7 Resolution IV and V Designs
8.7.1 Resolution IV Designs
8.7.2 Sequential Experimentation with Resolution IV Designs
8.7.3 Resolution V Designs
8.8 Supersaturated Designs
8.9 Summary
8.10 Problems
9 Three-Level and Mixed-Level Factorial and Fractional Factorial Designs
9.1 The 3 Factorial Design
9.1.1 Notation and Motivation for the 3 Design
9.1.2 The 3 Design
9.1.3 The 3 Design
9.1.4 The General 3′ Design
9.2 Confounding in the 3º Factorial Design
9.2.1 The 3º Factorial Design in Theee Blocks
9.2.2 The 3º Factorial Design in Nine Blocks
9.2.3 The 3 Factorial Design in 3 Blocks
9.3 Fractional Replication of the 3 Factorial Design
9.3.1 The One-Third Fraction of the 3º Factorial Design
9.3.2 Other 3 Fractional Factorial Desigas
9.4 Factorials with Mixed Levels
9.4.1 Factors at Two and Three Levek
9.4.2 Factors at Two and Four Levels
9.5 Problems
10 Fitting Regression Models
10.1 Introduction
10.2 Linear Regression Models
10.3 Estimation of the Parameters in Linear Regression Models
10.4 Hypothesis Testing in Multiple Regression
10.4.1 Test for Significance of Regression
10.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients
10.5 Confidence Intervals in Multiple Regression
10.5.1 Confidence Intervals on the Individual Regression Coefficients
10.5.2 Confidence Interval on the Mean Response
10.6 Prediction of New Response Observations
10.7 Regression Model Diagnostics
10.7.1 Scaled Residuals and PRESS
10.7.2 lafluence Diagnostics
10.8 Testing for Lack of Fit
10.9 Problems
11 Response Surface Methods and Designs
11.1 Introduction to Response Surface Methodology
11.2 The Method of Steepest Ascent
11.3 Analysis of a Second-Order Response Surface
11.3.1 Location of the Stationary Point
11.3.2 Characterizing the Response Surface
11.3.3 Ridge Systems
11.3.4 Multiple Responses
11.4 Experimental Designs for Fitting Response Surfaces
11.4.1 Designs for Fitting the First-Onder Model
11.4.2 Designs for Fitting the Second-Order Model
11.4.3 Blocking in Response Surface Desigas
11.4.4 Computer-Generated (Optimal) Designs
11.5 Experiments with Computer Models
11.6 Mixture Experiments
11.7 Evolutionary Operation
11.8 Problems
12 Robust Parameter Design and Process Robustness Studies
12.1 Introduction
12.2 Crossed Array Designs
12.3 Analysis of the Crossed Array Design
12.4 Combined Array Designs and the Response Model Approach
12.5 Choice of Designs
126 Problems
13
Experiments with Random Factors
13.1 The Random Effects Model
13.2 The Two-Factor Factorial with Random Factors
13.3 The Two-Factor Mixed Model
13.4 Sample Size Determination with Random Effects
13.5 Rules for Expected Mean Squares
13.6 Approximate F Tests
13.7 Some Additional Topics on Estimation of Variance Components
13.7.1 Approximate Confidence Intervals on Variance Components
13.7.2 The Modified Large-Sample Method
13.7.3 Maximun Likelihood Estimation of Variance Components
13.8 Problems
14
Nested and Split-Plot Designs
14.1 The Two-Stage Nested Design
14.1.1 Statistical Analysis
14.1.2 Diagnostic Checking
14.13 Variance Components
14.1.4 Staggered Nested Designs
14.2 The General m-Stage Nested Design
14.3 Designs with Both Nested and Factorial Factors
14.4 The Split-Plot Design
14.5 Other Variations of the Split-Plot Design
14.5.1 Split-Plot Designs with More Than Two Factors
14.52 The Split-Split-Plot Design
14.5.3 The Strip-Split-Plot Design
14.6 Problems
15
Other Design and Analysis Topics
15.1 Nomnormal Responses and Transformations
15.1.1 Selecting a Transformation: The Box-Cox Method
15.1.2 The Generalized Linear Model
15.2 Unbalanced Data in a Factorial Design
15.2.1 Proportional Data: An Easy Case
15.2.2 Approximate Methods
15.2.3 The Exact Method
15.3 The Analysis of Covariance
15.3.1 Description of the Procedure
15.3.2 Computer Solution
15.3.3 Development by the General Regression Significance Test
15.3.4 Factorial Experiments with Covariates
15.4 Repeated Measures
15.5 Problems
Appendix
Table 1. Cumulative Standard Normal Distribution
Table II. Percentage Points of the / Distribution
Table Percentage Points of the x Distribution
Table IV. Percentage Points of the F Distribution
Table V. Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance
Table VI. Operating Characteristic Curves for the Random Effects Model Analysis of Variance
Table VII.
Percentage Points of the Stadentized Range Statistic
Table VIII. Critical Values for Dunnett’s Test for Comparing Treatments with a Control
Table IX.
Coefficients of Orthogonal Polynomials
Table X. Alias Relationships for 2 Fractional Factorial Designs with 15 and n ≤ 64
Bibliography
Index
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