SOLUTION MANUAL
Design and Analysis of Experiments
Douglas C. Montgomery
10th Edition
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
Table of Contents
1. Introduction
2. Simple Comparative Experiments
3. Experiments with a Single Factor: The Analysis of Variance
4. Randomized Blocks, Latin Squares, and Related Designs
5. Introduction to Factorial Designs
6. The 2ᵏ Factorial Design
7. Blocking and Confounding in the 2ᵏ Factorial Design
8. Two-Level Fractional Factorial Designs
9. Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs
10. Fitting Regression Models
11. Response Surface Methods and Designs
12. Robust Parameter Design and Process Robustness Studies
13. Experiments with Random Factors
14. Nested and Split-Plot Designs
15. Other Design and Analysis Topics
1-1
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
Chapter 1
Introduction
Solutions
1.1S. Suppose that you want to design an experiment to study the proportion of unpopped kernels of
popcorn. Complete steps 1-3 of the guidelines for designing experiments in Section 1.4. Are there any major
sources of variation that would be difficult to control?
Step 1 – Recognition of and statement of the problem. Possible problem statement would be – find the best
combination of inputs that maximizes yield on popcorn – minimize unpopped kernels.
Step 2 – Selection of the response variable. Possible responses are number of unpopped kernels per 100
kernals in experiment, weight of unpopped kernels versus the total weight of kernels cooked.
Step 3 – Choice of factors, levels and range. Possible factors and levels are brand of popcorn (levels: cheap,
expensive), age of popcorn (levels: fresh, old), type of cooking method (levels: stovetop, microwave),
temperature (levels: 150C, 250C), cooking time (levels: 3 minutes, 5 minutes), amount of cooking oil (levels,
1 oz, 3 oz), etc.
1.2. Suppose that you want to investigate the factors that potentially affect cooked rice.
(a) What would you use as a response variable in this experiment? How would you measure the
response?
(b) List all of the potential sources of variability that could impact the response.
(c) Complete the first three steps of the guidelines for designing experiments in Section 1.4.
Step 1 – Recognition of and statement of the problem.
Step 2 – Selection of the response variable.
Step 3 – Choice of factors, levels and range.
1.3. Suppose that you want to compare the growth of garden flowers with different conditions of
sunlight, water, fertilizer and soil conditions. Complete steps 1-3 of the guidelines for designing
experiments in Section 1.4.
Step 1 – Recognition of and statement of the problem.
Step 2 – Selection of the response variable.
Step 3 – Choice of factors, levels and range.
1.4. Select an experiment of interest to you. Complete steps 1-3 of the guidelines for designing
experiments in Section 1.4.
1-2
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
1.5. Search the World Wide Web for information about Sir Ronald A. Fisher and his work on
experimental design in agricultural science at the Rothamsted Experimental Station.
Sample searches could include the following:
1.6. Find a Web Site for a business that you are interested in. Develop a list of factors that you would
use in an experimental design to improve the effectiveness of this Web Site.
1.7. Almost everyone is concerned about the rising price of gasoline. Construct a cause and effect
diagram identifying the factors that potentially influence the gasoline mileage that you get in your car.
How would you go about conducting an experiment to determine any of these factors actually affect your
gasoline mileage?
1.8. What is replication? Why do we need replication in an experiment? Present an example that
illustrates the differences between replication and repeated measures.
Repetition of the experimental runs. Replication enables the experimenter to estimate the experimental
error, and provides more precise estimate of the mean for the response variable.
1.9 S. Why is randomization important in an experiment?
To assure the observations, or errors, are independently distributed randome variables as required by
statistical methods. Also, to “average out” the effects of extraneous factors that might occur while running
the experiment.
1.10 S. What are the potential risks of a single, large, comprehensive experiment in contrast to a sequential
approach?
The important factors and levels are not always known at the beginning of the experimental process. Even
new response variables might be discovered during the experimental process. By running a large
comprehensive experiment, valuable information learned early in the experimental process can not likely
be incorporated in the remaining experimental runs.
1-3
Design and Analysis of Experiments
Douglas C. Montgomery
10th Edition
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
Table of Contents
1. Introduction
2. Simple Comparative Experiments
3. Experiments with a Single Factor: The Analysis of Variance
4. Randomized Blocks, Latin Squares, and Related Designs
5. Introduction to Factorial Designs
6. The 2ᵏ Factorial Design
7. Blocking and Confounding in the 2ᵏ Factorial Design
8. Two-Level Fractional Factorial Designs
9. Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs
10. Fitting Regression Models
11. Response Surface Methods and Designs
12. Robust Parameter Design and Process Robustness Studies
13. Experiments with Random Factors
14. Nested and Split-Plot Designs
15. Other Design and Analysis Topics
1-1
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
Chapter 1
Introduction
Solutions
1.1S. Suppose that you want to design an experiment to study the proportion of unpopped kernels of
popcorn. Complete steps 1-3 of the guidelines for designing experiments in Section 1.4. Are there any major
sources of variation that would be difficult to control?
Step 1 – Recognition of and statement of the problem. Possible problem statement would be – find the best
combination of inputs that maximizes yield on popcorn – minimize unpopped kernels.
Step 2 – Selection of the response variable. Possible responses are number of unpopped kernels per 100
kernals in experiment, weight of unpopped kernels versus the total weight of kernels cooked.
Step 3 – Choice of factors, levels and range. Possible factors and levels are brand of popcorn (levels: cheap,
expensive), age of popcorn (levels: fresh, old), type of cooking method (levels: stovetop, microwave),
temperature (levels: 150C, 250C), cooking time (levels: 3 minutes, 5 minutes), amount of cooking oil (levels,
1 oz, 3 oz), etc.
1.2. Suppose that you want to investigate the factors that potentially affect cooked rice.
(a) What would you use as a response variable in this experiment? How would you measure the
response?
(b) List all of the potential sources of variability that could impact the response.
(c) Complete the first three steps of the guidelines for designing experiments in Section 1.4.
Step 1 – Recognition of and statement of the problem.
Step 2 – Selection of the response variable.
Step 3 – Choice of factors, levels and range.
1.3. Suppose that you want to compare the growth of garden flowers with different conditions of
sunlight, water, fertilizer and soil conditions. Complete steps 1-3 of the guidelines for designing
experiments in Section 1.4.
Step 1 – Recognition of and statement of the problem.
Step 2 – Selection of the response variable.
Step 3 – Choice of factors, levels and range.
1.4. Select an experiment of interest to you. Complete steps 1-3 of the guidelines for designing
experiments in Section 1.4.
1-2
, Solutions from Montgomery, D. C. (2019) Design and Analysis of Experiments, Wiley, NY
1.5. Search the World Wide Web for information about Sir Ronald A. Fisher and his work on
experimental design in agricultural science at the Rothamsted Experimental Station.
Sample searches could include the following:
1.6. Find a Web Site for a business that you are interested in. Develop a list of factors that you would
use in an experimental design to improve the effectiveness of this Web Site.
1.7. Almost everyone is concerned about the rising price of gasoline. Construct a cause and effect
diagram identifying the factors that potentially influence the gasoline mileage that you get in your car.
How would you go about conducting an experiment to determine any of these factors actually affect your
gasoline mileage?
1.8. What is replication? Why do we need replication in an experiment? Present an example that
illustrates the differences between replication and repeated measures.
Repetition of the experimental runs. Replication enables the experimenter to estimate the experimental
error, and provides more precise estimate of the mean for the response variable.
1.9 S. Why is randomization important in an experiment?
To assure the observations, or errors, are independently distributed randome variables as required by
statistical methods. Also, to “average out” the effects of extraneous factors that might occur while running
the experiment.
1.10 S. What are the potential risks of a single, large, comprehensive experiment in contrast to a sequential
approach?
The important factors and levels are not always known at the beginning of the experimental process. Even
new response variables might be discovered during the experimental process. By running a large
comprehensive experiment, valuable information learned early in the experimental process can not likely
be incorporated in the remaining experimental runs.
1-3
