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Factorial and Fractional Factorial Designs

Douglas C. Montgomery

Many experiments in engineering, science and business involve several factors. This course is an introduction to these types of multifactor experiments. The appropriate experimental strategy for these situations is based on the factorial design, a type of experiment where factors are varied together. This course focuses on designing these types of experiments and on using the ANOVA for analyzing the resulting data. These types of experiments often include nuisance factors, and the blocking principle can be used in factorial designs to handle these situations. As the number of factors of interest grows full factorials become too expensive and fractional versions of the factorial design are useful. This course will cover the benefits of fractional factorials, along with methods for constructing and analyzing the data from these experiments.

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What's inside

Syllabus

Unit 1: Introduction to Factorial Design
Unit 2: The 2^k Factorial Design
Unit 3: Blocking and Confounding in the 2^k Factorial Design
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Suitable for learners with some prior knowledge in experimental design and statistics
Developed by Douglas C. Montgomery, a renowned professor in the field of statistics
Explores experimental design techniques, which are fundamental in various disciplines including engineering, science, and business
Covers topics such as factorial design, blocking, fractional factorials, and ANOVA, providing a comprehensive understanding of multifactor experiments
Provides practical knowledge applicable to real-world scenarios where multiple factors are involved

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Reviews summary

Mastering factorial and fractional experimental designs

According to students, this course provides a comprehensive and practical introduction to factorial and fractional factorial designs. Learners particularly praise the clear and effective explanations of complex statistical concepts and the direct applicability of the material to real-world engineering and research problems. However, some students note that the course assumes a solid background in basic statistics, and without it, the pace can be challenging. It is widely considered highly valuable for professionals seeking to apply experimental design principles.
The course maintains a fast pace and dives into significant theoretical depth.
"The pace was a bit fast for me in some sections, especially with the ANOVA concepts."
"I felt a bit overwhelmed by the theoretical depth at times."
"The content is dense, but the quality is high."
Content is directly applicable for engineers, scientists, and researchers.
"Highly recommended for anyone in R&D."
"Overall, very valuable for my work in quality control."
"This filled a significant gap in my knowledge for process optimization."
"Great for engineers and scientists looking to formalize their experimental approach."
The instructor provides highly clear explanations with real-world relevance.
"This course provided an incredibly thorough and practical understanding of factorial and fractional factorial designs. The lectures were clear, and the examples were highly relevant to real-world engineering problems."
"Excellent course! The structure from full factorial to fractional designs was logical and easy to follow. The professor clearly knows the material inside out."
"This course is a must-take for anyone dealing with experimental design. The concepts are explained beautifully, and the practical relevance is undeniable. I used what I learned directly in a project at work."
Some students suggest more hands-on exercises and software demonstrations.
"More practical exercises or guided software demos would have been beneficial."
"I think it could benefit from a few more case studies to illustrate practical challenges."
A strong background in basic statistics is essential for success.
"The course is definitely geared towards those with a solid foundation in basic statistics. If you're a beginner, prepare to do some extra reading on the side."
"I found it quite challenging without a strong background in statistics. The pace was a bit fast for me in some sections, especially with the ANOVA concepts."
"As a complete beginner to experimental design, I struggled significantly. The course assumes too much prior knowledge in statistics."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Factorial and Fractional Factorial Designs with these activities:
Review the book 'Factorial Designs' by Douglas C. Montgomery
Reading and reviewing this book will provide you with a comprehensive understanding of factorial design concepts.
Show steps
  • Purchase or borrow the book from a library.
  • Read and take notes on the chapters relevant to the course material.
  • Summarize the key concepts and ideas in your own words.
Follow online tutorials on fractional factorial designs
Following online tutorials will provide you with a structured and interactive way to learn about fractional factorial designs.
Browse courses on Factorial Design
Show steps
  • Search for online tutorials on fractional factorial designs using platforms like Coursera, edX, or YouTube.
  • Choose a tutorial that aligns with your learning style and level.
  • Follow the tutorial steps and complete the exercises or assignments.
Join a study group to discuss factorial design concepts
Joining a study group will provide you with a platform to discuss and clarify concepts with peers, enhancing your understanding.
Browse courses on Factorial Design
Show steps
  • Find classmates who are interested in forming a study group.
  • Decide on a regular meeting time and place.
  • Take turns leading the discussions and presenting on specific topics.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Practice 2^k factorial design exercises
Practice solving 2^k factorial design exercises to improve your understanding of the concept.
Browse courses on Factorial Design
Show steps
  • Review the lecture notes on 2^k factorial design.
  • Attempt to solve the practice problems provided in the textbook.
  • Seek help from the instructor or classmates if needed.
Create a presentation on blocking in factorial design
Creating a presentation on blocking in factorial design will help you understand the concept and improve your communication skills.
Browse courses on Factorial Design
Show steps
  • Gather information on blocking in factorial design from textbooks, research papers, and online resources.
  • Organize the information into a logical flow for your presentation.
  • Create visual aids such as slides or diagrams to illustrate your points.
  • Practice your presentation and get feedback from peers or the instructor.
Attend a workshop on ANOVA for factorial design analysis
Attending a workshop on ANOVA for factorial design analysis will provide you with hands-on experience and improve your understanding.
Browse courses on Factorial Design
Show steps
  • Search for workshops on ANOVA for factorial design analysis in your area or online.
  • Register for the workshop and pay the registration fee.
  • Attend the workshop and actively participate in the activities.
  • Follow up with the workshop organizers or instructors if you have any questions.
Contribute to an open-source project related to factorial design
Contributing to an open-source project will provide you with practical experience and enhance your understanding of real-world applications.
Browse courses on Factorial Design
Show steps
  • Identify open-source projects related to factorial design on platforms like GitHub.
  • Review the project documentation and identify areas where you can contribute.
  • Contact the project maintainers and express your interest in contributing.
  • Follow the project's guidelines and make your contributions.

Career center

Learners who complete Factorial and Fractional Factorial Designs will develop knowledge and skills that may be useful to these careers:
Statistician
Statisticians collect, analyze, and interpret data. They also work on developing new technologies for the statistics industry. Factorial and Fractional Factorial Designs is a core foundational element of statistics that is required for success. The course covers the benefits of fractional factorials, along with methods for constructing and analyzing the data from these experiments, and an understanding of ANOVA for analyzing the resulting data.
See salaries and explore the career path for Statistician
Biomedical Engineer
Biomedical Engineers design and develop medical devices and equipment. They also work on developing new technologies for healthcare. Factorial and Fractional Factorial Designs may be useful for Biomedical Engineers because it can help them to design experiments to test the effects of different factors on the performance of medical devices and equipment.
See salaries and explore the career path for Biomedical Engineer
Chemical Engineer
Chemical Engineers design and operate chemical plants and other facilities where chemicals are produced. They also work on developing new technologies for the chemical industry. Factorial and Fractional Factorial Designs may be useful for Chemical Engineers because it can help them to design experiments to test the effects of different factors on the performance of chemical plants and other facilities.
See salaries and explore the career path for Chemical Engineer
Civil Engineer
Civil Engineers design and build infrastructure, such as roads, bridges, and buildings. They also work on developing new technologies for the construction industry. Factorial and Fractional Factorial Designs may be useful for Civil Engineers because it can help them to design experiments to test the effects of different factors on the performance of infrastructure.
See salaries and explore the career path for Civil Engineer
Computer Engineer
Computer Engineers design and build computers and other electronic devices. They also work on developing new technologies for the computer industry. Factorial and Fractional Factorial Designs may be useful for Computer Engineers because it can help them to design experiments to test the effects of different factors on the performance of computers and other electronic devices.
See salaries and explore the career path for Computer Engineer
Electrical Engineer
Electrical Engineers design and build electrical systems and equipment. They also work on developing new technologies for the electrical industry. Factorial and Fractional Factorial Designs may be useful for Electrical Engineers because it can help them to design experiments to test the effects of different factors on the performance of electrical systems and equipment.
See salaries and explore the career path for Electrical Engineer
Industrial Engineer
Industrial Engineers design and improve industrial processes. They also work on developing new technologies for the manufacturing industry. Factorial and Fractional Factorial Designs may be useful for Industrial Engineers because it can help them to design experiments to test the effects of different factors on the performance of industrial processes.
See salaries and explore the career path for Industrial Engineer
Aerospace Engineer
Aerospace Engineers design and test aircraft, spacecraft, and missiles. They also work on developing new technologies for these vehicles. Factorial and Fractional Factorial Designs may be useful for Aerospace Engineers because it can help them to design experiments to test the effects of different factors on the performance of aircraft, spacecraft, and missiles.
See salaries and explore the career path for Aerospace Engineer
Mechanical Engineer
Mechanical Engineers design and build machines and other mechanical devices. They also work on developing new technologies for the mechanical industry. Factorial and Fractional Factorial Designs may be useful for Mechanical Engineers because it can help them to design experiments to test the effects of different factors on the performance of machines and other mechanical devices.
See salaries and explore the career path for Mechanical Engineer
Nuclear Engineer
Nuclear Engineers design and operate nuclear power plants and other nuclear facilities. They also work on developing new technologies for the nuclear industry. Factorial and Fractional Factorial Designs may be useful for Nuclear Engineers because it can help them to design experiments to test the effects of different factors on the performance of nuclear power plants and other nuclear facilities.
See salaries and explore the career path for Nuclear Engineer
Petroleum Engineer
Petroleum Engineers design and operate oil and gas wells. They also work on developing new technologies for the petroleum industry. Factorial and Fractional Factorial Designs may be useful for Petroleum Engineers because it can help them to design experiments to test the effects of different factors on the performance of oil and gas wells.
See salaries and explore the career path for Petroleum Engineer
Software Engineer
Software Engineers design and develop software. They also work on developing new technologies for the software industry. Factorial and Fractional Factorial Designs may be useful for Software Engineers because it can help them to design experiments to test the effects of different factors on the performance of software.
See salaries and explore the career path for Software Engineer
Systems Engineer
Systems Engineers design and develop complex systems. They also work on developing new technologies for the systems engineering industry. Factorial and Fractional Factorial Designs may be useful for Systems Engineers because it can help them to design experiments to test the effects of different factors on the performance of complex systems.
See salaries and explore the career path for Systems Engineer
Data Scientist
Data Scientists collect, analyze, and interpret data. They also work on developing new technologies for the data science industry. Factorial and Fractional Factorial Designs may be useful for Data Scientists because it can help them to design experiments to test the effects of different factors on the performance of data science models.
See salaries and explore the career path for Data Scientist
Materials Engineer
Materials Engineers design and develop new materials. They also work on developing new technologies for the materials industry. Factorial and Fractional Factorial Designs may be useful for Materials Engineers because it can help them to design experiments to test the effects of different factors on the performance of new materials.
See salaries and explore the career path for Materials Engineer

Reading list

We've selected 12 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Factorial and Fractional Factorial Designs.
Cover image
Design of Experiments for Reliability Achievement
Save
Classic textbook on the design and analysis of experiments, and it valuable resource for anyone who wants to learn more about factorial design. It provides a comprehensive overview of the topic, from the basics to advanced techniques.
Design of Experiments for Reliability Achievement...
Hardcover
$$$$
Design of Experiments for Reliability Achievement...
Kindle Edition
$$$$
Cover image
Student Solutions Manual Engineering Statistics, 5e
Save
Provides comprehensive coverage of the design and analysis of experiments, including factorial and fractional factorial designs. It valuable resource for students and professionals in engineering, science, and business.
Manual Engineering Statistics, 5e Student Solutions
Paperback
$$$
Cover image
Fact or Fluke?
Save
Classic work on the design of experiments, and it must-read for anyone who wants to learn more about the subject. It provides a clear and concise overview of the principles of experimental design, and it includes many examples.
Fact or Fluke?: A Critical Look at Statistical...
Paperback
$$
Cover image
Experiments
Save
Provides a more theoretical approach to the design and analysis of experiments, including factorial and fractional factorial designs. It valuable resource for students and professionals who want to gain a deeper understanding of the subject.
Experiments
Paperback
Check
Experiments
Kindle Edition
Check
Cover image
Chemistry of The Environment
Save
More specialized treatment of fractional factorial design, and it good choice for readers who want to learn more about this topic. It provides a detailed discussion of the theory and practice of fractional factorial design, and it includes many examples.
Chemistry of The Environment
Kindle Edition
$$$
Cover image
Response Surfaces: Designs and Analyses
Save
Specialized treatment of experiments with mixtures, and it valuable resource for anyone who wants to learn more about this topic. It provides a detailed discussion of the theory and practice of experiments with mixtures, and it includes many examples.
Response Surfaces: Designs and Analyses
Paperback
Check
Response Surfaces: Designs and Analyses
Kindle Edition
Check
Cover image
Solutions Manual to accompany Introduction to...
Save
Provides a comprehensive introduction to linear regression analysis, including the use of factorial and fractional factorial designs. It valuable resource for students and professionals who need to use linear regression analysis in their work.
Solutions Manual to accompany Introduction to...
Paperback
$$
Cover image
Applied Statistics and Probability for Engineers
Save
Provides a practical introduction to statistics and probability, including the use of factorial and fractional factorial designs. It valuable resource for students and professionals in engineering who need to apply statistics and probability to their work.
Applied Statistics and Probability for Engineers,...
Kindle Edition
$$$$
Applied Statistics and Probability for Engineers
Loose Leaf
$$$$
Applied Statistics and Probability for Engineers
Hardcover
$$$$
Applied Statistics and Probability for Engineers
Paperback
$$$
Applied Statistics and Probability for Engineers
Hardcover
$$$
Applied Statistics and Probability for Engineers,...
Paperback
$$$$
Applied Statistics And Probability for Engineers
Hardcover
$$$
Applied Statistics and Probability for Engineers,...
Loose Leaf
$$$$
Applied Statistics and Probability for Engineers
Hardcover
$$$$
Applied Statistics and Probability for Engineers,...
Loose Leaf
$$$$
Cover image
A Primer on the Taguchi Method, Second Edition
Save
Provides a comprehensive introduction to Taguchi methods for quality engineering, including the use of factorial and fractional factorial designs. It valuable resource for students and professionals who need to design and analyze experiments using Taguchi methods.
A Primer on the Taguchi Method, Second Edition
Paperback
Check
A Primer on the Taguchi Method, Second Edition
Kindle Edition
Check
Cover image
Sample Size Determination and Power
Save
Provides a comprehensive introduction to statistical methods for quality improvement, including the use of factorial and fractional factorial designs. It valuable resource for students and professionals who need to apply statistical methods for quality improvement to their work.
Sample Size Determination and Power
Hardcover
$$$
Sample Size Determination and Power (Wiley Series...
Kindle Edition
$$$$
Cover image
Response Surface Methodology
Save
Provides a comprehensive introduction to response surface methodology, including the use of factorial and fractional factorial designs. It valuable resource for students and professionals who need to design and analyze experiments using response surface methodology.
Response Surface Methodology
Paperback
Check
Response Surface Methodology
Kindle Edition
Check
Cover image
A Primer on Experiments with Mixtures
Save
Provides a comprehensive introduction to experiments with mixtures, including the use of factorial and fractional factorial designs. It valuable resource for students and professionals who need to design and analyze experiments with mixtures.
A Primer on Experiments with Mixtures
Paperback
Check
A Primer on Experiments with Mixtures
Kindle Edition
Check

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Course image
Effort
4 weeks of study, 4-8 hours/week
Level
Intermediate
Via
Coursera
Institution
Arizona State University
Instructor
Douglas C. Montgomery
Language
English
Transcripts
Español Français Português Deutsch Italiano 中文 العربية 한국어 日本語 हिंदी Nederlands Svenska Pусский Türkçe Polski Ελληνικά українська мова Bahasa Indonesia ไทย қазақша
This course belongs to a collection called Design of Experiments. It's comprised of four courses:
  1. Factorial and Fractional Factorial Designs (viewing)
  2. Experimental Design Basics
  3. Random Models, Nested and Split-plot Designs
  4. Response Surfaces, Mixtures, and Model Building
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Suitable for learners with some prior knowledge in experimental design and statistics
Developed by Douglas C. Montgomery, a renowned professor in the field of statistics
Explores experimental design techniques, which are fundamental in various disciplines including engineering, science, and business
Covers topics such as factorial design, blocking, fractional factorials, and ANOVA, providing a comprehensive understanding of multifactor experiments
Provides practical knowledge applicable to real-world scenarios where multiple factors are involved
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