Q 592. What are Box-Behnken Designs? Compare them with full factorial designs and highlight their advantages and disadvantages. Note for website visitors - This platform hosts two weekly questions, one on Tuesday and the other on Friday. All previous questions can be found here: https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/. To participate in the current question, please visit the forum homepage at https://www.benchmarksixsigma.com/forum/. The question will be open until Tuesday or Friday at 5 PM Indian Standard Time, depending on the launch day. Responses will not be visible until they are reviewed, and only non-plagiarised answers with less than 5-10% plagiarism will be approved. If you are unsure about plagiarism, please check your answer using a plagiarism checker tool such as https://smallseotools.com/plagiarism-checker/ before submitting. All correct answers shall be published, and the top-rated answer will be displayed first. The author will receive an honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term. Some people seem to be using AI platforms to find forum answers. This is a risky approach as AI responses are error prone as our questions are application-oriented (they are never straightforward). Have a look at this funny example - https://www.benchmarksixsigma.com/forum/topic/39458-using-ai-to-respond-to-forum-questions/ We also use an AI content detector at https://crossplag.com/ai-content-detector/. Only answers with less than 15-20% AI-generated content will be approved.

Box-Behnken Designs This design was explored by statisticians George E. P. Box and Donald R. Behnken. So, it gave name of Box-Behnken design. It is a type of experimental statistical design which is generally used in statistics and engineering to improve the process and conducting experiments. This is used to find the optimal combination of input variables which can lead to achieve desired output. This design is generally useful when we want to know the relationship between variables. This is used when there is quadratic, and interactions are considered among variables. Whereas a full factorial design generally consists of all possible combinations which are available. In this test we can study the effect of each factor. Below are the common differences: Box-Behnken Design Full Factorial Design No of experiments This is related to response surface methodology, so uses fewer experiments In this method we can test all possible combinations for each factor. Efficiency More efficient with fewer experiments More efficient with comprehensive experiments. It increases the experiments with the no of factors and levels. Complexity of analysis Simpler in comparison Complex when dealing with large numbers Application Useful when no of experiments are limited. More useful when no of experiments are more and have complex relationship Advantages and disadvantages of Box-Behnken Design: Advantages Disadvantages Box-Behnken is more efficient with full factorial when fewer experiments are allowed with limited resources It has limitations in experiments It is less complex that full factorial design Generally used selective sample for experiments, so sometimes missed optimal points Helps to identify optimal factor level It is very less flexible, so sometime results may not be accurate This design allows for interpolation It is not providing a comprehensive analysis as compared to full factorial designs Can distribute factor level evenly More focused on quadratic relationship, can ignore linear effects.

Message added by Mayank Gupta, August 22, 20232 yr

Box-Behnken Designs are experimental designs from the family of response surface designs that do not contain factorial or fractional factorial designs as they have treatment combinations that are at the midpoints of the edges of the experimental space. They were devised by George E. P. Box and Donald Behnken in 1960.

An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Pradeep Shukla on 22nd Aug 2023.

Applause for all the respondents - Pradeep Shukla.

Box-Behnken Designs

Followers

August 18, 20232 yr

Q 592. What are Box-Behnken Designs? Compare them with full factorial designs and highlight their advantages and disadvantages.

Note for website visitors -

This platform hosts two weekly questions, one on Tuesday and the other on Friday.
All previous questions can be found here: https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/.
To participate in the current question, please visit the forum homepage at https://www.benchmarksixsigma.com/forum/.
The question will be open until Tuesday or Friday at 5 PM Indian Standard Time, depending on the launch day.
Responses will not be visible until they are reviewed, and only non-plagiarised answers with less than 5-10% plagiarism will be approved.
If you are unsure about plagiarism, please check your answer using a plagiarism checker tool such as https://smallseotools.com/plagiarism-checker/ before submitting.
All correct answers shall be published, and the top-rated answer will be displayed first. The author will receive an honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term.
Some people seem to be using AI platforms to find forum answers. This is a risky approach as AI responses are error prone as our questions are application-oriented (they are never straightforward). Have a look at this funny example - https://www.benchmarksixsigma.com/forum/topic/39458-using-ai-to-respond-to-forum-questions/
We also use an AI content detector at https://crossplag.com/ai-content-detector/. Only answers with less than 15-20% AI-generated content will be approved.

Solved by Pradeep Shukla

August 22, 20232 yr

Go to solution

August 22, 20232 yr

Solution

Box-Behnken Designs

This design was explored by statisticians George E. P. Box and Donald R. Behnken. So, it gave name of Box-Behnken design.

It is a type of experimental statistical design which is generally used in statistics and engineering to improve the process and conducting experiments.

This is used to find the optimal combination of input variables which can lead to achieve desired output.

This design is generally useful when we want to know the relationship between variables. This is used when there is quadratic, and interactions are considered among variables.

Whereas a full factorial design generally consists of all possible combinations which are available. In this test we can study the effect of each factor.

Below are the common differences:

	Box-Behnken Design	Full Factorial Design
No of experiments	This is related to response surface methodology, so uses fewer experiments	In this method we can test all possible combinations for each factor.
Efficiency	More efficient with fewer experiments	More efficient with comprehensive experiments. It increases the experiments with the no of factors and levels.
Complexity of analysis	Simpler in comparison	Complex when dealing with large numbers
Application	Useful when no of experiments are limited.	More useful when no of experiments are more and have complex relationship

Advantages and disadvantages of Box-Behnken Design:

Advantages	Disadvantages
Box-Behnken is more efficient with full factorial when fewer experiments are allowed with limited resources	It has limitations in experiments
It is less complex that full factorial design	Generally used selective sample for experiments, so sometimes missed optimal points
Helps to identify optimal factor level	It is very less flexible, so sometime results may not be accurate
This design allows for interpolation	It is not providing a comprehensive analysis as compared to full factorial designs
Can distribute factor level evenly	More focused on quadratic relationship, can ignore linear effects.