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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.