Some new augmented fractional Box–Behnken designs

ABSTRACT

The augmented Box–Behnken designs are used in the situations in which Box–Behnken designs (BBDs) could not estimate the response surface model due to the presence of third-order terms in the response surface models. These designs are too large for experimental use. Usually experimenters prefer small response surface designs in order to save time, cost, and resources; therefore, using combinations of fractional BBD points, factorial design points, axial design points, and complementary design points, we augment these designs and develop new third-order response surface designs known as augmented fractional BBDs (AFBBDs). These AFBBDs have less design points and are more efficient than augmented BBDs.

KEYWORDS:

• Box–Behnken Designs (BBDs)
• Augmented Box–Behnken designs (ABBDs)
• Fractional Box–Behnken designs (FBBDs)
• Efficiency
• Response surface models
• Second-order designs
• Third-order designs