Sequential asymmetric third order rotatable designs (SATORDs).

Area of Science:

• Statistics
• Experimental Design
• Industrial Optimization

Background:

• Traditional rotatable designs are often symmetric, limiting their applicability in practical scenarios with mixed factor levels.
• Asymmetric second-order rotatable designs (ASORDs) offer broader exploration but may suffer from significant lack of fit, necessitating higher-order models.
• Developing new third-order rotatable designs (TORDs) can be expensive, potentially underutilizing initial experimental data.

Purpose of the Study:

• To propose an economical method for constructing asymmetric third-order rotatable designs (TORDs).
• To enable sequential augmentation of existing asymmetric second-order rotatable designs (ASORDs) to achieve TORDs.
• To avoid discarding initial experimental runs when upgrading to a higher-order model.

Main Methods:

• Sequential augmentation of asymmetric second-order rotatable designs (ASORDs) with additional points.
• Construction of asymmetric third-order rotatable designs (TORDs) by building upon existing ASORDs.
• Utilizing initial stage runs for second-order model fitting and subsequent runs for third-order model fitting.

Main Results:

• The proposed method allows for the construction of asymmetric TORDs.
• The augmentation strategy is economical, leveraging previously collected data.
• Initial experimental runs are not discarded, improving efficiency.

Conclusions:

• The developed method provides a cost-effective approach to obtaining asymmetric TORDs.
• This approach enhances the utility of experimental data by allowing for model order upgrades.
• Researchers can achieve optimal response estimation more efficiently using the proposed sequential augmentation technique.