Selecting a 𝒟-Optimal Follow-Up Experiment Among Candidate Choices

ABSTRACT

Augmenting an initial screening experiment with additional runs is often needed to resolve ambiguities involving aliasing of effects. 𝒟-optimal augmentation is an efficient means of selecting a follow-up experiment that provides for precise estimation of a user-specified model by selecting runs such that the combined design maximizes the determinant of the information matrix. Optimal design augmentation offers greater flexibility with respect to run size and model specification than traditional follow-up strategies such as foldover and semifoldover. In this article, we consider the use of multiple criteria for selecting among candidate 𝒟-optimal follow-up designs. For situations in which optimization is an objective of experimentation, we also suggest a Bayesian posterior predictive approach to help select among candidate follow-up experiments through the computation of probabilities that follow-up treatment combinations achieve some desirable quality level or meet required specifications. The approach will be illustrated using an injection molding example.

KEYWORDS:

• alias matrix
• Bayesian inference
• 𝒟-optimality
• follow-up design
• multiple criteria
• posterior predictive distribution
• variance inflation factor

Notes

For each run size, the best value for each column has been underlined.

For each run size, the best value for each column has been underlined.

For each run size, the best value for each column has been underlined.

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