A-optimal versus D-optimal design of screening experiments. Issue 4 (8th August 2021)

• Record Type: Journal Article
• Authors: Jones, Bradley; Allen-Moyer, Katherine; Goos, Peter
• Is Part Of: Journal of quality technology. Volume 53:Issue 4(2021)
• Page Start: 369
• Page End: 382
• Publication Date: 2021-08-08
• Subjects: main effect -- orthogonal array -- prediction variance -- two-factor interaction effect -- two-level design; Quality control -- Periodicals; Qualité -- Contrôle -- Périodiques; Quality control; Quality control; Periodicals; 620.0045
• DOI: 10.1080/00224065.2020.1757391
• Languages: English
• ISSNs: 0022-4065

Abstract

Abstract: The purpose of this article is to persuade experimenters to choose A-optimal designs rather than D-optimal designs for screening experiments. The primary reason for this advice is that the A-optimality criterion is more consistent with the screening objective than the D-optimality criterion. The goal of screening experiments is to identify an active subset of the factors. An A-optimal design minimizes the average variance of the parameter estimates, which is directly related to that goal. While there are many cases where A- and D-optimal designs coincide, the A-optimal designs tend to have better statistical properties when the A- and D-optimal designs differ. In such cases, A-optimal designs generally have more uncorrelated columns in their model matrices than D-optimal designs. Also, even though A-optimal designs minimize the average variance of the parameter estimates, various cases exist where they outperform D-optimal designs in terms of the variances of all individual parameter estimates. Finally, A-optimal designs can also substantially reduce the worst prediction variance compared with D-optimal designs.