Pena Pardo, MonicaSarkar, Jyotirmoy2023-02-172023-02-172021Monica Pena Pardo & Jyotirmoy Sarkar. (2021). Combinatorial Patterns of D-Optimal Weighing Designs Using a Spring Balance. Statistics and Applications, 19(2), 63–76.2454-7395https://hdl.handle.net/1805/31304Given a spring balance that reports the true total weight of items plus a white noise of an unknown variance, which n subsets of n items will you weigh in order to estimate the true weights of each item with the highest possible precision? For n ≤ 6, we classify all D-optimal weighing designs according to the combinatorial patterns they exhibit (modulo permutation), we count the D-optimal designs exhibiting each pattern, and we explain how a D-optimal design for n items may arise out of a D-optimal design for (n − 1) items. For n = 7, 11 we exhibit D-optimal designs obtained from balanced incomplete block designs (BIBDs). We discuss some strategies to construct D-optimal designs of larger sizes, and pose some unsolved problems.en-USPublisher PolicyDesign of experimentsEstimable parameterInformation matrixCredibility regionArticle