D-Optimal Chemical Balance Weighing Designs with N ≡ 0 (mod 4) and 3 Objects

Abstract

In this article, the problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of first-order autoregressive process. Such problems were discussed in Li and Yang (2005) and also in Yeh and Lo Huang (2005). We present some results of D-optimal designs in certain class of designs with the design matrix X  ∈ M _n×3(±1) such that each column of matrix X has at least one 1 and one −1.

Keywords:

• Chemical balance weighing design
• D-optimality
• First-order autoregressive process

Mathematics Subject Classification:

• 62K05
• 05B20