A note on D-optimal chemical balance weighing designs with autocorrelated observations

In this paper, D-optimal chemical balance weighing designs with three objects are considered. The error terms are assumed to form a first-order autoregressive process, which implies that the covariance matrix of the vector of errors depends on the known parameter $$\rho $$ . It is shown that the designs constructed by Katulska and Smaga (Metrika 76:393–407, 2013) are still D-optimal weighing designs with three objects under a wider interval of possible values for parameter $$\rho $$ than that considered in that paper. Those designs are also proved to be highly D-efficient designs, when D-optimal design is not known.