D-optimal weighing designs with circular string property under SLS estimation

Spring balance weighing designs with a circular string property are consid-ered in the context of second-order least squares estimation which is known to be better than ordinary least squares estimation when the error distribution is not symmetric. Optimal design measures are derived under the D-optimality criteria. The robustness of optimal designs against the unknown skewness parameter of the error distribution is examined. The problem of constructing exact (N-run) designs that are highly efficient, if not optimal, is also considered.