On the Optimality of Spring Balance Weighing Designs

Abstract

This paper deals with techniques for finding $\Phi$-optimal designs for weighing $v$ objects in $b$ weighings using a spring balance. The optimality functions considered encompass a large class of functions. Results are applied to find $A$-, $D$- and $E$-optimal designs and the optimal designs obtained are seen to be related to certain types of well known block designs.