On Hotelling's Weighing Problem

摘要: The paper contains some solutions of the weighing problems proposed by Hotelling [1]. experimental designs are applicable to a broad class measurement similar objects. chemical balance problem (in which objects may be placed in either two pans balance) is almost completely solved means constructed from Hadamard matrices. Designs provided both for has bias and one no bias. spring only pan) when biased. For an unbiased balance, given small numbers operations. Also most efficient found but it shown that cases these cannot used unless number weighings as large binomial coefficient $\binom {p}{\frac{1}{2}p}$ or {p}{\frac{1}{2}(p + 1)}$ where $p$ It weighed $N \geq p$ weighings, variances estimates weights order $\sigma^2/N$ case $(\sigma^2$ variance single weighing), $4\sigma^2/N$ case.