Calibration designs based on solutions to the tournament problem

Abstract

In high precision ca librations one measures diffe re nces be tween nominally equal objects or group of objects and establi shes a value for the individuals with refere nce to one or more standards. The so lutions to the class ica l tournament problem, which ca ll s fo r arranging v individual s into tea ms of I) players so that a player is teamed the same number of times with each of the other players and also that ea ch player is pitted equally often aga inst each of the other players, provide balanced designs for scheduling the meas ure ments. These designs are useful in weighing and ot he r meas ure me nt s wh en the objects to be measured ca n be combin ed into groups without loss of prec ision or acc uracy in the co mparisons.