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ON THE ESTIMATION OF TOTAL WEIGHT IN SINGULAR SPRING BALANCE WEIGHING DESIGNS UNDER THE CO VARIANCE MATRIX OF ERRORS s 2 G
Author(s) -
Katulska Krystyna
Publication year - 1989
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1989.tb00397.x
Subject(s) - mathematics , variance (accounting) , spring (device) , balance (ability) , matrix (chemical analysis) , statistics , upper and lower bounds , variance components , chemistry , mathematical analysis , chromatography , engineering , mechanical engineering , medicine , accounting , business , physical medicine and rehabilitation
Summary The problem of the estimation of the linear combination of weights, c′w, in a singular spring balance weighing design when the error structure takes the form E(ee′) =s̀ 2 G has been studied. A lower bound for the variance of the estimated linear combination of weights is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The general results are applied to the case of the total of the weights. For a specified form for G, some optimum spring balance weighing designs for the estimated total weight are found.