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OPTIMUM SINGULAR SPRING BALANCE WEIGHING DESIGNS WITH NON‐HOMOGENEITY OF THE VARIANCES OF ERRORS FOR ESTIMATING THE TOTAL WEIGHT
Author(s) -
Ceranka B.,
Katulska K.
Publication year - 1986
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.1986.tb00599.x
Subject(s) - mathematics , homogeneity (statistics) , upper and lower bounds , block design , statistics , block (permutation group theory) , variance (accounting) , balance (ability) , combinatorics , mathematical analysis , medicine , accounting , business , physical medicine and rehabilitation
The problem of estimation of the total weight of objects using a singular spring balance weighing design with non‐homogeneity of the variances of errors has been dealt with in this paper. Based on a theorem by Katulska (1984) giving a lower bound for the variance of the estimated total weight, a necessary and sufficient condition for this lower bound to be attained is obtained. It is shown that weighing designs for which the the lower bound is attainable, can be constructed from the incidence matrices of (α 1 ,.,α t )‐resolvable block designs, α‐resolvable block designs, singular group divisible designs, and semi‐regular group divisible designs.