Vol: 41 Page: 143

Authors:
Krystyna Katulska
Łukasz Smaga

Title:
 D-optimal biased chemical balance weighing designs

Language: English

Keywords:
chemical balance weighing design
D-optimality
first–order autoregressive process

Summary:
In this paper, we consider the D-optimal chemical balance weighing designs for estimation of individual unknown weights of objects. We assume that the error terms create a first–order autoregressive process. Then the covariance matrix of errors has known form, which does not have to be identity matrix and depends on known parameter In the literature, some results about the D-optimal designs, when there are three objects are known. We present the biased chemical balance weighing design given by its design matrix and we prove that it is D-optimal biased design in some class of designs, if the number of objects is three and ρ≥0. For such we show also the theorem giving the necessary and sufficient condition under which the biased design for three objects is D-optimal. Finally, we describe some relations between D-optimal designs and D-optimal biased designs for three objects and ρ≥0.

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