Vol: 44 Page: 25

Authors:
Krystyna Katulska
Łukasz Smaga

Title:
 A note on D-efficiency of biased chemical balance weighing designs

Language: English

Keywords:
biased chemical balance weighing design
D-efficiency
first-order autoregressive process

Summary:
In this paper, the D-efficiency of biased chemical balance weighing designs for the estimation of individual unknown weights of objects is considered. The error components are assumed to create a first-order autoregressive process. Then the covariance matrix of error terms has known form, which does not have to be identity matrix and it depends on the known parameter ρ. When the number of observations n≡0(mod4) Katulska and Smaga (2011) showed that some designs are D-optimal biased designs, if the number of objects is three and ρ∈[0;1/(n-2)]. In this paper the lower bound for D-efficiency of biased chemical balance weighing designs with three objects is given for all ρ∈[1/(n-2),1] and n≡0(mod4). Moreover, using that lower bound for D-efficiency, it is shown that the designs constructed in Katulska and Smaga (2011) are highly D-efficient when ρ∈[1/(n-2),1] and n≡0(mod4).

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