Vol: 42 Page: 67

Authors:
Krystyna Katulska
Łukasz Smaga

Title:
 On some D-optimal chemical balance weighing design with n≡2(mod4)

Language: English

Keywords:
D-optimal chemical balance weighing design
first-order autoregressive process AR(1)

Summary:
In this paper, we consider the chemical balance weighing designs for estimation of individual unknown weights of three objects using D-optimality criterion. We assume that the error components create a first-order autoregressive process AR(1). Then, the covariance matrix of random errors has known form, which does not have to be identity matrix and depends on known parameter ρ In this paper, we prove D-optimality of some design from Bora-Senta and Moyssiadis (1999), if n ≡2 (mod 4) in the whole class of designs for three objects and some ρ ≤ 0 Under these assumptions, we present the necessary and sufficient conditions such that the weighing design for three objects is D-optimal. These conditions can be used to construct D-optimal designs.

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