Multiplicative algorithm for computing D-optimum designs for pVT measurements
2011 - R. Martín-Martín, L.J. Rodríguez-Aragón, B. Torsney
Chemometrics and Intelligent Laboratory Systems , 111(1): 20–27 (2011)
Abtract
Multifactor models are present in industry and in biological experiments; therefore optimum designs are a valuable tool for experimenters, leading to estimators of the parameters with minimum variance. A generalization of the Multiplicative algorithm to find locally D-optimum designs for multifactor models as Tait-like equations is here proposed. The method consists of transforming a conceived set of design points over a finite interval into proportions of the design interval defined by the sub-intervals between successive points. Examples for different modifications of the Tait equation are here presented: a three parameter model under isothermal conditions with pressure as the independent variable and two different modifications of an eight parameter model (Rackett equation) with pressure and temperature as design variables. Optimum design for the first example is equally supported at three points while the two-factor modifications of the Tait equation show designs with more support points than unknown parameters and different weights for each point. Efficiencies of real experimental designs are computed and suitable more efficient experimental designs, satisfying experimental demands are also proposed.