Optimal Experimental Designs in the Flow Rate of Particles

This paper focuses on analysing the process of jam formation during the discharge by gravity of granular material stored in a 2D silo. The aim of the paper is twofold. Firstly, optimal experimental designs are computed, in which four approaches are considered: D–optimality, a combination of D–optimality and a cost/gain function, Bayesian D–optimality and sequential designing. These results reveal that the efficiency of the design used by the experimenters can be improved dramatically. A sensitivity analysis with respect to the most important parameter is also performed. Secondly, estimation of the unknown parameters is done using least squares, i.e. assuming normality, and also via maximum likelihood assuming the exponential distribution. Simulations for the designs considered in this paper show that the variance, the mean square error and the bias of the estimators using maximum likelihood are in most cases lower than those using least squares.