Designing experiments for estimating an appropriate outlet size for a silo type problem

Jam formation is a problem that may occur when granular material is discharged by gravity from a silo. The estimation of the minimum outlet size which guarantees that the time to the next jamming event is long enough can be crucial in the industry. The time is modeled by an exponential distribution with two unknown parameters, and this goal translates to precise estimation of a non-linear transformation of the parameters. We obtain $c$-optimum experimental designs with that purpose, applying the graphic Elfving method. Because the optimal experimental designs depend on the nominal values of the parameters, we conduct a sensitivity analysis on our dataset. Finally, a simulation study checks the performance of the approximations, first with the Fisher Information matrix, then with the linearization of the function to be estimated. The results are useful for experimenting in a laboratory and translating then the results to a real scenario. From the application, we develop a general methodology for estimating a one-dimensional transformation of the parameters of a nonlinear model.