  The problem of jam formation during the discharge by gravity of granular
material through a two-dimensional silo has a number of practical applications.
In many problems the estimation of the minimum outlet size which guarantees
that the time to the next jamming event is long enough is crucial. Assuming
that the time is modeled by an exponential distribution with two unknown
parameters, this goal translates to the optimal estimation of a non-linear
transformation of the parameters. We obtain $c$-optimum experimental designs
with that purpose, applying the graphic Elfving method. Since the optimal
designs depend on the nominal values of the parameters, a sensitivity study is
additionally provided. Finally, a simulation study checks the performance of
the approximations made, 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 larger
scenario. Apart from the application a general methodology is developed in the
paper for the problem of precise estimation of a one-dimensional parametric
transformation in a non-linear model.
