Optimal Design of Experiments for Minimum Outlet Size Estimation
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[1] Universidad de Navarra
Universidad de Navarra
Pamplona, España
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[2] Universidad Pública de Navarra
Universidad Pública de Navarra
Pamplona, España
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[3] Universit`a degli Studi del Piemonte Orientale
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- Localización: BEIO, Boletín de Estadística e Investigación Operativa, ISSN 1889-3805, Vol. 42, Nº. 2, 2026, págs. 7-17
- Idioma: inglés
- Enlaces
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Resumen
Jam formation can occur when granular material is discharged by gravity from a silo. Estimating the minimum outlet size that ensures a sufficiently long time before the next jamming event can be crucial in industrial applications. The time between two jams is modeled by an exponential distribution with two unknown parameters. The main objective is to estimate the outlet diameter of the silo for a user-selected threshold for the expected time of a jam. This quantity to be estimated is a nonlinear transformation of the parameters. Optimal design of experiments guarantee a desired precision in estimation reducing the cost of experimentation. We obtain c-optimum experimental designs with that purpose, applying the graphical Elfving method. Since the optimal experimental designs depend on the nominal values of the parameters, we conduct a sensitivity analysis to detect changes in the efficiency. Finally, a simulation study assesses the performance of two approximations used in the method: one based on the Fisher information matrix and the other on linearization of the target function. The results support laboratory experimentation and their transfer to real-world settings. Building on this application, we develop a general methodology for estimating a one-dimensional transformation of the parameters of a nonlinear model.
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