Classical sensitivity testing addresses mainly problems where the level of one stimulus only governs an abrupt transition in output, or response. Both parametric and nonparametric methods developed, and successfully applied over last century to tackle such problems, provide estimates of critical levels beyond which an item will either respond, or not, to a single stimulus, and of related statistics. However classical methods sometimes may not readily provide an answer, namely when more than one stimulus may reach critical level, and either singularly or jointly trigger transition. Factorial and response surface designs, adequate when dealing with continuous responses, may not perform as well for transition threshold estimation. A practical case at hand in chemical engineering concerns the production, through hydrolysis of a specific precursor, of titania sols and gels that find industrial use as additive for paints, concrete and other building materials due to its optical, photo-catalytic and super-hydrophilic properties. Particles formation and aggregation — controlled by varying the primary process parameters, namely initial alkoxide concentration, water to alkoxide and acid to alkoxide ratios, mixing conditions — may yield either stable, transparent nanometric sols, or monolithic gels, where aggregation of nanometric particles produces a final ceramic object. Depending on the application, one of the two products may be desirable, and therefore it is crucial to control the final product properties. Aggregation kinetics and physical properties of sols, and sol to gel transition, were found to depend strongly upon several factors, that is water to alkoxide initial concentration ratio, acid to alkoxide initial concentration ratio, and their interaction. The approach developed in order to estimate parameters pertaining to transition, and related uncertainty, is presented in the paper, and discussed in the light of experimental results.

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