Model analysis and optimization under uncertainty needs efficient n-dimensional integration techniques, particularly when n (number of uncertain parameters) is large and the numerical model heavy. New thinned cubature formulae, recently tested by us and still practically unknown in engineering areas, have significantly changed the status of cubatures vs. quasi-Monte Carlo integration, for moderately high values of n. This paper presents these new cubatures (based on orthogonal arrays) from a practitioner's point of view and illustrates their remarkable efficiency in solving process systems engineering problems, namely those under the classes of simulation under uncertainty, variance-based global sensitivity analysis and optimization under uncertainty. Thinned cubatures allow efficient solution of these problems up to dimension n around 20, producing very reasonable estimates with only a few hundred or thousand of integration points. Three practical applications are provided: (i) analysis of a large-scale mass transfer model, (ii) optimal planning of a production network, (iii) preliminary design of a batch process under high levels of uncertainty and from different sources. (C) 2016 Elsevier Ltd. All rights reserved.