The existing procedures for robust design, devised for physical experiments, may be too limiting when the system can be simulated by a computer model. In this paper we introduce a modification of the dual response surface modelling, which incorporates the option of stochastically simulating some of the noise factors when their probabilistic behaviour is known. Our method generalizes both the crossed and the combined array approaches and finds a natural application to integrated parameter and tolerance design. The method appears suitable for designing complex measurement systems and in this paper is applied to the design of a high-precision optical profilometer.