AbstractA primary requirement of quality‐based design and offline quality control methods is the determination of nominal design parameter values which are such as to minimize the risk that the resulting device or system will function inadequately, or fail, under specified operational conditions. It may also be desirable to control the degree of variability in certain properties or outputs of the device or system. Both requirements are to be satisfied, in the presence of unavoidable tolerances on component parameters, which may also have been optimized, using a cost balance criterion.It is shown that these requirements can be expressed in terms of constrained optimization of probability contents of defined sets in the space of the design parameters and that the probabilities can be estimated using well‐established convolution methods, permitting optimization by standard numerical methods. This procedure avoids the need for simulation or the use of specialized statistical techniques based on analysis of variance, and may permit solution of such problems by non‐specialists using available computing facilities. It does, however, require a suitable probability model to be associated with the design variables of interest. Analytic and numerical examples are presented and discussed.For those readers unfamiliar with the theoretical methods employed, Section 1.2 provides a qualitative description of the method and may be read in conjunction with the examples of Sect