Multivariate tolerance design for a quadratic design parameter model

The determination of tolerance allocations among design parameters is an integral phase of product/process design. Such allocations are often necessary to achieve desired levels of product performance. Parametric and nonparametric methods have recently been developed for allocating multivariate tolerances. Parametric methods assume full information about the probability distribution of design parameter processes, whereas, nonparametric methods assume that only partial information is available, which consists of only design parameter process variances. These methods currently assume that the relationship between the design parameters and each of the performance measures is linear. However, quadratic response functions are increasingly being used to provide better approximations of the relationships between performance measures and design parameters. This is especially prevalent where there is a multivariate set of performance measures that are functions of a common set of design parameters. In this research we propose both parametric and nonparametric multivariate tolerance allocation procedures which consider the more general case where these relationships can be represented by quadratic functions of the design parameters. We develop the corresponding methodology and nonlinear optimization models to accommodate and take advantage of the presence of interactions and other nonlinearities among suppliers.