Multivariate tolerance design using quality loss

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. We extend our prior research on tolerance allocation by developing both parametric and nonparametric methods for a multivariate set of performance measures that are functions of a common set of design parameters. The parametric method is novel and assumes full information about the probability distribution of design parameter processes. The proposed nonparametric method assumes that only partial information is available and significantly extends prior research by considering a more contemporary and realistic model for manufacturer costs. For both methods we derive economically based models that represent the costs, both internal (supplier) and external (manufacturer), of tolerance allocation under several different process scenarios. These scenarios are based on the manner of disposition of nonconforming product. For the parametric methods we derive tolerance allocation solutions that jointly minimize expected total cost of the supplier and manufacturer. For the nonparametric methods we derive solutions for tolerance allocation that jointly minimizes the maximum expected total cost. An example in the fabrication of a rubber tread compound is used to: (i) demonstrate the implementation of our proposed methodologies for tolerance allocation; (ii) illustrate and compare the nonparametric and parametric methods; land iii) assess the sensitivity of optimal tolerance allocations to changes in process model types, cost coefficient estimates, and manner of disposition of nonconforming product.