Multivariate tolerance design using quality loss

The determination of tolerance allocations among design parameters is an in tegral phase of product/process design. Such allocations are often necessar y to achieve desired levels of product performance. We extend our prior res earch on tolerance allocation by developing both parametric and nonparametr ic methods for a multivariate set of performance measures that are function s of a common set of design parameters. The parametric method is novel and assumes full information about the probability distribution of design param eter processes. The proposed nonparametric method assumes that only partial information is available and significantly extends prior research by consi dering 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 allocati on under several different process scenarios. These scenarios are based on the manner of disposition of nonconforming product. For the parametric meth ods 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 ma ximum expected total cost. An example in the fabrication of a rubber tread compound is used to: (i) demonstrate the implementation of our proposed met hodologies for tolerance allocation; (ii) illustrate and compare the nonpar ametric and parametric methods; and (iii) assess the sensitivity of optimal tolerance allocations to changes in process model types, cost coefficient estimates, and manner of disposition of nonconforming product.