The partial information case for multivariate tolerance design using scrap or rework costs

Contemporary product and/or process design consists of three phases, which involves system design, parameter design, and tolerance design. The focus of this paper is on tolerance design, where cases considered involve multiple performance measures that are influenced by a common set of design parameters. Procedures are developed for assessing tolerances on design parameters where the only information available consists of the mean and variance of each design parameter. This is called the partial information case (as opposed to the full information case, where design parameter distributions are known). Minimax cost models are derived to determine appropriate tolerance allocations. Models are constructed that consider operational environments for both suppliers and manufacturers where a nonconforming product is scrapped and/or reworked. Examples are also used to compare the minimax model tolerance allocations to those achieved by standard, full information, statistical models.