This paper discusses a set of models which determine optimal product tolerance and minimize combined manufacturing and quality related costs. These models include the cases of the 'nominal-the-best', the 'smaller-the-better', the 'larger-thebetter', and 'asymmetric loss function'. The process capability index is applied to build the functional relationship between the product variability and product tolerance. Based on this relationship, the total cost of each model can be expressed as a function of product tolerance from which the optimal tolerance can be determined. Finally, using these models, a design tolerance approach which increases quality and reduces cost can be achieved in early stages of design.
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Angus Jeang (1997) studied this question.