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Tolerance design based on specified process capability value

In this paper, the authors propose a modification of the model, presented by Kapur and Wang in 1987, for obtaining optimal product specification limits (tolerance) with minimum expected total cost per unit of product under the satisfaction of specified process capability values, i.e. assuming the product target value is equal to the specification center, that the value of the specified process capability index, Cp or Cpk, is given, and that 100% inspection is executed before the product is shipped to the customer. The asymmetric quadratic quality loss function presented by Taguchi in 1986 is applied for evaluating product quality. The mathematical optimization model and its solution procedure are formulated. Finally, a numerical example and a sensitivity analysis of the parameters are provided for illustration.