Optimal tolerance design for products with correlated characteristics by considering the present worth of quality loss

The quality loss function proposed by Taguchi provides a quantitative measurement of product quality when product’s quality characteristic value deviates from the ideal target at an arbitrary time. However, product use causes degradation on its quality characteristic, and since such a deviation can be changing over time, so can its quality loss. The quality loss caused by degradation on quality characteristic has not been considered in most research. In this paper, the time value of money for quality loss and product degradation over time is integrated into the total cost model, and a new optimization model for the tolerance design of products with correlated characteristics is established. The discussions focus on the multivariate quality loss function as an extension of the Taguchi loss function, which is used to model quality loss due to product degradation as a continuous cash flow function under continuous compounding. The optimal tolerance design is achieved by minimizing the total cost, which is the sum of manufacturing cost and the present worth of expected quality loss. An illustrative example is presented to demonstrate the effectiveness of the proposed model.