Concurrent tolerancing for design and manufacturing based on the present worth of quality loss

Abstract

The quality loss function developed by Taguchi provides a monetary measure for the deviation of the product quality characteristic from the target value. Product use causes degradation on its quality characteristic, and since such a deviation can be changing over time, so can the quality loss. However, most studies on concurrent tolerancing theory do not consider the quality loss caused by the degradation. In this paper, the present worth of expected quality loss expressed as the function of the pertinent process tolerances in a concurrent tolerancing environment is derived to capture the quality loss due to product degradation over time as a continuous cash flow function under continuous compounding. A new tolerance optimization model, which is to minimize the summation of manufacturing cost and the present worth of expected quality loss, is established to realize the concurrent tolerance allocation for products with multiple quality characteristics. An example of the bevel gear assembly involving concurrent allocation of design and process tolerances is given, demonstrating that the proposed model is feasible in practice.