Use of a Quality Loss Function to Select Statistical Tolerances

In this paper, we present a method for the selection of processes to manufacture various parts of an assembly by establishing a compromise between product quality and part manufacturing cost. We quantify the impact the precision of a part characteristic has on the overall quality of a product by using a standard Taguchi loss function. Part manufacturing cost is modeled as a function of process precision (i.e., standard deviation of the output characteristic) as opposed to previous models where manufacturing cost is a function of part tolerance. This approach is more realistic and does not assume, a priori, a relationship between conventional tolerance and process spread. Rather than allocating conventional tolerances on the assembly parts, we use statistical tolerances that are more pertinent when using a quality loss function. The model adopted makes it possible to investigate the relationship between optimum quality loss and tolerance variations. As expected, the optimum quality loss generally decreases when the tolerance increases. Exceptions may be encountered when changes of process occur. The manufacture of a simple three component assembly is studied to illustrate the findings.