An economic selective assembly procedure for two mating components with equal variance

An economic procedure of selective assembly is proposed when a product is composed of two mating components. The major quality characteristic of the product is the clearance between the two components. The components are divided into several classes prior to assembly. The component characteristics are assumed to be independently and normally distributed with equal variance. The procedure is designed so that the proportions of both components in their corresponding classes are the same. A cost model is developed based on a quadratic loss function and methods of obtaining the optimal class limits as well as the optimal number of classes are provided. Formulas for obtaining the proportion of rejection and the unavailability of mating components are also provided. The proposed model is compared with the equal width and the equal area partitioning methods using a numerical example.