Optimal process design in selective assembly when components with smaller variance are manufactured at three shifted means

Selective assembly is an effective approach for improving the quality of a product that is composed of two mating components, when the quality characteristic of the product is the clearance between the mating components. In this approach, the components are sorted into several groups according to their dimensions, and the product is assembled by randomly selecting mating components from corresponding groups. A number of previous studies focused on equal width partitioning schemes, in which the dimensional distributions of the two components are partitioned so that all groups have equal widths. When there is a large difference between the variances of the two component dimensions, equal width partitioning will result in a large number of surplus components due to differences between the numbers of components in corresponding groups. Some authors have proposed a method of manufacturing the component with smaller variance at three shifted means to cope with this difficulty. In the present paper, an optimal manufacturing mean design that minimises the number of surplus components is derived. It is shown that the use of the optimal design considerably reduces the number of surplus components compared with using another previously proposed manufacturing mean design and the no-shift design.