Optimal binning strategies under squared error loss in selective assembly with a tolerance constraint

Selective assembly is an effective approach for improving the quality of a product assembled from two types of components when the quality characteristic is the clearance between the mating components. In this article, optimal binning strategies under squared error loss in selective assembly when the clearance is constrained by a tolerance parameter are discussed. Conditions for a set of constrained optimal partition limits are given, and uniqueness of this set is shown for the case when the dimensional distributions of the two components are identical and strongly unimodal. Some numerical results are reported that compare constrained optimal partitioning, unconstrained optimal partitioning, and equal width partitioning.