Optimal partitioning of probability distributions under general convex loss functions in selective assembly

Selective assembly is an effective approach for improving the quality of a product which is composed of two mating components. This article studies optimal partitioning of the dimensional distributions of the components in selective assembly. It extends previous results for squared error loss function to cover general convex loss functions, including asymmetric convex loss functions. Equations for the optimal partition are derived. Assuming that the density function of the dimensional distribution is log-concave, uniqueness of solutions is established and some properties of the optimal partition are shown. Some numerical results compare the optimal partition with some heuristic partitioning schemes.