Quality of an assembly of any manufactured product is mainly based on the quality of mating components. Due to random variations in sources such as materials, machines, operators, and measurements, mating components manufactured by even the same process may vary in their dimensions. When mating components are assembled linearly, the resulting assembly tolerance will be the sum of the mating components tolerances. All precision assemblies demand for a closer assembly tolerance. A significant amount of research has already been done to minimize assembly variation using selective assembly, when the dimensions of components follow normal distribution. However, in reality, the dimensions of components produced especially in smaller to medium size batches, invariably have some skewness (non-normality), which makes the methods developed and reported in the literature, often not suitable for practice. In this work, batch selective assembly methodology is proposed for components having non-normal distributions to minimize the assembly tolerance variations. The proposed method which employs a genetic algorithm for obtaining the best combination of mating components is able to achieve minimum variations in assembly tolerances and also maximum number of acceptable assemblies. The proposed algorithm is tested with a set of experimental problem datasets and is found outperforming the other existing methods found in the literature, in producing solutions with minimum assembly variation. © 2011 Springer-Verlag London Limited.