How much can sorting improve the capability in assembly tasks?

We formulate the probability of succeeding the assembly of two parts, knowing the distributions of dimensions of the single parts, for uniform and gaussian distributions. We show the optimal relation between part dimension dispersions. We then define the assembly capability from the single parts capabilities; we introduce a rule of thumb to quickly evaluate the assembly capability from the single parts capabilities, with the introduction of a concept of assembly impedance. After that we examine the opportunity to increase the capability of the assembly task by sorting and matching parts. It is evaluated against the cost of sorting.