Improvability theory for a simple assembly system consisting of two components and one assembly machine is developed. Both constrained and unconstrained formulations are addressed. In the constrained case, it is shown that the assembly is unimprovable with respect to workforce if each component machine is blocked as frequently as the assembly machine is starved for parts produced by this particular assembly machine. The system is unimprovable with respect to work-in-process if, roughly speaking, all buffers have equal average steady state occupancy. In the unconstrained improvability case, it is shown that the bottleneck machine can be identified by analyzing the probabilities of the so-called manufacturing blockages and starvations. A generalization to n component-one assembly machine system is also included.