We address the problem of controlling an assembly system in which the processing times as well as the types of subassemblies are stochastic. The quality (or performance) of the final part depends on the characteristics of the subassemblies to be assembled, which are not constant. Furthermore, the processing time of a subassembly is random. We analyze the trade-off between the increase in the potential value of parts gained by delaying the assembly operation and the inventory costs caused by this delay. We also consider the effects of processing time uncertainty. Our problem is motivated by the assembly of passive and active plates in flat panel display manufacturing. We formulate the optimal control problem as a Markov decision process. However, the optimal policy is very complex, and we therefore develop simple heuristic policies. We report the results of a simulation study that tests the performance of our heuristics. The computational results indicate that the heuristics are effective for a wide variety of cases.