In this paper we address the evaluation of the criticality of important components in Manufacturing-To-Order and Assembly-To-Order processes, where the management of the inventory is a critical problem, especially very expensive ones. In these situations, if an item is purchased only when needed for a specific order, the delivery time could cause the delay of the entire production process. In addition, these manufacturing environments are often affected by uncertainty, caused by the execution of several activities by human operators, and by the intrinsic complexity of the process (especially in assembly processes). In this background, we provide a method to evaluate the criticality level of each important component in an assembly process exploiting the AoA project network formalization. In particular we put the focus on the coordination between the scheduled arrive of an element from the supplier, and the actual needed of the component in the assembly process. To this aim we develop a method taking into consideration two different criticality indexes. The approach is validate in a real manufacturing case. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.