ERCN* merged nets for modeling degraded behavior and parallel processes in semiconductor manufacturing systems

This paper presents a new class of "well-behaved" Petri nets called extended resource control net (ERCN*) merged nets that generalize the class of ERCN merged nets proposed in a previous paper by Xie and Jeng. ERCN merged nets can model parallel and synchronized processes in semiconductor manufacturing such as lot split and lot merging, which occurs frequently in a research and development (R&D) semiconductor fab (semiconductor plant) for engineering purposes. However, processing cycles for each resource type must include the initial state of the resource type. In other words, no local processing cycles are allowed. This makes the modeling of degraded behavior in semiconductor manufacturing such as rework, failure, and maintenance difficult. In the current work, this constraint is relaxed under the "extended free-choice (EFC)" or "asymmetric choice (AC)" condition. Specifically, for each operation place with degrading outgoing arcs, the FC or AC condition is satisfied. In addition, degraded behavior is modeled as blocks within ERCNs. We show that conditions for liveness and reversibility of an ERCN* merged net correspond to the absence of unmarked siphons. The "well-behaved" conditions can be transformed into inequalities of the initial marking. Examples are shown to illustrate the proposed methodology.