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

This paper presents a new class of "well-behaved" Petrinets called ERCN merged nets that generalize the class of ERCN merged nets proposed in (X.L. Xie and M.D. Jeng, 1999). ERCN merged nets can model parallel and synchronized processes in semiconductor manufacturing such as lot split and merging. 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 additions, degraded behavior is modeled as blocks within ERCNs. We show that conditions for liveness and reversibility of an unmarked siphons. The "well-behaved" conditions can be transforms into inequalities of the initial marking. Examples are shown to illustrate the proposed methodology.