Modeling and analysis of semiconductor manufacturing systems with degraded behavior using Petri nets and siphons

Degraded behavior, such as reworks, failures, and maintenance, of a semiconductor manufacturing system (SMS) is not negligible in practice. When modeled by Petri nets, degraded behavior may be represented as initially-unmarked elementary circuits, interpreted as local processing cycles. Most existing "well-behaved" net classes for manufacturing have problems with describing such cycles and thus may have difficulties in modeling SMSs. We extend the class of nets in Jeng and DiCesare (1995) into the class of RCN* merged nets that model SMSs with such cycles. To model an SMS, we first describe the behavior of each resource type using a state-machine module, called RCN. Any RCN can be constructed as a connection of acyclic sub-nets called blocks, where one of them denotes the normal behavior of the resource type and the others denote its degraded behavior. Next, an RCN* merged net for the entire system is built by fusing all modules, conforming to three constraints, along their common transition sub-nets, which represent their synchronization. In the analysis of RCN* merged nets, we prove that their liveness and reversibility depend on the absence of unmarked siphons, which are structural objects that mixed integer programming can check rapidly. Examples are given to illustrate the proposed approach.