Stability of Real-Time Lot-Scheduling and Machine Replacement Policies with Quality Levels

We consider a single machine, multiproduct manufacturing system, which can operate at finitely many quality levels. The quality of the machine deteriorates according to a continuous-time Markov process and the only way to improve the quality is by replacing the machine by a new one. In this framework we derive conditions for the stability of the system under a simple class of real-time scheduling/replacement policies. The stability notion that we employ is the recurrence of the total work backlog