Stability of real-time lot-scheduling and machine replacement policies with quality levels

In this note we show how the main result of Lou et al. can be generalized to an unreliable machine with various quality levels. We consider a single machine which can process parts of different types. The machine can process at most one part at a time and it needs a setup period whenever it switches from one part-type to another. Parts enter the system in type-specific input rates and require type-specific processing times. 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. We postulate a simple form of real-time replacement and scheduling policies, and derive conditions ensuring the stability of the system under these policies. (author's abstract)