Impact of integrating equipment health in production scheduling for semiconductor fabrication

Monitoring the Equipment Health Indicator (EHI) of critical machines helps effectively to maintain process quality and reduce wafer scrap, rework, and machine breakdowns. To model and illustrate the integration of EHI in scheduling decisions to balance between productivity and quality risk, this paper presents two mixed integer linear programs to schedule jobs on heterogeneous parallel batching machines. The capability of a machine to process a job is categorized as preferred, acceptable, and unfavorable based on the job requirements. The quality risk of processing a job by a machine is a function of its EHI and the capability level of the machine for the job, which is modeled as a penalty in the objective function of trading-off between productivity and quality risk. The first model is static and assumes constant EHI of machines on the scheduling horizon, whereas the second model considers the EHI dynamics, i.e., the machine condition deteriorates over time based on the scheduled jobs. Numerical experiments indicate the potential applications of using EHI-integrated scheduling approaches to analyze and optimize the trade-off between productivity and quality risk.