Abstract: Mold production process is fraught with uncertainty, especially the uncertainty of process and number of reworks which has made accurate estimates and control mold production cycle to become a worldwide problem. To address this issue, tandem and hybrid manufacturing queuing system considering reworks is used to presents the mold manufacturing process, respectively. Under the assumption that the orders are processing under the first come first served principal and both the normal processing and rework time are exponential distributed, the event-based state transition process of the manufacturing queuing system has been analyzed, meanwhile, the concept of the rework strength is proposed and the event interval is approximately exponential distribution. On that basis, the mold remaining duration approximate mathematical distribution model is deducted by combining the sum of independent gamma random variables. A comparative analysis of the numerical results and simulation results under different rework strength and initial states verified the reliability of proposed approximate model of remaining duration.

Key words: mold;queuing system;reworks;remaining duration;mathematical models