Discrete event modeling and optimization of unreliable production lines with random rates

We consider a serial production system with unreliable machines maintained by a limited number of repairmen, and finite storage between machines. Processing times may be random variables with exponential or gamma distributions, or deterministic. We develop a continuous-flow model for such a system utilizing simulation and analysis. Random processing times are approximated by sums of deterministic variables using a simple probabilistic technique. The model observes a limited number of events which are sufficient to determine system performance and mean buffer levels. By appropriately reducing the rates of starved and blocked machines and using analysis to compute the times of next event at each machine and buffer, discrete part computations are avoided. It is demonstrated that this approximate model is highly accurate and faster by a factor of 3 or more when compared to conventional simulators. The paper addresses also optimal repair allocation to maximize the expected throughput of the system. Two different approaches are proposed: perturbation analysis and experimental evaluation of various nonpreemptive rules for assigning a repairman to failed machines