Modeling and Analysis of Two-Stage Systems with Parallel Machines and Limited Repair Capacity

A method to study the performance of two-stage systems with unreliable parallel machines is presented. Once failed, machines require the intervention of a repair operator. In contrast to previous works which consider one repairman dedicated to each machine, a limited number of repairmen is assumed to be available for each stage. The resulting two machine system is modeled as a general multiple up and multiple down two-stage fluid system, for which an exact analytical solution is available. Results show that while considering parallel stages integrated in a system the allocation of repairmen is all but trivial and a new behaviour of the production rate as a function of the number of machines at the stage is described. Furthermore, for non-identical machines, the method makes it possible to suitably set priorities among failed machines. Finally, the results suggest the definition of new cost-oriented design problems for the optimal allocation of the operators in parallel machine lines.