Machine repairing models for manufacturing systems

We consider manufacturing systems of m identical unreliable machines producing one type of product. The operating time of each machine is exponentially distributed. The repairing process of a machine requires more than one phase. In each phase, the repair time is exponentially distributed and more than one operator may require in fixing a down machine. In this paper, we first study the case that r operators are assigned in one server to repair a down machine. The repairing rate in each phase depends on the number of operators there. This is a generalized model discussed in Buzacott and Shanthikumar (1993). We then consider a two-phase repairing model. Two groups of operators are assigned in the two phases. Each operator can handle one down machine in each phase individually. This model is a generalization of Eben-Chaime´s model (1995). Average profit functions are derived for both cases and can be optimized by suitable allocation of the number of machines and operators in the system