Machine repairing models for production systems

In this paper 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 be required for fixing a broken machine. Here we consider two models of manufacturing systems. In the first model, there are r operators assigned in one server to repair a broken machine. The repairing rate in each phase depends on the number of operators there. This is a generalized model discussed in Buzacott and Shanthikumar [11]. We then consider a two-phase repairing model. Two groups of operators are assigned in the two phases. Each operator can handle one broken machine in each phase individually. This model is a generalization of Eben–Chaime's model [8]. Average profits are derived for both models and can be optimized by suitable allocation of the number of machines and operators in the systems.