An important issue in maintaining the industrial equipment is to introduce an appropriate maintenance policy to monitor the conditions of the equipment. In this research, an investigation on the concurrent effects of erosion and random shocks during the useful life of the equipment is studied. In this regard a model is introduced to optimize the total cost including logistic, complete repair and incomplete repair costs. The proposed model determines the optimal number of the incomplete repairs, the time duration between inspections and the probability of equipment to be failed. A numerical example is solved by means of computer simulation. The results indicate that the proposed model performs well for minimizing the costs of maintenance and repair.

From a wide variety of queuing models, the finite-capacity queuing models are the most commonly used, where arrival and service rates follow an exponential distribution. Based on two criteria of system cost and expected degree of customer satisfaction, the present study defines a new productivity rate index and evaluates the optimization of a queuing model with finite capacity. In queuing models, obviously, as the number of servers increases, the length of waiting lines decreases, the expected degree of customer satisfaction enhances, and obviously the system cost increases. This study deals with the mathematical relationships involved in the computations of these two criteria, and proposes a novel approach to determine an optimal number of servers by considering a decision-maker's priority and establishing a trade-off between criteria.