Search

The state of a machine is modeled as a controlled continuous-time Markov chain. Moreover, the machine is being serviced at random times. The aim is to maximize the time until the machine must be repaired, while taking the maintenance costs into account. The dynamic programming equation satisfied by the value function is derived, enabling optimal decision-making regarding inspection rates, and special problems are solved explicitly. This approach minimizes direct maintenance costs along with potential failure expenses, establishing a robust methodology for determining inspection frequencies in reliability-centered maintenance. The results contribute to the advancement of maintenance strategies and provide explicit solutions for particular cases, offering ideas for application in reliability engineering. [ABSTRACT FROM AUTHOR]

Suppose that in an M / G / 1 waiting queue, the server can choose between two service time distributions. We look for the choice that enables us to minimize the expected value of a cost criterion that takes into account the cost incurred by working faster and the time needed to empty the waiting line. The random final time is the first time there is no customer waiting for service. When the service times are exponential random variables, we can appeal to dynamic programming to obtain the optimal solution. In the general case, conditional probability is used. Particular problems in which the capacity of the system is finite are solved explicitly. [ABSTRACT FROM AUTHOR]