In order to remain highly competitive, industrial companies found their business strategies on the quality and the cost of the product/service they deliver to their clients. Therefore, it is crucial for them to guarantee the availability and reliability of their industrial equipment through maintenance. However, while applying maintenance, industrials face a major issue: what is the optimal maintenance strategy to adopt in order to minimize the total cost of maintenance while maintaining an acceptable level of system availability? In this paper, we answer this question by proposing an optimization approach that takes in consideration the various costs related to maintenance and integrates them in a global cost function to minimize. A critical threshold of the remaining useful life under which the system should be replaced is identified, as well as an inspection step giving the regularity with which the system should be inspected. We then illustrate the approach with an example: a mechanical bearing system of a train motor subject to degradation and to monitoring. This example has allowed us to determine the remaining useful life threshold as well as the number of inspections that minimize the total cost of maintenance.  Index Terms-remaining useful life, weibull distribution, cost optimization, predictive maintenance, rolling bearing system.