Periodic Inspection Policy for a System with Two Levels of Degradation

Abstract

The use of a mechanical system causes a permanent degradation of the latter. This degradation progresses from one level to another until the critical phase where the system is breaks down. To avoid these failures we must know the exact state of the system at every moment. Furthermore, the degradation states are only detected by inspections. Thus, in order to meet the economic and customer requirements at the same time, we must set an inspection policy that will allow us to optimize a certain criterion such as: minimizing maintenance costs, maximizing the availability duration of the system. In the present work, we are interested firstly in the modeling of a mechanical system, with two degradation levels, by a gamma process. The first level repre-sents the preventive replacement threshold where any exceeding of this threshold requires preventive maintenance on the system. While the second level is the criti-cal degradation, threshold that causes system failure. Secondly, the economic model of the inspection/replacement policy, in the sense of minimizing the total cost of maintaining the system in a replacement cycle, was developed. Finally, a numerical and graphical analysis of the sensitivity of the different mathematical models, with respect to their parameters, is carried out. We are interested by the modeling of a system, with two levels of degradation, by a gamma process. The sensitivity analysis of the mathematical model, whose solution is the optimal inspection/replacement policy minimizing the maintenance costs, is provided. The various models and quantities introduced are illustrated and analyzed in case of variation of their parameters by numerical examples.