^{1,a}, Inma T. Castro

^{1,b}, and Reza Ahmadi

^{2}

^{1}Department of Mathematics, Universidad de Extremadura, Spain.

^{a}luciabb@unex.es

^{b}inmatorres@unex.es

^{2}Department of Mathematics, Iran University of Science and Technology, Iran.

A system consisting of n identical components in parallel is analyzed. We assume that the system is less efficient when there are d components failed, which is called defective state. If there are less than d failed components, the system is properly working. Periodic inspections are performed on the system to evaluate its state and detect the defective state to perform preventive or corrective maintenance actions. Maintenance actions are based on the state dependent mean residual life (SDMRL), which is the expected residual time to reach the defective state, knowing the number of components in an inspection time. It is a good indicator for maintenance planning and determining the health state of the system. Two models are described to optimize the maintenance strategy proposed;one of them including minimal repairs for the failed components. Numerical examples are computed to evaluate the expected cost rate and obtain the optimal parameters for both models.