Reliability modeling and maintenance planning for a parallel system with respect to the state-dependent mean residual time

Parallel configuration is one of the most important structures for complex systems. Due to its role in reliability analysis, there has been a growing interest in using the mean residual lifetime as index of the failure prognosis and also maintenance planning. When inspections of the system are involved, mean residual life can be improved through incorporating the information gathered in the inspection times. In this article, maintenance actions are performed based on a mean residual time index and the information about the number of failed components gathered in the inspection times. The main novelty of this article is that the mean residual time is computed as the expected remaining time to reach a defective state instead of the expected remaining time to reach the system failure. Different properties of the expected remaining time to reach a defective state are shown in this article. Based on the expected remaining time to reach a defective state, two maintenance models (Model I and Model) are developed. Compared to Model I, Model II allows the inclusion of minimal repairs. Different numerical examples are computed to highlight distinctions between the two models.