On repairable systems with time redundancy and operational constraints

For some repairable systems executing missions/tasks, a functional failure, i.e., a failure of a mission or task can occur not immediately after equipment failure but with some delay. This happens when a failure/defect is not repaired within some specified period of time. Alternatively, a functional failure can also occur when a new failure/defect happens relatively soon after the completion of the previous repair. In this paper, we present a new stochastic model that defines and describes the lifetimes of this kind of repairable systems with operational constraints. A new approach based on Laplace transforms is developed to study the reliability function and the mean time to failure for these systems. Furthermore, we consider the stochastic model when only a finite number of repairs are allowed and obtain relevant reliability indices for this case as well. Detailed numerical examples illustrate our findings.