Reliability of Non-Coherent Warm Standby Systems With Reworking

In this paper we model and analyze non-repairable 1-out-of- N : G warm standby systems subject to periodic backups and dynamic reworking. Particularly, in such systems, a standby element must redo some portion of already performed work by the failed online element before taking over the mission task, which makes the actual mission time dynamic. The considered systems are widely used in applications such as computing and manufacturing, but have not been well studied in reliability theory. In this work, we make new contributions by suggesting a numerical algorithm to evaluate the reliability of the considered warm standby systems. It is revealed that these systems are non-coherent, where the system reliability has non-monotonic dependence on the reliability of individual elements. Numerical examples further show that the non-coherency phenomenon is more distinguished for elements initiated earlier than those initiated later in the warm standby list. Example results also imply that placing highly unreliable elements at the end of the warm standby waiting list, or even removing them from the system planning, can enhance the reliability of a warm standby system subject to reworking. Findings from this work can guide the reliability design of the considered warm standby systems in practice.