Optimal Design of Hybrid Redundant Systems With Delayed Failure-Driven Standby Mode Transfer

Standby redundancy is a design technique that has been widely adopted to enhance system reliability and achieve fault tolerance in many critical applications. In this paper, we consider a 1-out-of-N: G hybrid standby redundant system with unrepairable elements being subject to delayed failure-driven standby mode transfers. Specifically, in the considered system, all the standby elements are initially in a warm standby mode (WSM) but can be transferred to a hot standby mode (HSM) so as to be ready to replace the online operating element when it fails. The WSM to HSM transfer is performed with a fixed time delay after no element resides in HSM either due to the element failure or because the element leaves the HSM to replace the failed online element for operation. A new iterative numerical algorithm is first proposed for evaluating reliability and expected mission cost (relevant to elements' standby expense, operation expense, as well as mode transfer expense) of the considered hybrid standby system. The algorithm has no restriction on element time-to-failure distribution types. Based on the proposed evaluation algorithm, we further formulate and solve a new optimization problem that finds the optimal delay and optimal sequence of standby elements with the objective to minimize expected mission cost while satisfying a certain level of mission reliability constraint. Examples are presented to demonstrate applications of the proposed methodology.