Heterogeneous 1-Out-of-N Warm Standby Systems With Dynamic Uneven Backups

Abstract

In this paper, mission reliability, expected mission completion time, and cost of non-repairable 1-out-of-: G warm standby sparing systems subject to uneven backup actions are modeled and optimized. The backup actions are used to facilitate the data recovery process in the case of an online operating element failure, which enables an activated standby element to take over the mission task through subsequent data retrievals. Both data backup and retrieval times are dynamic, and physically dependent on the amount of work performed. The system elements are not necessarily identical; each element can be characterized by a different time-to-failure distribution, a different performance, and a different level of readiness to take over the system task during the warm standby mode. An iterative numerical method is first proposed to simultaneously evaluate mission reliability, expected mission completion time, and the cost of the considered heterogeneous warm standby systems. Due to the non-monotonic effect of the backup distribution on the mission reliability, time, and cost, we formulate and solve the optimal backup distribution problem considering different combinations of optimization objectives and constraints. In the case of system elements being non-identical, their activation order can influence the mission reliability, expected mission completion time, and mission cost significantly. Therefore, we also formulate and solve the optimal element sequencing problem for the considered system. Furthermore, new integrated optimization problems are formulated and addressed. The integrated optimization aims to identify the optimal combination of backup distribution and element activation order that maximizes the mission reliability, or minimizes the expected mission time or mission cost. As shown through examples, the proposed methodology can implement a tradeoff analysis among the three mission requirements of reliability, cost, and completion time, leading to the optimal decision on both backup and standby policies of warm standby systems.

Optimization of Full versus Incremental Periodic Backup Policy

“…Another direction is to consider standby sparing systems where different standby modes (hot, cold, and warm) can be implemented. The model presented in this paper can be combined with models of [7,45] for this purpose.…”

Cold Standby Systems With Imperfect Backup

“…The assumptions about fixed replacement and backup times can be relaxed using the approach suggested in [41]. The dynamic backup and retrieval time can be incorporated into imperfect backup model based on the work [42]. Another direction of our future work is to consider -out-of-: G cold standby systems where multiple elements are online and operating, their failure sequence impacts the waiting and operation times of standby elements, and their backup actions must be coordinated.…”

Reliability analysis of standby systems with multi‐state elements subject to constant transition rates

“…The system reliability is R (1000) = 0.9295. As it was shown in Levitin et al, in the heterogeneous systems, the sequence of the elements activation affects the system reliability. Therefore, the optimal activation sequence maximizing the reliability can be found.…”

“…The methods for reliability evaluation can be classified into simulations and analytic techniques . Simulation methods are flexible and can be applied to a wide range of systems; however, they usually need more computational effort and only provide approximate results .…”

“…[14][15][16][17][18][19][20][21][22] Simulation methods are flexible and can be applied to a wide range of systems; however, they usually need more computational effort and only provide approximate results. 13 Analytic techniques including state-space based methods, 14,15 universal generating function techniques, 16,17 decision diagram techniques, 18,19 and numerical methods [20][21][22] have been conducted for evaluating reliability of standby systems. State-space based methods, for example, Markov process models 14 are powerful in modelling dynamic processes, but are limited to exponential time-to-failure distributions and face the space explosion problem when applied to complex systems.…”