Sequencing Optimization ink-out-of-nCold-Standby Systems Considering Mission Cost

Abstract

The k-out-of-n: G heterogeneous cold-standby system structure is a widely used fault-tolerant system design method, where the sequence in which the different system elements are initiated can greatly affect the system reliability and mission cost. This paper considers the optimal standby element sequencing problem (SESP) for such systems. Given the desired cold-standby redundancy level and fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected system mission cost while meeting a certain level of system reliability constraint. Based on a discrete approximation of time-to-failure distributions of the system elements, the system reliability and expected mission cost are evaluated simultaneously using a numerical method. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem for k-out-of-n: G heterogeneous cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology.

Optimal choice of standby modes in 1-out-of-N system with respect to mission reliability and cost

“…In practice, however the element operation cost and thus the entire mission cost depend on factors such as energy and materials consumption associated with actual lifetimes of used elements. Recently, more practical cost models considering these factors and elements' actual working times have been developed for different types of standby systems, including cold [36,37], mixed cold and hot [38], and warm [39,40]. All these works have assumed a predefined standby mode for each standby element and solved the optimal standby element sequencing problem for the system design.…”

Cold Standby Systems With Imperfect Backup

“…Thus, element can complete the mission after operating during time (25) The total mission completion time in this case is (26) Having the functions , , , and , one can obtain the conditional probability of the mission completion by element given the BS fails at time as (27) and the expected time of mission completion by element given as (28) The events of the mission completion by different elements are mutually exclusive. Therefore, the overall probability of the mission success is (29) and the expected mission completion time is (30) Observe that when the time of the BS failure exceeds , the value of does not affect the conditional probability and time of the mission completion by any element, i.e., and for any .…”

“…Extensive research has been conducted into reliability modeling and analysis of 1-out-of-: G and -out-of-: G cold standby systems using diverse techniques such as state-space-based approaches (including Markov [4], [14], [15] and non-Markovian processes [16]- [18]), Pearson distributions-based method [19], counting process-based method [20], central limit theorem-based approximate method [21], [22], sequential binary decision diagrams [23], and numerical methods [24], [25]. Considerable efforts have also been dedicated to optimizing cold standby systems considering reliability and/or costs using exact methods (e.g., integer programming [3]) and heuristic/meta-heuristic methods (e.g., genetic algorithm [24]- [26]).…”

Multi-Valued Decision Diagram-Based Reliability Analysis of <formula formulatype="inline"><tex Notation="TeX">$k$</tex> </formula>-out-of-<formula formulatype="inline"><tex Notation="TeX">$n$</tex> </formula> Cold Standby Systems Subject to Scheduled Backups

“…Further, a central limit theorem based approximation approach [12] was proposed to evaluate the reliability of -out-of-cold standby systems with identical components. Reference [19] proposed a discrete approximation method to evaluate the system reliability, and studied the optimal sequence for the -out-of-heterogeneous cold standby system. Reference [20] considered a cold standby system with three identical but statistically-dependent components, and studied its reliability characteristics.…”