可维护随机系统的可用性优化研究

Availability optimization of a maintainable system with diverse cost functions

可用性是综合反映系统的可靠性和可修性的指标。研究从成本角度来优化配置用于系统可靠性和可修性的投入。鉴于系统可靠性降低和系统的维护时间均具有随机性,以随机过程方法描述并分析了可维护系统的可用性,并建立以平均运转时间(MTTF)和平均维护时间(MTTR)作为决策变量的约束优化模型。此模型的约束条件是系统的可用性要求,优化目标是最小化系统长期时间成本率。模型求解过程结合了工程中几种常见的成本函数形式,并依据对应模型的数量结构,最终推出最优系统参数的解析形式。建立了可维护系统的可用性优化的数学结构及求解方法。

Maintenance is a practical way to ensure the operating of the system, whereas it raises the system cost largely. Taking the long-run cost rate as the optimal object, studies the adequate structure of the availability optimization of the system. A good-asnew repair is adopted as the maintenance envelope. The costs of system unavailability and of repair are considered into the longrun cost of the system. By emphasizing the stochastic distinctions, i. e. the time to fail and the time to repair, as decision variables,the optimization problem is formulated and resolved analytically. As a result, a framework for optimizing the long-run cost rate of a maintainable system is established.