Manufacturers and consumers prefer reliable products, or systems in general, since they need to assure that systems work satisfactory for given mission times. The redundancy allocation to original system components is a common technique to improve reliabilities. But, allocation of redundants is not an easy task and must be considered properly with respect to environmental working conditions and possible restrictions such as cost, volume and weight. Therefore, the problem of finding optimal allocations is important and studied extensively in literature. The existing studies usually assume restrictive conditions such as stochastically independent component and spare lifetimes. This article deals with this problem under a general setting in which component and spare lifetimes can be dependent and heterogeneous. Two common policies, called active and standby, are studied in details. Stochastic orders are implemented for comparing various allocation policies. Findings of this article are derived under general conditions and hold for arbitrary dependency structures among lifetimes. Illustrative examples are also given.

中文翻译：

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系统中的冗余分配：一个通用的基于依赖关系的框架

制造商和消费者通常更喜欢可靠的产品或系统，因为他们需要确保系统在给定的任务时间内工作令人满意。对原始系统组件进行冗余分配是提高可靠性的常用技术。但是，冗余设备的分配并非易事，必须根据环境工作条件和可能的限制（例如成本、体积和重量）进行适当考虑。因此，寻找最优分配的问题很重要，并且在文献中得到了广泛的研究。现有的研究通常假设限制性条件，例如随机独立的组件和备用寿命。本文在组件和备用生命周期可以相互依赖和异构的一般设置下处理这个问题。两个共同的政策，称为主备，详细研究。执行随机订单以比较各种分配策略。本文的发现是在一般条件下得出的，并且适用于生命周期之间的任意依赖结构。还给出了说明性示例。