Mathematical Sciences: Multiunit Reliability Systems: Optimal Allocations of Resources, Stochastic Order and Aging

本研究关注的是概念的应用 多变量条件风险率函数，以及 随机凸性和随机性，目的是 表征最优分配策略、随机订单和 可靠性理论中的老化 在许多可靠性应用中 理论上，主要利益不一定在于总量 系统组件的寿命，但在整个 系统在其生命周期内提供的益处。 这是 特别重要的是，当有限的资源可用于 增强组成系统的组件。 使用 控制、随机凸性和随机 其次，寻求最优配置策略。 的 可靠性组件的性能通常 受其所处环境的影响。 使用 多变量条件风险率函数，有可能 以相对简单的数学方式模拟这种环境， 方式 本研究关注的是概念的应用 从统计学和概率的目的， 可靠性理论中的最优分配策略和老化问题。 可靠性组件的性能通常很强 受其所处环境的影响。 数学模型将被描述和分析，并优化 分配有限资源的政策将 表征了

This research is concerned with applications of the concepts of multivariate conditional hazard rate functions, and of stochastic convexity and concavity, for the purpose of characterizing optimal allocation policies, stochastic orders and aging in reliability theory. In many applications in reliability theory, the main interest lies not necessarily in the total lifetime of the components of the system, but in the total benefit delivered by the system during its lifetime. This is particularly important when a limited resource is available for enhancement of the components which make up the system. Using the notions of majorization, stochastic convexity and stochastic concavity, the optimal allocation policies will be sought. The performance of reliability components is often strongly influenced by the environment in which they function. Using the multivariate conditional hazard rate functions, it is possible to mathematically model such environments in a relatively simple manner. This research is concerned with the applications of concepts from statistics and probability for the purpose of characterizing optimal allocation policies and aging in reliability theory. Performance of reliability components is often strongly influenced by the environment in which they function. Mathematical models will be described and analyzed, and optimal policies for allocation of limited resources will be characterized.