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

为了刻画可靠性理论中的最优分配策略、随机序和老化，研究了多元条件风险率函数、随机凸凹性等概念的应用。在可靠性理论的许多应用中，主要关注的不一定是系统部件的总寿命，而是系统在其生命周期内所带来的总效益。当可用于增强组成系统的组件的资源有限时，这一点尤其重要。利用优化性、随机凸性和随机凹性的概念，寻求最优分配策略。可靠性组件的性能往往受到其运行环境的强烈影响。使用多变量条件风险率函数，可以以相对简单的方式对这样的环境进行数学建模。本研究的目的是应用统计学和概率学中的概念来刻画可靠性理论中的最优分配策略和老化。可靠性组件的性能通常受其运行环境的强烈影响。将描述和分析数学模型，并描述有限资源分配的最佳策略。

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.