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

本文研究了多变量条件风险率函数、随机凸性和随机凹性等概念在可靠性理论中最优分配策略、随机顺序和老化等方面的应用。在可靠性理论的许多应用中，主要关注的不一定是系统组件的总寿命，而是系统在其生命周期内提供的总效益。当有限的资源可用于增强组成系统的各部分时，这一点尤其重要。利用多数化、随机凸性和随机凹性的概念，寻求最优分配策略。可靠性组件的性能通常受到其工作环境的强烈影响。使用多变量条件风险率函数，可以以相对简单的方式对这种环境进行数学建模。本文研究了统计和概率论概念在可靠性理论中最优分配策略和老化问题的应用。可靠性组件的性能通常受到其工作环境的强烈影响。数学模型将被描述和分析，以及分配有限资源的最优策略将被描述。

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.