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.
