On Optimal Allocation Strategies Of Redundant Components In Reliability Systems

In this thesis, we investigate the optimal allocation strategies of redundant components through the tool of stochastic ordering. Firstly, under the framework of the exponential distribution, we discuss the problem of optimal allocation of one spare as active(or standby) redundancy in a system consisting of n(n ≥ 2)components. In both the active and standby cases, we establish sufficient and necessary conditions of reversed hazard rate order and likelihood ratio order, respectively. Our results indicate that one should allocate the redundancy to the relatively weaker component will make the resulting system live longer. Moreover,we explore the optimal allocation policy in a system of n(n ≥ 2) components.For the active case, under some appropriate assumptions, some results associated with the likelihood ratio and reversed hazard rate orders are presented are provided. For the standby case, we establish a result in the likelihood ratio order. Finally, this thesis also studies the problem of allocating two spares in a two-component system with general distribution. The results of reversed hazard rate and usual stochastic orders are presented. Some numerical examples are also given to explicate the theoretic results.