Research On Optimal Allocation Of Redundancies To Parallel System Under The Exponential Distribution

Under the condition of component's lifetime follow exponential distribution,this thesis studies the problem of allocating single standby redundancy to parallel system consisting of two components.The necessary and sufficient conditions for the comparison of the lifetimes of redundant systems under the hazard rate order and the reversed hazard rate order have been established,and the results obtained under the hazard rate order cannot be enhanced to likelihood ratio order and proportional hazard rate model by counterexamples.Finally,numerical examples are given for some obtained results to better illustrate the effectiveness of the obtained results.