Some results on active redundancy at component level versus system level

Optimum lifetime of a series system with active spares always depends on the allocation of spares at component /system level. We prove that under some sufficient conditions, component redundancy offers greater reliability than the system redundancy in likelihood ratio ordering for n-component matching spares. We also show that this principle holds under some sufficient conditions in likelihood ratio ordering for 2-component non-matching spares of iid components and iid spares. Further, we give some sufficient conditions under which reversed hazard rate order does not exist between two 2-component systems of matching spares.