Component redundancy vs system redundancy in the hazard rate ordering

Abstract

Design engineers are well aware of the stochastic result which says that (under the appropriate assumptions) redundancy at the component level is superior to redundancy at the system level. Given the importance of the hazard rate in reliability and life testing, we investigate to what extent this principle holds for the stronger stochastic ordering, viz, hazard rate ordering. Surprisingly, this does not hold for even series systems if the spares do not match the original components in distribution. It is true for series systems however for matching spares, and we conjecture that this is the case in general for k-out-of-n:G systems. We also investigate this principle for cold-standby redundancy (as opposed to active or parallel redundancy).