On the increase of the expected lifetime by parallel redundancy

Parallel redundancy is an important technique to increase system reliability. It is well known that for components having exponential life distributions, adding a parallel component increases mean time to failure, but the more parallel components there are, the less the increase in mean time to failure due to an additional component. In this paper we study the effectiveness of adding parallel redundancy to a single component in complex system. It is shown that the effectiveness is strongly dependent on the class of life distributions assumed. We use the convex ordering approach to compare the failure rates of two life distributions. It is proved that adding parallel redundancy on an increasing failure rate component is less effective than that for a decreasing failure rate component. We also show that for any life distribution, the improvement in expected lifetime also decreases as the number of redundant components increases. The problem of adding parallel redundancy to meet a requirement on mean time to failure is also discussed.