Design diversity has long been used to protect redundant systems against common-mode failures. The conventional notion of diversity relies on "independent" generation of "different" implementations. This concept is qualitative and does not provide a basis to compare the reliabilities of two diverse systems. In this paper, for the first time, we present a metric to quantify diversity among several designs. Based on this metric, we derive analytical reliability models that show a simple relationship between design diversity, system failure rate, and mission time. In addition, we present simulation results to demonstrate the effectiveness of design diversity in Duplex and Triple Modular Redundant (TMR) systems. For independent multiple-module failures, we show that, mere use of different implementations does not always guarantee higher reliability compared to redundant systems with identical implementations-it is important to analyze the reliability of redundant systems using our metric. For common-mode failures and design faults, there is a significant gain in using different implementations-however, as our analysis shows, the gain diminishes as the mission time increases. Our simulation results also demonstrate the usefulness of diversity for enhancing the self-testing properties of redundant systems.
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