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As Deep Neural Networks (DNNs) are increasingly deployed in safety critical and privacy sensitive applications such as autonomous driving and biometric authentication, it is critical to understand the fault-tolerance nature of DNNs. Prior work primarily focuses on metrics such as Failures In Time (FIT) rate and the Silent Data Corruption (SDC) rate, which quantify how often a device fails. Instead, this paper focuses on quantifying the DNN accuracy given that a transient error has occurred, which tells us how well a network behaves when a transient error occurs. We call this metric Resiliency Accuracy (RA). We show that existing RA formulation is fundamentally inaccurate, because it incorrectly assumes that software variables (model weights/activations) have equal faulty probability under hardware transient faults. We present an algorithm that captures the faulty probabilities of DNN variables under transient faults and, thus, provides correct RA estimations validated by hardware. To accelerate RA estimation, we reformulate RA calculation as a Monte Carlo integration problem, and solve it using importance sampling driven by DNN specific heuristics. Using our lightweight RA estimation method, we show that transient faults lead to far greater accuracy degradation than what todays DNN resiliency tools estimate. We show how our RA estimation tool can help design more resilient DNNs by integrating it with a Network Architecture Search framework.