Recently, there has been a significant growth of interest in applying software engineering techniques for the quality assurance of deep learning (DL) systems. One popular direction is deep learning testing, where adversarial examples (a.k.a.~bugs) of DL systems are found either by fuzzing or guided search with the help of certain testing metrics. However, recent studies have revealed that the commonly used neuron coverage metrics by existing DL testing approaches are not correlated to model robustness. It is also not an effective measurement on the confidence of the model robustness after testing. In this work, we address this gap by proposing a novel testing framework called \emph{Rob}ustness-\emph{O}riented \emph{T}esting (RobOT). A key part of RobOT is a quantitative measurement on 1) the value of each test case in improving model robustness (often via retraining), and 2) the convergence quality of the model robustness improvement. RobOT utilizes the proposed metrics to automatically generate test cases valuable for improving model robustness. The proposed metrics are also a strong indicator on how well robustness improvement has converged through testing. Experiments on multiple benchmark datasets confirm the effectiveness and efficiency of RobOT in improving DL model robustness, with 67.02% increase on the adversarial robustness that is 50.65% higher than the state-of-the-art work DeepGini.