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Cascading failure in power grids has long been recognized as a sever security threat to national economy and society, which happens infrequent but can cause severe consequences. The causes of cascading phenomena can be extremely complicated due to the many different and interactive mechanisms such as transmission overloads, protection equipment failures, transient instability, voltage collapse, etc. In the literature a number of vulnerability measures to cascading failures have been proposed to identify the most critical components in the grid and evaluate the damages caused by the removal of such recognized components from the grid. In this paper we propose a novel power grid vulnerability measure called the minimum safety time after 1 line trip, defined based on the stochastic cascading failure model. We compare its performance with several other vulnerability measures through a set of statistical analysis.