Major blackouts of electric power systems in which many customers are left without power are rare events. However, the effects of blackouts, for instance, can be catastrophic. It has been observed that protective system failures are a contributing factor in a large proportion of these blackouts. The most troublesome protection system failures are hidden failures, which remain dormant during normal system conditions, and are exposed during system disturbances. A study of hidden failures of the protective systems is undertaken to uncover their modes of failures, and to determine means of supervising their actions in times of highly stressed power system operations. The main contribution of this paper is to develop and document a method of quantitative analysis of the significance of hidden failures of protection systems. A complete protection system was designed for the New England 39-bus system and the hidden failure modes were used to develop regions of vulnerability and a vulnerability index. Through this analysis, critical protection systems, whose hidden failures would have a major impact on cascading failures or blackouts of the power system, can be identified These protection systems are candidates for increased monitoring and control, which would help alleviate the problems posed by hidden failures.