Supply disruptions are attracting growing attention. Even in geographically, politically and economically stable locations, companies are exposed to disruptions, because they depend on their suppliers and suppliers' suppliers. The analysis of these disruptions helps mitigate risks: for example, instead of relying on local measures such as safety stock or insurance, a company can introduce new supply contracts or backup risky suppliers. In this article, we analyze risks caused by supplier disruptions by introducing concepts from probabilistic risk assessment (PRA), which is a widely employed methodology for the risk analysis of complex engineering systems. We apply PRA to examine simple networks such as triads analytically, and use simulation to analyze disruption risks in random networks of realistic size. We also illustrate how PRA can support strategic decisions such as whether or not to use single or multiple suppliers; which suppliers are more risky than others; and what impacts the complexity of the supply base has on the reliability of the supplier network.