## 1 Introduction  
The security of critical infrastructures (CIs)--\"The framework of interdependent networks and systems comprising identifiable industries, institutions (including people and procedures), and distribution capabilities that provide a reliable flow of products and services essential to the defense and economic security\", examples of which include power supply, transportation, communication, energy and water, governance infrastructures and more [1]--has been the subject of increased governmental attention due to the expanding threat of terrorism [2]. Following the September 11 attacks in the United States, the list of CIs was expanded to 17, including energy and power systems; food, water supply and health care systems; and other service systems [3]. Since CIs are integral to the normal functioning of society, their failure is associated with immense risk. CIs are complex systems comprising various subsystem components, and their functionalities are based on the operations of the subsystems within the CIs. The complexity of CIs make them vulnerable, with minor failures sometimes resulting in significant losses [4]. For example, the unexpected and unalarmed shutdown of one high-voltage power line in northern Ohio in 2004 resulted in up to two days of blackout to 50 million people, costing an estimated $6 billion and leading to 11 fatalities [5]. As compared to random infrastructure failures, terrorist attacks specifically targeting the most vulnerable components in CIs can result in much higher losses. The terrorist attack on the World Trade Center (WTC) in 2001, for example, resulted in an estimated total loss of $123 billion, a larger amount than most natural disasters for which such figures are available [6]. Additionally, the collapse of the WTC also caused the failure of the water-supply system beneath it, which resulted in serious flooding to nearby places and the flood-related loss of 200,000 voice lines, 100,000 private branch exchange lines and 4.4 million data circuits [3]. Apart from such major high-profile terrorist attacks, a large number of terrorist attacks against CIs occur in various countries, with great frequency and significant consequences. On average, nearly eight terrorist attacks take place per day, causing up to 18,000 fatalities worldwide yearly [7; 8]. The substation studied in this paper, which is a first degree strategic facility in Israel and the central electric power supplier of a regional town, has experienced continuous terror threats, and losses as high as $600,000 per year due to terrorist attacks [9]. Considering the high levels of damage that CI failures may cause to human life, the economy, national security, and the normal functioning of society, accurate estimation of the vulnerability of CIs to terrorism hazards is of profound importance, as is the development of strategies that could protect CIs from such hazards, or reduce losses. Many models and methods have been developed for these purposes. [PERSON] et al. [10] proposed a method for identifying and classifying different types of interdependencies between infrastructural elements, and for recognizing rippling effects caused by interruptions based on such interdependencies. [PERSON] et al. [11] devised mathematical definitions for each type of interdependency between infrastructure and the problem space, and modeled the potential effects on a community caused by the loss of power to an electrical-distribution substation. A variety of novel methodologies--for instance, using network theory, rating matrices, and system dynamics methods--have been used in recent years to estimate the vulnerability of infrastructure systems, especially power-supply systems [12]. However, there has hitherto been little research on vulnerability within a specific infrastructure during specific critical events, particularly terrorist attacks, and the potential risk due to the interactions between subsystems and components within that infrastructure.