  Reactive point processes (RPPs) are a new statistical model designed for
predicting discrete events in time based on past history. RPPs were developed
to handle an important problem within the domain of electrical grid
reliability: short-term prediction of electrical grid failures ("manhole
events"), including outages, fires, explosions and smoking manholes, which can
cause threats to public safety and reliability of electrical service in cities.
RPPs incorporate self-exciting, self-regulating and saturating components. The
self-excitement occurs as a result of a past event, which causes a temporary
rise in vulner ability to future events. The self-regulation occurs as a result
of an external inspection which temporarily lowers vulnerability to future
events. RPPs can saturate when too many events or inspections occur close
together, which ensures that the probability of an event stays within a
realistic range. Two of the operational challenges for power companies are (i)
making continuous-time failure predictions, and (ii) cost/benefit analysis for
decision making and proactive maintenance. RPPs are naturally suited for
handling both of these challenges. We use the model to predict power-grid
failures in Manhattan over a short-term horizon, and to provide a cost/benefit
analysis of different proactive maintenance programs.
