Factories are controlled environments, designed to put out consistent products in volumes according to a plan. Controls, however, are never perfect, and managers respond to series of events of both internal and external origin.

An event is an instantaneous state change, with a timestamp but no duration. An operation on a manufacturing shop floor is not an event but its start and its completion are. Machine failures and quality problem reports from customers are all events. Customer orders and truck arrivals are also events.

For rare events, you measure times between occurrences and mark each occurrence on a timeline. For frequent events, you count occurrences per unit of time and plot these numbers over time. On individual machines, you record the times between failures. For incoming online orders for a product, you count how many you receive each hour or each day. Every 200,000 years, compass needles reverse directions. That is a rare event, recorded in basalt oozing from the mid-Atlantic ridge as it cools down, as on a magnetic tape. (See Paleomagnetism.)

Once a year, an American TV viewer tuning in to the Academy Awards is a frequent event. For this, we care how many millions do it, but not how much time elapses between two tune-ins.

Responding to series of events is central to many businesses. Stores respond to customers coming in, airlines to passengers with reservations showing up to fly — or not, maintenance crews to machine failures, social networks to subscriber activities,… The challenges posed by the randomness of the arrival and service processes has given rise to queuing theory and commonly used results like Little’s Law about lead times, throughput and inventory in steady-state, or Kingman’s Rule about the way lead times explode when systems saturate.

We are concerned here with a different and simpler topic: monitoring series of events to detect changes in their rates of occurrence and tell fluctuations apart from shifts with assignable causes. If the arrival rate of quality problem reports from the field suddenly doubles, a sophisticated analysis is not needed. If it increases by 10%, the conclusion is not so obvious.

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