Reliability theory describes the probability of a system completing its expected function during an interval of time. It is the basis of reliability engineering, which is an area of study focused on optimizing the reliability, or probability of successful functioning, of systems, such as airplanes, linear accelerators, and any other product. It developed apart from the mainstream of probability and statistics. It was originally a tool to help nineteenth century maritime insurance and life insurance companies compute profitable rates to charge their customers. Even today, the terms "failure rate" and "hazard rate" are often used interchangeably.
The failure of mechanical devices such as ships, trains, and cars, is similar in many ways to the life or death of biological organisms. Statistical models appropriate for any of these topics are generically called "time-to-event" models. Death or failure is called an "event", and the goal is to project or forecast the rate of events for a given population or the probability of an event for an individual.
When reliability is considered from the perspective of the consumer of a technology or service, actual reliability measures may differ dramatically from perceived reliability. One bad experience can be magnified in the mind of the customer, inflating the perceived unreliability of the product. One plane crash where hundreds of passengers die will immediately instill fear in a large percentage of the flying consumer population, regardless of actual reliability data about the safety of air travel.
Reliability period of any object is measured within the durability period of that object.