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Failure rate is the frequency with which an engineered system or component fails. Usually it is expressed in a number of failures per time period, like failures per hour. It is often written as the Greek letter λ (lambda) and is important in reliability theory. In practice, the closely related Mean Time Between Failures (MTBF) is more commonly expressed and used for high quality components or systems.
Failure rate is usually time dependent, and an intuitive corollary is that the rate changes over time versus the expected life cycle of a system. For example, as an automobile grows older, the failure rate in its fifth year of service may be many times greater than its failure rate during its first year of service–one simply does not expect to replace an exhaust pipe, overhaul the brakes, or have major transmission problems in a new vehicle. Mean Time Between Failures (MTBF) is closely related to failure rate. In the special case when the likelihood of failure remains constant with respect to time (for example, in some product like a brick or protected steel beam), and ignoring the time to recover from failure, failure rate is simply the inverse of the Mean Time Between Failures (MTBF). MTBF is an important specification parameter in all aspects of high importance engineering design–such as naval architecture, aerospace engineering, automotive design, etc.–in short, any task where failure in a key part or of the whole of a system needs be minimized and severely curtailed, particularly where lives might be lost if such factors are not taken into account. These factors account for many safety and maintenance practices in engineering and industry practices and government regulations, such as how often certain inspections and overhauls are required on an aircraft.
A similar ratio used in the transport industries, especially in railways and trucking is 'Mean Distance Between Failure', a variation which attempts to correlate actual loaded distances to similar reliability needs and practices.
Failure rates are important factors in insurance, business, and regulation practices as well as fundamental to design of safe systems throughout a national or international economy.