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Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is often denoted by the Greek letter λ (lambda) and is highly used in reliability engineering. The failure rate of a system usually depends on time, with the rate varying over the life cycle of the system. For example, an automobile's failure rate in its fifth year of service may be many times greater than its failure rate during its first year of service. One does not expect to replace an exhaust pipe, overhaul the brakes, or have major transmission problems in a new vehicle. In practice, the mean time between failures (MTBF, 1/λ) is often reported instead of the failure rate. This is valid and useful if the failure rate may be assumed constant – often used for complex units / systems, electronics – and is a general agreement in some reliability standards (Military and Aerospace). It does in this case ''only'' relate to the flat region of the bathtub curve, also called the "useful life period". Because of this, it is incorrect to extrapolate MTBF to give an estimate of the service life time of a component, which will typically be much less than suggested by the MTBF due to the much higher failure rates in the "end-of-life wearout" part of the "bathtub curve". The reason for the preferred use for MTBF numbers is that the use of large positive numbers (such as 2000 hours) is more intuitive and easier to remember than very small numbers (such as 0.0005 per hour). The MTBF is an important system parameter in systems where failure rate needs to be managed, in particular for safety systems. The MTBF appears frequently in the engineering design requirements, and governs frequency of required system maintenance and inspections. In special processes called renewal processes, where the time to recover from failure can be neglected and the likelihood of failure remains constant with respect to time, the failure rate is simply the multiplicative inverse of the MTBF (1/λ). A similar ratio used in the transport industries, especially in railways and trucking is "mean distance between failures", a variation which attempts to correlate actual loaded distances to similar reliability needs and practices. Failure rates are important factors in the insurance, finance, commerce and regulatory industries and fundamental to the design of safe systems in a wide variety of applications. ==Failure rate in the discrete sense== The failure rate can be defined as the following: :The total number of failures within an item population, divided by the total time expended by that population, during a particular measurement interval under stated conditions. (MacDiarmid, ''et al.'') Although the failure rate, , is often thought of as the probability that a failure occurs in a specified interval given no failure before time , it is not actually a probability because it can exceed 1. Erroneous expression of the failure rate in % could result in incorrect perception of the measure, especially if it would be measured from repairable systems and multiple systems with non-constant failure rates or different operation times. It can be defined with the aid of the reliability function, also called the survival function, , the probability of no failure before time . ::, where is the time to (first) failure distribution (i.e. the failure density function) and . :: over a time interval from (or ) to and is defined as . Note that this is a conditional probability, hence the in the denominator. The function is a CONDITIONAL probability of the failure DENSITY function. The condition is that the failure has not occurred at time . Hazard rate and ROCOF (rate of occurrence of failures) are often incorrectly seen as the same and equal to the failure rate. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Failure rate」の詳細全文を読む スポンサード リンク
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