「利用者:YasuakiH/Weibull distribution」の版間の差分

{{short description|Frequency with which an engineered system or component fails}}

'''Failure rate''' is the [[:en:frequency|frequency]] with which an [[:en:systems engineering|engineered system]] or component fails, expressed in failures per unit of time. It is usually denoted by the [[:en:Greek alphabet|Greek letter]] [[:en:λ|λ]] (lambda) and is often used in [[:en:reliability engineering|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 [[:en:Transmission (mechanics)|transmission]] problems in a new vehicle.

 

In practice, the [[:en:mean time between failures|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 [[:en:bathtub curve|bathtub curve]], which is also called the "useful life period". Because of this, it is incorrect to extrapolate MTBF to give an estimate of the service lifetime 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 [[:en:engineering|engineering]] design requirements, and governs frequency of required system maintenance and inspections. In special processes called [[:en:renewal process|renewal process]]es, 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 [[:en:transport industry|transport industries]], especially in [[:en:railway|railway]]s and [[:en:Truck driver|trucking]] is "mean distance between failures", a variation which attempts to [[:en:Correlation|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 [[:en:data|data]] can be obtained in several ways. The most common means are:

;Estimation:From field failure rate reports, statistical analysis techniques can be used to estimate failure rates. For accurate failure rates the analyst must have a good understanding of equipment operation, procedures for data collection, the key environmental variables impacting failure rates, how the equipment is used at the system level, and how the failure data will be used by system designers.

[[:en:Failure modes, effects, and diagnostic analysis|Failure modes, effects, and diagnostic analysis]]

 

 

The failure rate can be defined as the following:

Hazard rate and ROCOF (rate of occurrence of failures) are often incorrectly seen as the same and equal to the failure rate. {{clarify|date=April 2015}} To clarify; the more promptly items are repaired, the sooner they will break again, so the higher the ROCOF. The hazard rate is however independent of the time to repair and of the logistic delay time.

 

[[File:Loglogistichaz.svg|thumb|right|300px|Hazard function <math>h(t)</math> plotted for a selection of [[:en:log-logistic distribution|log-logistic distribution]]s.]] Calculating the failure rate for ever smaller intervals of time results in the '''{{visible anchor|hazard function}}''' (also called '''hazard rate'''), <math>h(t)</math>. This becomes the ''instantaneous'' failure rate or we say instantaneous hazard rate as <math>\Delta t </math> approaches to zero:

 

:<math>F(t) = 1 - \exp{\left(-\int_0^t h(t) dt \right)}.</math>

 

A decreasing failure rate (DFR) describes a phenomenon where the probability of an event in a fixed time interval in the future decreases over time. A decreasing failure rate can describe a period of "infant mortality" where earlier failures are eliminated or corrected<ref>{{Cite book | doi = 10.1007/978-1-84800-986-8_1 | chapter = Introduction | first = Maxim | last = Finkelstein| title = Failure Rate Modelling for Reliability and Risk | series = Springer Series in Reliability Engineering | pages = 1–84 | year = 2008 | isbn = 978-1-84800-985-1 }}</ref> and corresponds to the situation where λ(''t'') is a [[:en:decreasing function|decreasing function]].