平均故障间隔时间 (MTBF) is a reliability metric representing the predicted elapsed time between inherent failures of a repairable system. For systems with a constant failure rate [乳胶]\lambda[/latex], MTBF is its reciprocal: [latex]MTBF = 1/\lambda[/latex]. This simple relationship is fundamental in reliability engineering for predicting system uptime and planning maintenance schedules, assuming failures follow an exponential distribution.
MTBF is a core parameter in reliability and availability analysis. It quantifies the average time that a system is operational before a failure occurs. The calculation [latex]MTBF = 1/\lambda[/latex] assumes that the system’s failures follow an exponential distribution, which corresponds to a constant failure rate. This assumption is often valid for electronic components during their useful life, after the initial ‘infant mortality’ phase and before the ‘wear-out’ phase, as depicted by the 浴缸曲线 model of reliability.
The failure rate, [latex]\lambda[/latex], is typically expressed in failures per unit of time, such as failures per million hours. For example, if a component has a failure rate of 100 failures per 10^6 hours, its MTBF would be [latex]1 / (100 \times 10^{-6}) = 10,000[/latex] hours. It is crucial to understand that MTBF is a statistical average, not a guarantee of minimum operational time. In fact, for an exponential distribution, the probability of a system surviving up to its MTBF is only about 36.8% ([latex]e^{-1}[/latex]).
此指标主要用于可修复系统，即故障发生后，经过修复后系统恢复到正常运行状态。对于不可修复的系统，更合适的指标是平均故障时间 (MTTF)。
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(如果日期不详或不相关，例如 "流体力学"，则对其显著出现的时间作了四舍五入的估计）。
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