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可靠性工程
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可靠性工程
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engines
威布尔可靠度 R(t)=e^−(t/η)^β
Weibull Reliability R(t)=e^−(t/η)^β
R(t)=e^(−(t/η)^β) · β<1早夭/β=1恒定/β>1耗损 · η处63.2%失效 · B10
Shape β sets the failure mode; η=1000 h is the characteristic life, R=e⁻¹≈0.368 at t=η (63.2% failed)
指数可靠度 R(t)=e^−λt 与 MTBF
Exponential Reliability R(t)=e^−λt & MTBF
R(t)=e^(−λt) · MTBF=1/λ · 无记忆 · t=MTBF→R=36.8% · 中位=0.693MTBF
Constant failure rate λ (Weibull with β=1); at t=MTBF, R=e⁻¹≈36.8%, not 50%
浴盆曲线:失效率 λ(t) 的三个阶段
The Bathtub Curve: Three Regions of λ(t)
失效率λ(t) · 早夭递减→偶发恒定→耗损递增 · 三区
The classic lifetime failure-rate shape: early-decreasing → constant → late-increasing
威布尔失效率:h(t)、R(t) 与 H(t)
Weibull Hazard Rate: h(t), R(t) & H(t)
h(t)=f(t)/R(t) · R=exp(−∫h) · H(t)=−lnR · 恒定h⇒指数
Hazard h(t)=f(t)/R(t) sets reliability R(t)=e^(−H(t)); switch shape β to see three failure regimes.
可修系统可用度:MTBF、MTTR 与 A
Repairable-System Availability: MTBF, MTTR & A
A=MTBF/(MTBF+MTTR)=μ/(λ+μ) · 500/508=98.43% · 年停机
Inherent availability A = MTBF/(MTBF+MTTR); drag MTBF and MTTR to see annual up/down time.
系统可靠度:串联 vs 并联
System Reliability: Series vs Parallel
串联∏Rᵢ=0.729 · 并联1−∏(1−Rᵢ)=0.999 · 3×0.9
Series R=∏Rᵢ (weakest link); parallel R=1−∏(1−Rᵢ) (redundancy); toggle the structure and set component R.
k-out-of-n 表决冗余系统可靠度
k-out-of-n redundancy reliability
ΣC(n,i)Rⁱ(1−R)ⁿ⁻ⁱ · n=5,R=0.9 · 2oo3表决 · k=n串/k=1并
The system works when at least k of n identical components work; reliability is the binomial upper tail
冷备份与热并联冗余的 MTBF
Cold-standby vs active-parallel redundancy MTBF
冷备2/λ=2000h · 有源并联1.5/λ=1500h · 单机1000h · Erlang
Both are two-unit redundancy, but cold standby (spare kept off) outlasts active parallel — at the cost of a reliable switch
FMEA 风险优先数 RPN
FMEA Risk Priority Number
RPN=S×O×D · 各1–10 · 1..1000 · 阈值>100排序
Rank failure modes by Severity × Occurrence × Detection; a higher RPN gets priority
故障树分析 · 自顶向下概率合成
Fault Tree Analysis · top-down probability roll-up
与门∏pᵢ · 或门1−∏(1−pᵢ) · TOP=1−0.98·0.95=0.069
Top-event probability is built up from basic events through AND/OR gates
杜安可靠性增长模型 · 双对数直线
Duane reliability-growth model · log-log line
λ_c=K·T^(−α) · MTBF_c=(1/K)T^α · 双对数斜率α · 瞬时/(1−α)
During development testing cumulative MTBF grows as a power law — a straight line of slope α on log-log axes
老化筛选 · 剔除早期失效
Burn-in Screening · weeding out infant mortality
β<1递减危险 · 老化t_b剔早夭 · 条件R(t_b+m)/R(t_b)提升
Burn-in before shipping so field life begins on the flat, low-hazard part of the bathtub curve