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Reliability Lecture 25 ME EN 372 Andrew Ning aning@byu.edu - - PDF document
Reliability Lecture 25 ME EN 372 Andrew Ning aning@byu.edu - - PDF document
Reliability Lecture 25 ME EN 372 Andrew Ning aning@byu.edu Outline Statistics Review Reliability Statistics Review Probability Distribution Function 1.2 1.0 0.8 f(x) 0.6 0.4 0.2 0.0 0 1 2 3 4 5 x Cumulative Distribution
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Cumulative Distribution Function
1 2 3 4 5 x 0.0 0.2 0.4 0.6 0.8 1.0 F(x)
Expectation
E(X) = µx = ∞
−∞
xf(x) E(X) = ¯ x =
N
- i=1
xif(xi)
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Variance
σ2 = ∞
−∞
x2f(x)dx − µ2 s2
x =
1 N − 1 N
- i=1
x2
i
- − N ¯
x2
- Common Probability Distributions
4 3 2 1 1 2 3 4 z 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 f(z)
f(x) = 1 σ √ 2π exp
- −1
2 x − µ σ 2
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Error Propagation
c = a + b
Reliability
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Reliability
Factor of Safety: Capacity / Load Margin of Safety: Capacity - Load Failure probability: p = P(Load ≥ Capacity) Reliability: R = P(Load < Capacity) R = P(S - L > 0)
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