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 Function 1.0 0.8 0.6 F(x) 0.4 0.2 0.0 0 1 2 3 4 5 x Expectation � ∞ E ( X ) = µ x = xf ( x ) −∞ N � E ( X ) = ¯ x = x i f ( x i ) i =1

Variance � ∞ σ 2 = x 2 f ( x ) dx − µ 2 −∞ �� N � � 1 � s 2 x 2 x 2 x = − N ¯ i N − 1 i =1 Common Probability Distributions 0.40 0.35 0.30 0.25 0.20 f(z) 0.15 0.10 0.05 0.00 4 3 2 1 0 1 2 3 4 z � � 2 � � x − µ 1 − 1 f ( x ) = 2 π exp √ 2 σ σ

Error Propagation c = a + b Reliability

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)

Example