Assignment 7.pdf

# Assignment 7.pdf - Assignment 7 Physical reliability models...

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1 Assignment # 7: Physical reliability models 1. The time to failure of a drill bit is lognormal with s = 1.43. From field data the median life of the bit has been found to depend on the Brinell hardness and the density of the material being drilled. The following function was empirically derived: ( ) 2 1 35 . 0 0157 . 0 31 . 12 x x x u = where x 1 is the Brinell hardness and x 2 is the density (mg/m 3 ). If a steel plate has been heat-treated to a Brinell hardness of 200 and has a density of 7.3 mg/m 3 , determine its reliability over 20 cutting hours. 2. Consider the following load distribution: ( ) otherwise kg 1000 x 0 x x f x Ω Ψ Χ = 0 10 / 3 9 2 If the strength is a constant 950 kg, determine the static reliability. 3. The strength of a concrete structure designed to support a fixed load of 464 lb has the following probability density function: ( ) lb 1000 y 0 y y f y = 9 2 10 3 (a) Compute the static reliability. (b) If the load is also random having the probability density function below, find the static reliability. lb x x x f x 1000 0 ) 000001 . 0 001 . 0 ( 2 ) (

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