### Determine what is the probability of failure of the antenna

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##### Reference no: EM13317553

A large parabolic antenna is designed against wind load. During a wind storm, the maximum wind-induced pressure on the antenna, P, is computed as P= 1/2CRV^2 Where C = drag coefficient, R = air mass density in slugs/ft3, V = maximum wind speed in ft/sec, and P = pressure in lb/ft2. C, R, and V are statistically independent lognormal variates with the following respective means and c.o.v's: mean of c= 1.80 standard deviation= .20 mean of r= 2.3*10^-3 slugs/ft3 standard deviation= .10 mean of v= 120 ft/sec standard deviation= .45

a. Determine the probability distribution of the maximum wind pressure P and evaluate its parameters.

b. What is the probability that the maximum wind pressure will exceed 30 lb/ft2?

c. The actual wind resistance capacity of the antenna is also a lognormal random variable with a amean of 90 lb/ft2 and a c.o.v. of 0.15. Failure in the antenna will occur whenever the maximum applied wind pressure exceeds its wind resistance capacity. During a wind storm, what is the probability of failure of the antenna?

d. If the occurrences of wind storms in (c) constitute a Poisson process with a mean occurrence rate of once every 5 years, what is the probability of failure of the antenna in 25 years?

e. Suppose five antennas were built and installed in a given region. What is the probability that at least two of the five antennas will not fail in 25 years? Assume that failures between antennas are statistically independent.

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