Suppose that four identical diesel engines are used to generate backup electrica

Question

Suppose that four identical diesel engines are used to generate backup electrical power for the emergency control system of a nuclear power plant. Assume that at least two of the diesel-powered units are required to supply the needed emergency power; in other words, at least two of the four engines must start automatically during sudden loss of outside electrical power. The operational life T of each diesel engine may be modeled with the shifted exponential distribution with a rated mean operational life of 15 years and a guaranteed minimum life of 2 years. The shifted exponential distribution is an exponential distribution that has been shifted to begin at a positive number a instead of zero: f_x(x) = {lambda e^-lambda(x - a) x greaterthanorequalto a 0 x

Explanation / Answer

a. Rate constant = ?

Rated mean operational life = 15 years

guaraneteed minimum life = 2 years = a

E(x) = a + 1/ = 15 years

so 1/ = 15 - a = 15 -2 = 13 years

so = 1/13 years-1

so rate constant = 0.077 years-1

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