A shaft is subjected to a maximum load of 10 kN. It is designed to withstand a l

Question

A shaft is subjected to a maximum load of 10 kN. It is designed to withstand a load of 15 kN. If the maximum load encountered is normally distributed with a standard deviation of 2.5 kN and a failure rate of 3% is required, what is the standard deviation acceptable in the shaft strength, assuming a normal distribution?

Explanation / Answer

P( Y2 > Y1) = the probability that it will be overloaded; P( Y2 > Y1) = P( Y2 - Y1 > 0 ) = P( Y1 - Y2 < 0 ) ; E[Y1 - Y2] = 500-4000 = 1000 Var(Y1 - Y2) = Var(Y1) + Var(Y2) =90000 + 160000 = 250000 P( Y2 > Y1) = 1P( Y1 - Y2 < 0 ) =P( ((Y1 - Y2) - 1000)/50

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