Question

The allowable stress X of a mechanical component is normally distributed, X ∼ N(120, 20) MPa , and the maximum stress y is normally distributed,            y ∼ N(100, 10) MPa .

a) What is the probability of failure pf ?

b) What is standard deviation of failure σf ?

Answer 1

a)

The mechanical component will fail if Y will be greater than X. Since X and Y both are normally distributed so the distribution o Y-X will be normally distributed with mean and SD follows:

and

The z-score for Y-X = 0 is

The probability of failure is

P(Y-X > 0) = P(z > -0.89) = 1 - P(z <= -0.89) = 1 - 0.1867 = 0.8133

b)

The standard deviation of failure σf is