Question

A design has an expected distribution of stress with a mean value of 1 MPa and a standard deviation of 0.3 MPa. The strength of the design is expected to have a mean value of 2 MPa and a standard deviation of 0.2 MPa. Both can be assumed to be normal distributions. What is the expected failure rate of the design?

Answer 1

Let the stress be represented by random variable X and the strength by Y.

Then the design fails if X > Y

We are given here:

Now the distribution of X - Y is obtained as:

The failure rate is computed here as:

P(X > Y) = P(X - Y > 0)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore the failure probability of the design is 0.0028 or 0.28%