Rivets used to secure the stainless steel sheet metal of aircraft wings are designed to withstand certain shearing forces. It is knownthat because of random variations in location the load on a rivet is Weibull distributed with a scale parameter of 750 pounds and a shape parameter of 3.0. The strength of the rivetsin pounds is also random because of variations in the material characteristics and the dimensional tolerances. It has been found that the strength is also Weibull distributed with the same shape parameter but with a scale parameter of 1000 pounds.
Let x denote the load on a given rivet and let y denote the strength of that rivet. The rivet will not fail if x is less than y.The Reliability may therefore be expressed as P[X]