Probabilistic life prediction isn't as easy as it looks

Many engineers effect "probabilistic life prediction" by replacing constants with probability distributions and carefully modeling the physical relationships among the parameters. Surprisingly, the statistical relationships among the "constants" are often given short shrift, if not ignored altogether. Few recognize that while this simple substitution of distributions for constants will indeed produce a nondeterministic result, the corresponding "probabilities" are often woefully inaccurate. In fact, even the "trend" can be wrong, so these results cant even be used for sensitivity studies. This paper explores the familiar Paris equation relating crack growth rate and applied stress intensity to illustrate many statistical realities that are often ignored by otherwise careful engineers. Although the examples are Monte Carlo, the lessons also apply to other methods of probabilistic life prediction, including FORM/SORM (First/Second Order Reliability Method) and related "fast probability integration" methods.