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**Source: **STP11275S

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 can't 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.

**Keywords:**

life prediction, crack growth, Paris equation, probability, statistics, simulation, Monte Carlo, nondeterministic, probabilistic, joint, conditional, marginal, multivariate

**Author Information:**

Annis, C *Principal, Charles Annis, P.E., Statistical Engineering, Palm Beach Gardens, FL*

**Committee/Subcommittee:** E08.06

**DOI:** 10.1520/STP11275S