On the Behavior of Statistical Models Used for Design

[+] Author and Article Information
P. H. Wirsching

Aerospace and Mechanical Engineering, The University of Arizona, Tucson, Ariz.

J. Eng. Ind 98(2), 601-606 (May 01, 1976) (6 pages) doi:10.1115/1.3438944 History: Received August 05, 1975; Revised August 15, 1975; Online July 15, 2010


In probabilistic design, it is common practice to use two parameter statistical models (e.g., normal, lognormal) to describe random design factors. However, given a random sample of data, it is often difficult to distinguish which of several competing models provides the best description. It is demonstrated herein that the choice of model has a profound effect on probability estimates, particularly in the tails of the distributions. Given only the mean and standard deviation of a random variable, the Tchebycheff or Camp-Meidell inequalities can be used to provide upper-bound estimates of probabilities. However, these inequalities are usually too weak for design purposes. Probability models which yield more reasonable results are proposed. The two parameter exponential and power models are proposed for quasi-upper bounds of right and left tail probabilities, respectively. The exponential and power models are used for stress and strength, respectively, to derive, from inference theory, quasi-upper bounds for probability of failure of a structural element.

Copyright © 1976 by ASME
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