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.

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