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Compounded conservatism (or "creeping safety") describes the impact of using conservative, upper-bound estimates of the values of multiple input variates to obtain a conservative estimate of risk modeled as an increasing function of those variates. In a simple multiplicative model of risk, for example, of upper p-fractile (100pth percentile) values are used for each of several statistically independent input variates, the resulting risk estimate will be the upper p'-fractile of risk predicted according to that multiplicative model, where p'>p. The amount of compounded conservativism reflected by the difference between p' and p may be substantial, depending on the number of inputs, their relative uncertainties, and the value of p selected. Particular numerical examples of compounded conservatism are often cited, but an analytic approach may better serve to conceptualize and communicate its potential quantitative impact. This note briefly outlines such an approach and illustrates its application to the case of risk modeled as a product of lognormally distributed inputs. Keywords: uncertainty, conservatism, safety, lognormal, probability
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