Comparisons between an unknown-but-bounded imperfection model and a random imperfection model show that for simple pointwise failure measures, at least, the two models give the same expressions for their measures of response, but each measure has a distinctly different interpretation. The former gives the maximum possible response for any imperfection within a specified bound. The latter gives the standard deviation of response, which, together with the statistical distribution, can be used to specify the maximum response at a specified confidence level. However, since the statistical distributions of imperfections, and hence of the response are often unknown, confidence levels are difficult to define, especially in the tail of the distribution at high confidence levels. The unknown-but-bounded model requires less information about the imperfections to come to a well-defined bound on response. It is further shown that, while the maximum possible response might seem to be a severe failure avoidance criterion, it can be less constricting than having to impose artificially high confidence levels with poorly known statistical distributions.

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