Abstract
Accurate estimation of reliability of a system is a challenging task when only limited samples are available. This paper presents the use of the bootstrap method to safely estimate the reliability with the objective of obtaining a conservative but not overly conservative estimate. The performance of the bootstrap method is compared with alternative conservative estimation methods, based on biasing the distribution of system response. The relationship between accuracy and conservativeness of the estimates is explored for normal and lognormal distributions. In particular, detailed results are presented for the case when the goal has a 95% likelihood to be conservative. The bootstrap approach is found to be more accurate for this level of conservativeness. We explore the influence of sample size and target probability of failure on the quality of estimates, and show that for a given level of conservativeness, small sample sizes and low probabilities of failure can lead to a high likelihood of large overestimation. However, this likelihood can be reduced by increasing the sample size. Finally, the conservative approach is applied to the reliability-based optimization of a composite panel under thermal loading.
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