Calculating Confidence Bounds for Reliability Index to Quantify Effect of Distribution Parameter Uncertainty

Abstract

Probabilistic methods for risk and reliability assessment require knowledge of statistical variation of design parameters. Often the parameters themselves are uncertain. In such cases it is important to quantify the effect of parameter uncertainty on the reliability calculations. Since parameter uncertainty is a reducible uncertainty, the use of confidence interval bounds to quantify the uncertainty in the reliability predictions is preferred. Obtaining confidence bounds for reliability requires characterizing the uncertainty of distribution parameters of the uncertain variables, and calculating confidence intervals for reliability index based on parameter uncertainty. In this paper, we present different options for calculating confidence intervals for reliability when the distributions of the distribution parameters of the uncertain variables are specified. This accuracy, computational cost and limitations of the different methods presented to calculate lower confidence bound of reliability index ( β ) are discussed. The methods are applied to calculating lower confidence bound of reliability index for a simple beam example.

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