Influence of data sampling on confidence in the calculation of reliability index for simple performance functions

Abstract

The mean (point) estimate of reliability index (β) for simple limit state performance functions is most often based on load and resistance model bias statistics taken from bias data of limited size. The paper shows how the confidence in the point estimate of β can be computed using the bootstrap method and a closed-form solution for the special case of lognormally distributed nominal and bias random variables. Bias data collected for the pullout limit state for steel strip mechanically stabilized earth walls are used to demonstrate the approach but the method is general. Mean and confidence intervals on β are computed using the entire available bias data sets and smaller sample sizes located in the tails of the original populations, or smaller sample sizes that result in upper and lower extreme point estimates of β. The closed-form solution for β varies linearly with the logarithm of the nominal factor of safety for the example pullout limit state. Depending on the load and resistance bias sample sizes and where they are taken from in the original larger population, results in a wide range of nominal factors of safety to satisfy a target β at time of design.