Confidence intervals for reliability indices using likelihood ratio statistics

Structural reliability theory has found numerous applications in various engineering fields, due primarily to its introduction of the probability of failure or reliability index as a quantitative decision metric in the face of uncertain capacity and demand. In the development of first-generation probability-based design standards, the aleatory (inherent) and epistemic (knowledge-based) uncertainties were combined, leading to a point estimate of reliability. However, a critical aspect of quantified reliability assessment is the confidence level of the estimated failure probability, an aspect that becomes particularly significant in a reliability or risk assessment of an existing facility. The present study addresses this issue through an assessment of the confidence intervals on reliability indices using likelihood ratio statistics for cases where the capacity and/or demand models are derived from finite samples of data, expert opinion, or simulations. The proposed approach is applied to two realistic reliability assessment problems, revealing their applicability and accuracy in confidence interval estimation of reliability indices.

► A novel method is proposed to quantify confidence intervals of reliability indices. ► The method is based on modified signed log-likelihood ratio statistics. ► The approach is applied to two realistic reliability assessment problems. ► MC simulations support the accuracy of signed log-likelihood methods. ► Modified signed log-likelihood method is very accurate even for small sample sizes.