The classical cross-entropy method (CEM) performs independent importance sampling of component states under the assumption that high-dimensional discrete random variables (RVs) are independent of each other. While CEM significantly accelerates power system reliability evaluation

this assumption limits its speed-up potential. To address this issue

an efficient variant of CEM

termed cross-entropy method with direction-radius co-optimization (CEM-DR)

is developed based on the direction-radius co-optimization of the random vector. First

a space transformation is applied to convert the discrete RV space into the standard normal space (SNS). Additionally

a direction-radius mixture distribution model is introduced to describe the random vector in the SNS

and cross-entropy co-optimization is performed on the multiple direction-radius distribution components. This method highlights the high-risk joint component failures

enabling joint importance sampling. Reliability evaluations on IEEE-RTS79

IEEE-RTS96

and other test systems are conducted to validate the superiority of CEM-DR over the conventional CEM.