The conventional stochastic data envelopment analysis (SDEA) model suffers from biased efficiency scores for units located at the weak efficient frontier or compared to the weak frontier. This study modifies the weak efficient hyperplane(s) while maintaining the general production function by restricting the gradients of weak efficient hyperplanes in the original model using facet analysis. Empirical analysis on environmental efficiency of sustainable development goals validates the results of the modification. Results of the modified model compared to the conventional model show change in efficiency scores of weak efficient units and those compared to the weak part of the frontier while the efficiency scores of the strong efficient frontier remain the same. Furthermore, the proposed model shows greater discriminatory power compared to the conventional model, hence, providing a reliable benchmark and improvement strategy post efficiency analysis.