The increasing complexity of modern aircraft systems presents many challenges to the current process for aircraft safety assessment and certification. Automated features and equipment are becoming so complex that potential dysfunctional interactions and requirements flaws are much more difficult to recognize and prevent than in the past. We believe that the current process for assessing safety and certifying aircraft described in ARP 4761 is limited in its effectiveness for modern complex and software intensive systems and that a better approach is needed. This paper describes the ARP 4761 methodology and then a new accident causality model and associated hazard analysis technique is introduced and applied to the Wheel and Brake System example used in ARP 4761. We conclude with a comparison of the two approaches.