Hypothesis testing is a valuable method used to investigate ideas and test predictions arising from theories based on available data. In the context of critical system architecture, there is a need to effectively utilize hypothesis testing to identify faulty paths and improve system safety. This research aims to propose guidelines and best practices for presenting hypothesis testing in critical system architecture. The problem addressed in this study is the underutilization of hypothesis testing in life-critical system methods, resulting in a lack of identification of faulty paths. To address this challenge, we propose an enhanced pathway analysis technique that integrates error-derived information from a system's architectural description, thereby augmenting traditional hypothesis testing methods. By investigating various paths, we aim to identify false positive and false negative errors in life-critical system architecture. Furthermore, the proposed method is validated based on specific validation criteria for each step such as system boundary, assumption, content/architecture, and traceability validations. Also, the method is evaluated based on our claims. The results of our research highlight the significance of tracing errors in early system knowledge. By leveraging the augmented hypothesis testing method, we are able to identify hazards, safety constraints, and specific causes of unsafe actions more effectively. The findings emphasize the importance of integrating early design knowledge into hypothesis testing for enhanced hazard identification and improved system safety.