What is the term for a systematic examination or detailed inquiry?

The term that best describes a systematic examination or detailed inquiry is "Investigation." This term specifically refers to a thorough and methodical process of exploring, studying, and analyzing information to uncover facts or understand a situation better. In various fields, including fire science and emergency management, investigations are crucial for assessing incidents, understanding causes, and improving future responses.

While other terms like "Inquiry," "Analysis," and "Research" do relate to examination or examination-like processes, they don't capture the comprehensive nature of an investigation as effectively. Inquiry tends to imply a general questioning or probing process, which may not necessarily be systematic. Analysis focuses on breaking down information into its components to understand it better, but it lacks the broader context of actively seeking out new data or facts. Research usually involves a more formal, structured approach to gathering information and knowledge but is not always synonymous with the detailed inquiry aspect. Thus, "Investigation" is the most fitting term in this context.