According to the PMBOK® Guide (Project Management Body of Knowledge), specifically within the Project Quality Management knowledge area and the Manage Quality process (historically referred to as " Perform Quality Assurance " ):

Root Cause Analysis (RCA) (Option D): This is the specific analytical technique used to determine the basic underlying reason that causes a variance, defect, or risk. The process involves identifying a problem, discovering the underlying causes (the " root " ), and developing preventative actions to ensure the problem does not recur. Common tools used within RCA include the Ishikawa (Fishbone) Diagram and the 5 Whys technique.

Quality Audits (Option B): While audits are a key tool of Manage Quality/Quality Assurance, their primary purpose is to determine if project activities comply with organizational and project policies, processes, and procedures. An audit might identify a non-compliance, but the subsequent deep dive into why it happened is the RCA.

Inspection (Option A): This is a tool primarily used in the Control Quality and Validate Scope processes. It involves examining a work product to determine if it conforms to documented standards. Inspection is reactive (finding defects), whereas RCA is used to develop proactive preventative measures.

Design of Experiments (DOE) (Option C): This is a statistical method used to identify which factors may influence specific variables of a product or process. It is used during Plan Quality Management to optimize products or processes, rather than to diagnose the cause of a specific existing failure.

In the PMI framework, Root Cause Analysis is essential for continuous process improvement. By addressing the source of a problem rather than just the symptoms, the Project Manager reduces the Cost of Quality by preventing future rework and defects.