Final answer:
Fault tree analysis is an analytic technique used to identify the causes of system failures, which can explain why a defective repair led to an incident.
Step-by-step explanation:
The analytic technique available to show why the defective repair occurred and contributed to the incident is the fault tree analysis. This technique systematically identifies potential causes of system failures before they occur. By starting with a top event, such as an accident or incident, and working backwards to map out all possible causes and their logical relationships using a graphical representation, fault tree analysis helps identify the likelihood of different faults contributing to the incident. A safety engineer, as mentioned in the example, might use this tool to trace back an accident resulting from the failure of employees to follow instructions, and to uncover contributing factors that led to this breakdown in process adherence.