What type of inspection should be conducted to ensure the operational integrity of a turbine engine's exhaust system?

A visual inspection for cracks is essential for ensuring the operational integrity of a turbine engine's exhaust system. This type of inspection directly assesses the physical condition of the components, including the exhaust system, which can be subject to high temperatures and stresses during operation. Cracks in the exhaust system can lead to significant issues, such as exhaust leaks or structural failures, which could compromise engine performance and safety.

In contrast, the other options play different roles in maintenance and monitoring. An operational performance test evaluates the entire engine's functionality under normal operating conditions, but it does not specifically focus on the structural integrity of the exhaust components. Exhaust gas temperature monitoring is useful for detecting anomalies in engine performance but does not provide a direct assessment of the physical state of the exhaust system. A calibration check ensures instrumentation is accurate, but it does not relate to the condition of the engine's components themselves. Thus, the visual inspection is the most direct means of ensuring that the exhaust system remains intact and reliable.