Probabilistic Worst-Case Execution Time estimates, through Measurement-Based Probabilistic Timing Analyses and statistical inference, desperately need for formal definition and reliability. The automatic DIAGnostic tool for applying the eXTReMe value theory within the Probabilistic Timing Analysis framework we are proposing defines a complete set of statistical tests for studying execution time traces, e.g., the real-time task average execution behavior, and estimating the extreme behavior of the task execution time, in particular the probabilistic Worst-Case Execution Time. The tool allows also defining and evaluating the reliability of the probabilistic Worst-Case Execution Time estimates with the Extreme Value Theory by applying a fuzzy logic approach. We apply the tool to traces of execution time measurements of a task running on a Commercial off-the-shelf real-time multi-core system under different execution conditions. Application of the diagnostic tool to the traces of execution time measurements particularly validates the hypothesis of using the Extreme Value Theory for estimating the probabilistic Worst-Case Execution Time for this kind of system.