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Explore the evolution from traditional deterministic safety approaches to statistical methods in this 49-minute conference talk from the Linux Foundation's Open Source Summit. Learn how modern safety-related systems, with their inherent non-determinism and complexity, challenge conventional safety techniques that rely on element-by-element analysis. Discover why highly complex systems exhibit emergent properties that cannot be adequately captured through traditional Cartesian approaches of dividing problems into smaller parts. Examine the shift toward holistic statistical modeling as the future of system safety analysis. Understand statistical methods such as Probabilistic Worst Case Execution Time and Statistical Path Coverage, and see how these approaches can effectively assure complex systems. Analyze the limitations of current traditional techniques while exploring the opportunities that statistical approaches offer through practical examples. Investigate the specific requirements needed for statistical methods to be successfully implemented in the functional safety domain, addressing the growing need for high-performance and secure systems in safety-critical applications.