This book clearly explains how to do probabilistic calculations to accomplish SIL verification for safety systems. Starting with a description of the safety lifecycle, the authors show where and how SIL verification fits into the key activities from conceptual design through commissioning. The book not only explains the theory and methods for doing the calculations, the authors also provide many examples from the chemical, petrochemical, power and oil & gas industries. Through numerous examples, the authors make the material understandable, plus the data tables give readers important information needed to do the verification calculations. The authors provide example failure rate data and other important metrics needed for probabilistic calculations. Appendices cover probability, failure modes, diagnostic analysis, fault tree analysis, Markov Models, and system architectures.