Comparison of the approaches for PFD evaluation of safety instrumented systems with non-exponential distributions

The probability of failure on demand (PFD) is an important performance index to evaluate the reliability of safety instrumented systems (SIS) and determine their safety integrity level. In practice, some failure processes and repair processes in the SIS have a non-exponential distribution in nature. A SIS with non-exponential distributions can be described by a semi-Markov model. This paper aims to provide an overview of current developments in the evaluation of the PFD for SIS described by a semi-Markov model. Different approaches to calculate the PFD are compared in terms of accuracy of calculation results, computational efforts, and required pre-knowledge. Finally, a numerical example illustrates the application, advantages and disadvantages of each approach.