Probability of dangerous failure of a system: explanations and example of the calculation

In the area of machine safety, new standards (CEI 61508 and CD CEI 62061) have been drawn up aimed at quantifying the probability of dangerous failure of the system, termed PDF, resulting from random hardware failures. This quantification is one of the means allowing for classification of systems by safety integrity level (SIL).
This document firstly reviews various concepts useful for calculating the probability of dangerous failure, in particular an explanation of the different parameters involved in estimating PDF. It then goes on to describe the approach that should be followed to perform this calculation.
Finally, an example of an application is described in detail, highlighting an architecture based on identical PLCs and another architecture based on heterogeneous PLCs. This scientific and technical note is intended as a support allowing a better understanding of the PDF calculation. The hypotheses made are detailed and several calculation methods are explained.