PFD calculation in case of non-constant failure rates

Abstract

The probability of failure on demand (PFD) of real safety equipment can be calculated with the help of the formulas given in VDI/VDE 2180 or EN 61508 only under certain conditions. If these conditions are not fulfilled (e.g. in case of an incomplete proof test or a non-constant failure rate), the formulas cannot be applied right away. In such cases, the PFD calculation can be carried out relatively easily using time-varying Markov models. EN 61508 Part 6 Edition 2 presents the method of multiphase Markov models. If components subject to wear shall be observed in the PFD calculation, this method has to be further generalized; in this generalization, the transition probabilities of the corresponding Markov model are presented as a time-varying function. This is described in detail in the present contribution, based on a fictitious example. The time-dependent PFD(t) is calculated for the total plant lifetime which is then used to determine the average probability of failure on demand PFDavg. All calculations are carried out with Mathcad as this tool offers the necessary flexibility and is easy to handle compared to others.