Step-width control for PFD calculations – Efficient algorithms for large systems

Abstract

In order to evaluate the dependability of an automation system by means of parameters such as lifetime, availability, failure likelihood, or the safety integrity level, a suitable approach is needed for analysing the transient state behaviour. In this paper, modelling methods are described, followed by the derivation of numerical algorithms and the computer based calculations. By modifying existing approaches and controlling step width in accordance with convergence and stability behaviour, a significant improvement can be obtained in comparison with previous calculations. This is in particular the case when considering very large numbers of error states, long time intervals, widely differing fault and repair rates, or even specific accuracy requirements. Numerical results are given for two practical applications.