| dc.description.abstract | The frequency of demands are crucial when analysing a safety instrumented system (SIS). IEC 61508 distinguishes between low and high demand mode when calculating risk for such a system. In reality there are systems that can not clearly be placed in one of the two modes. These types of systems are called intermediate demand mode systems, which we will analyse in this thesis. Not many published SIS reliability studies focus on the problems related to this borderline. Oliveira \cite{Oliveira2} predicts somewhat strange behaviour for the hazard rate in the intermediate demand mode, as well as \cite{Jin} with a focus on the demand duration. \\ The results from the analyses of a redundant system show that the standard Probability of Failure on Demand (PFD) formulae are usable for very low demand rates, but become increasingly more conservative as one moves into the intermediate mode, while the Probability of Failure per Hour (PFH) is non-conservative. This can cause major consequences for the operator of a safety system in the sense of not obtaining the optimal testing strategy, or even worse encounter a hazard.\\ For more complex systems with several components the Markov approach has its limits, choice of distributions and maintenance details are also restricted. Discrete Event simulation can deal with such complex systems, and also the rare event problem that often is a challenge for safety system analysis can be handled satisfactorily. \\ By use of Harel Statechart and discrete event Monte Carlo simulations for different safety systems, it is shown that the intermediate demand mode is dependent on the relationship between the proof-tests, demands and repair duration. When a demand rate increases to a significant level, demands can be used as tests. With Harel Statecharts we can calculate realistic models that go beyond what a Markov model is capable of. | eng |