A formal approach to derive configurable Markov modelsfor arbitrarily structured safety loops

摘要

The basic PFD-calculation formulas as can be found in IEC 61508 do not apply for non-standardrnSIFs e.g. systems that are equipped with diverse components. A more powerful mathematicalrntoolkit is therefore necessary in order to enable to calculate for more complex safety loops. Markovrnmodels are capable of calculating all safety-relevant measures such as the probability of failure onrndemand (PFD) or the probability of tripping spuriously (PTS) for arbitrarily structured systems. Onrnthe other hand a specific model for every single setup has to be constructed – normally resulting in arntime-consuming engineering and verification process. Most approaches lead to a library of Markovrnmodels that has to be totally reengineered if only minor changes in the company's repair strategyrnoccur. This paper presents a formal approach to construct arbitrary Markov models adequate for PFD-calculation.rnA set of equations enables to generate the Markov state space as well as the transitionrnmatrix by using commonly used configuration and system-behavior parameters as input. The inputrndata is in terms of standard description language, using e.g. the M out of N (MooN) formula. Anyrnpossible loop dynamic can be realized by simply varying parameters or – if necessary – adding newrnstructure equations. Verification for such a generically created Markov model becomes redundantrnsince the model has to be considered valid if the underlying set of equations is.rnOur approach is basically verified by using the equations in a proprietary software tool and comparingrncalculation results with tables from IEC 61508.