A formal approach to derive configurable Markov models for arbitrarily structured safety loops

摘要

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