Extending the Possibilities of Quantitative Determination of SIL ‐ a Procedure Based on IEC 61508 and the Markov Model with Common Cause Failures

Generalized equations for calculating the probability of failure on demand (PFD) in accordance with the IEC 61508 standard and a model based on Markov processes, taking into account common cause failures, are proposed in this paper. The solutions presented in the standard and in many references concentrate on simple k‐out‐of‐n architectures. The equations proposed in the standard concern cases for n ≤ 3. In safety‐related systems applied in industry, architectures of a number of elements n larger than three often occur. For this reason, a generalized equation for calculating PFD was proposed. For cases presented in the standard, the proposed equation provides identical results. The presented simplified Markov model allows the determination of the system availability (A(t)) and unavailability (1–A(t)) as well as their values in the steady state (A and 1–A). This model can be an alternative method of PDF calculations for various k‐out‐of‐n architectures with self‐diagnostic elements. Calculations performed according to the proposed models provide very similar results. The developed models are suitable for practical implementations in calculations of the safety integrity level.