Unavailability of K-out-of-N: G Systems with non-identical Components Based on Markov Model

The process industry has always been faced with the challenging tasks of determining the overall unavailability of safety instrumented systems (SISs). The unavailability of the safety instrumented system is quantified by considering the average probability of failure on demand. To mitigate these challenges, the IEC 61508 has established analytical formulas for estimating the average probability of failure on demand for K-out-of-N (KooN) architectures. However, these formulas are limited to the system with identical components and this limitation has not been addressed in many researches. Hence, this paper proposes an unavailability model based on Markov Model for different redundant system architectures with non-identical components and generalised formulas are established for non-identical k-out-of-n and n-out-of-n configurations. Furthermore, the proposed model incorporates undetected failure rate and evaluates its impact on the unavailability quantification of SIS. The accuracy of the proposed model is verified with the existing unavailability methods and it is shown that the proposed approach provides a sufficiently robust result for all system architectures.