IEC 61508 requires the establishment of a safety integrity level for any safety-related system to mitigate risk. The purpose of safety integrity level is to establish acceptable probability of failure on demand. The standard cites the quantitative techniques to be used to calculate the probability of failure on demand. However, the average probability of failure on demand (PFD_(avg)) is interpreted as steady state unavailability and the equations used for calculating the PFD_(avg) are obtained as unavailability. In practical applications, a system may fail right after a proof test, right before the proof test or at any time in proof test interval. In such a circumstance, the system will not reach steady state. In this paper, the failure modes of safety-related systems are analysed. In addition, Markov method is introduced to perform the quantitative analysis through the detailed mathematical derivation.
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