Dynamic Markov‐Coupled SIL Assessment and Test Interval Optimization for Safety Instrumented Systems with Hierarchical Voting Structures

ABSTRACT

Safety instrumented systems (SISs) with hierarchical voting structures require safety integrity level (SIL) assessment across coupled voting layers. Conventional static fault tree analysis (FTA) and layerwise Markov calculations usually pass the probability of failure on demand (PFD) of an inner voting unit to the outer layer as a fixed event probability, although it changes with operating time, repair, common cause failure (CCF), and proof testing. We propose a dynamic Markov coupled method for low demand SISs. The method solves the inner voting Markov models first, maps stepwise inner PFD to equivalent outer channel dangerous failure rates through the low demand PFD _avg approximation, and updates the outer Markov model recursively. In the gas treatment case, the proposed calculation gives PFD _avg = 1.537 × 10 ⁻⁵ , compared with 18.164 × 10 ⁻⁵ from the static FTA baseline. In the storage tank interlock, the SIL 3/SIL 2 boundary changes from 18,136 h to 19,316 h, giving a calculated proof test interval margin of 1180 h under the stated assumptions. OAT sensitivity and a ±20% scenario envelope show that undetected dangerous failure rates control the interval estimate and bound the proof test interval under parameter variation.