Dynamic validation of safety integrity level for safety instrumented system considering random/fuzzy uncertainty

Abstract

This study proposes a dynamic safety integrity level (SIL) validation framework integrating stochastic and fuzzy uncertainty theories to overcome the limitations of conventional static methods. By combining long short-term memory (LSTM) networks for stochastic failure rate prediction and fuzzy support degree (FSD) algorithms for subjective parameter fusion, the methodology enables real-time SIL updates and quantifies parameter impacts through random forest-based feature importance analysis. Two industrial case studies validate the framework’s efficacy: For the n-hexane buffer tank level high-high interlock SIS (Case 1), the total probability of failure on demand (PFD_avg) increased by 1.71× to 2.48 × 10⁻³ over three years, with the actuator subsystem exhibiting the fastest-growing PFD_avg (2.78×) and a low safe failure fraction (SFF = 0.4589). In the acrylic purification tank outlet flow low interlock SIS (Case 2), the PFD_avg of the sensor subsystem sharply increased by a factor of 3.31 over a 33-month period, and the SFF dropped to 0.1927. The framework classifies 33 types of parameters into stochastic, fuzzy, and constant types, achieving 18–25 % higher accuracy than single-uncertainty methods. Dynamic monthly updates reveal critical trends, such as solenoid valve λ_SU rising to 2.44 × 10⁻⁸ (Case 1) and valve λ_SD3 contributing 76.3 % to PFD_avg growth (Case 2). Feature importance analysis prioritizes high-impact parameters (e.g., λ_DU6 in Case 1; λ_SD3 in Case 2), guiding targeted maintenance. Both cases confirm SIL compliance, with actuator subsystems identified as reliability bottlenecks. This framework bridges static validation and operational dynamics, offering actionable insights for predictive maintenance and industrial safety intelligence.