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Derivation of an equation for quantitative SIL assignment.

Edward M Marszal1

  • 1Exida. emarszal@exida.com

ISA Transactions
|January 28, 2003
PubMed
Summary

Quantitative risk analysis for selecting Safety Integrity Levels (SILs) is gaining traction. This study rigorously derives a key equation for Probability of Failure on Demand (PFD) in Safety Instrumented Functions (SIFs), aiming to improve accuracy and adoption.

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Area of Science:

  • Risk Management
  • Functional Safety Engineering
  • Probability Theory

Background:

  • Quantitative risk analysis is increasingly used for Safety Integrity Level (SIL) selection, driven by high costs of qualitative methods.
  • Current quantitative SIL selection procedures are underdeveloped, with limited literature and often flawed ad hoc engineering approaches.
  • A common equation relates Probability of Failure on Demand (PFD) to tolerable risk and unmitigated event frequency, but lacks rigorous derivation.

Purpose of the Study:

  • To provide a scientifically rigorous derivation for the commonly used SIL selection equation.
  • To enhance the credibility and encourage wider adoption of quantitative SIL selection methods in the process industries.
  • To standardize the mathematical basis for PFD calculations in Safety Instrumented Functions (SIFs).

Main Methods:

  • Derivation of the PFD(SIF) = f(Tolerable Risk)/f(Unmitigated Event) equation.
  • Application of fundamental probability laws.
  • Adherence to standardized definitions within Safety Instrumented Systems (SIS) engineering.

Main Results:

  • A mathematically sound derivation of the PFD equation for SIFs.
  • Validation of the equation based on established probability principles.
  • Establishment of a credible foundation for quantitative SIL assessment.

Conclusions:

  • The rigorous derivation lends significant credibility to the quantitative SIL selection process.
  • Increased usage of this validated method is expected in the process industries.
  • This work addresses a critical gap in the literature and practice of functional safety engineering.

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