A Hierarchical Bayesian Approach to IEC 61511 Prior Use

Understanding the quality of failure rate data is vital to successful application of SIS, as emphasized in the latest IEC 61511 standard. This includes quantifying the relevant uncertainties of the inputs and communicating the confidence metrics in SIL verification calculations. The methods for analyzing these issues are unfamiliar to many practicing instrument engineers, and the mathematics may initially appear daunting.

This paper discusses the application of Bayesian credibility intervals to determining prior use failure rates for field instruments, valves, and logic solvers in SIS service. This approach is compared to traditional frequentist approaches. Guidelines for developing Bayesian a priori distributions are given, including practical examples of a priori distributions based on industry data and a demonstration of the Bayesian updating process. The concept of hierarchical prior distributions is introduced, and a practical model for managing enterprise failure rate data is developed. The advantages (and potential pitfalls) of the Bayesian approach are discussed, including the inherent handling of uncertainty, as well as the potential to significantly reduce the total service hours required for prior use justification.