Reverend Bayes, meet Process Safety-Use Bayes’ Theorem to establish site specific confidence in LOPA

by Dave Grattan PE, CFSE & Keith Brumbaugh PE, CFSE

The Process Industry has an established practice of crediting IPLs (Independent Protection Layers) to meet risk reduction targets as part of LOPA (Layer of Protection Analysis) studies. Often the risk targets are calculated to be on the order of 1E-4 per year or lower. Achieving the risk target on paper is one thing, but what is missing from the LOPA calculation is a statement of the confidence in the result. LOPA is an order-of-magnitude method, however, this only reflects the tolerance of error, not the tolerance of uncertainty. It is often stated that LOPA uses generic credits that are conservative, thereby implying the LOPA result should be conservative. By itself this statement is dubious because the generic data used in LOPA did not originate from the facility for which the statistical inferences are being made (which for frequentist-based statistics makes the inference invalid). Worse, when conservative credits are multiplied together to produce a rare-event number, does the conservative property emerge from the combination?

There is no way to answer this question without performing IPL Validation (i.e., ensuring the IPL will function when needed). However, IPL Validation and related Safety Life-cycle methods (e.g. functional safety assessments and cyber-security audits related to barrier integrity) are purely qualitative and have no apparent relation to the quantitative risk target. There is a need therefore, to bridge the qualitative results of IPL validation with the quantitative result of the associated LOPA calculation, as a way to establish a site-specific confidence level in the risk target we are trying to achieve.

This is where Bayes’ Theorem comes in. Bayes’ Theorem is an epistemological statement of knowledge, versus a statement of proportions and relative frequencies. It is therefore a method that can bridge qualitative knowledge with the rare-event numbers that are intended to represent that knowledge.

Bayes’ Theorem is sorely missing from the toolbox of Process Safety practitioners. This paper will introduce Bayes’ Theorem to the reader and discuss the reasons and applications for using Bayes in Process Safety related to IPLs and LOPA. While intended to be introductory (to not discourage potential users), this paper will describe simple ExcelTM based Bayesian calculations that the practitioner can begin to use immediately to address issues such as uncertainty, establishing confidence intervals, properly evaluating LOPA gaps, and incorporating site specific data, all related to IPLs and barriers used to meet LOPA targets.

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