Hierarchical Bayesian Prior Use

I presented my paper “A Hierarchical Bayesian Approach to IEC 61511 Prior Use” [full paper] at the 14^th Global Congress on Process Safety in Orlando last month.  Thank you to everyone that was able to attend and to those who expressed support and interest online!

Update:  The full video of my presentation is available free from AIChE for employees of CCPS member companies.  Good news!  If you are reading this post, there is a good chance you are an employee of a CCPS member company!  Check the CCPS company member list now.

This paper represents my third foray into this topic, first with ISA, then the Triconex User Group, and finally with the AIChE/CCPS conference.  The main points of the paper include:

• IEC 61511 requires SIS modelling using real world data based on field feedback in similar service, with data uncertainties assessed and ongoing performance monitoring.
• Traditional frequentist methods are not well suited to these requirements due to sparse failure data. For example, demonstrating SIL3 performance requires 1500 successful proof tests.
• Bayesian methods are an excellent match due to their incorporation of "prior knowledge".  Simple Bayesian methods using conjugate priors can make prior use justification much more feasible.
• More advanced Hierarchical Bayesian methods can be used to analyze complex non-homogenous data sets such as plant failure rate data from multiple services.
• While the mathematics of Bayesian approaches can initially be daunting, there are a variety of free software tools and resources that make it feasible for working engineers.

I welcome your feedback on the paper. Please feel free to comment or contact me directly with any questions.  My experience is that once you "get over the hump" with the mathematics, you will find Bayesian approaches far more intuitive than traditional statistics.

More on Hierarchical Bayesian

If you are interested in learning more about Bayesian methods for reliability analysis, I encourage you to check out the following online papers, reports, and books as a starting point:

• NIST Engineering Statistics Handbook (Sections 1.10, 8.2.5, 8.4.6)
• Handbook of Parameter Estimation for Probabilistic Risk Assessment (NUREG-CR-6823)
• System Reliability Theory: Models, Statistical Methods, and Applications
• Reliability Engineering and Risk Analysis: A Practical Guide

You may download the free RStudio here.  Resources on R and JAGS include:

• Getting Started with JAGS, rjags, and Bayesian Modelling
• The Comprehensive R Archive Network (CRAN)
• R Cookbook
• Doing Bayesian Data Analysis

Also check out our post on System Safety and PRA Resources for more info on Bayesian analysis, including several free books!

Training

Also, please check out the training available from our affiliate partners. (Some courses are free to audit!)

Bayesian Statistics
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R Programming
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