To estimate failure probabilities of chemical plant safety systems using Bayesian analysis, prior probability distributions are used in conjunction with likelihood probability distributions to calculate posterior probability distributions. The prior distributions are classically calculated from expert knowledge and/or plant data, and the likelihood distributions from plant data. When safety systems of a plant are rarely activated, the plant alarm data are sparse, which leads to Bayesian-analysis-calculated posterior distributions that depend more on prior distributions.
Moskowitz et al. (2015) introduced a method of repeated simulation to construct informed prior distributions for the failure probabilities of alarm and safety interlock systems. The resulting posterior distributions were shown to be more reliable than those obtained using a few alarm occurrences over extended operating periods.
In this paper, we present a method of evaluating plant models in terms of their ability to predict safety-system failure probabilities. The application and performance of the method are shown by developing and evaluating four mathematical models of an industrial steam-methane reformer (Moskowitz et al., 2015). The quality of these models is evaluated using plant measurements of effluent temperatures from reformer tubes and the surrounding furnace.
Informed prior distributions are generated using each model. When using plant feed stream data, dynamic simulations yield a close alignment between model quality and informed prior distribution quality. Steady-state simulations yield a weaker alignment.
When modeling the operator safety system, skill and attentiveness are difficult to estimate. Herein, operator responses are modeled as a function of the number of active alarms and past operator successes. Typical operator response times and response accuracies are estimated as functions of alarm count intervals and operator skill types. Resulting informed prior distributions show the effect of increasing operator skill level and process over-alarming.
Moskowitz, I. H., W. D. Seider, M. Soroush, U. G. Oktem, and J. E. Arbogast, "Chemical Process Simulation for Dynamic Risk Analysis: A Steam-Methane Reformer Case Study", Ind. Eng. Chem. Res., 54, 4347-4359 (2015).