(54q) Joint Probability Density Estimation for Complex Variables and Its Application to Dynamic Risk Assessment Using Bayesian Method

Kumari, P., Texas A&M University
Mannan, M. S., Texas A&M University
Karim, N., Texas A&M University

Risk assessment concept had been developed for nuclear industry in 1960s and then it got adopted in chemical process industry around 1980s. Since then it has been an integral part of making the chemical processes safer. To assess the risks associated with a process, the first step is identification and prioritization of process parameters that have crucial impact on the process operation. The second step is frequency and consequence modelling of rare events. An extensive literature is available for dynamic risk assessment (DRA) of rare events from accident precursor data, process history, and alarm databases using Bayesian method, Bow-Tie approach and multivariate techniques [1]. Bayesian method when applied with Copula analysis to model dependence structure of variables, is very efficient tool for DRA. However, the models developed still need to deal with highly non-linear, non-monotonic and complex nature of the variables [2].

The first part of the present work makes use of Shannon’s information entropy [3] to identify the important process variables of a process based on maximization of mutual information between precursor and process variables. A cross-correlation analysis is performed to identify the process variables with similar impact on the process. After identifying the contribution of selected process variables to system, in the second part we model the frequency of rare events using Bayesian technique for identifying disturbances. A novel method is employed to get joint probability distribution function of failures of safety levels, which efficiently models and accounts for the complexity and non-monotonicity of variables. Then, Bayesian model is applied to get posterior estimate of safety level failure probability, and rare event frequency corresponding to upsets in process variables. Based on the weights of the process variables from the first part, and frequency of rare events from the second part, a risk indicator has been proposed to reflect the process health. This method is applied on Tennessee Eastman problem to identify faulty process variables, assign weights, and perform dynamic risk assessment.

Keywords: Dynamic risk assessment, joint probability distribution function, information entropy


  1. Pasman H. J., Rogers W. J., Mannan M. S. “Risk assessment: What is it worth? Shall we just do away with it, or can it do a better job?” Safety Science, Volume 99, Part B (November 2017), 140-155
  2. Khan F., Hashemi S. J., Paltrinieri N., Amyotte P., Cozzani V. and Reniers G. “Dynamic risk management: a contemporary approach to process safety management” Curr Opin Chem Eng, 14 (2016), pp. 9-17
  3. Shannon. C.E. “A Mathematical Theory of Communication” Bell Syst. Tech. J., 27 (1948), pp. 379-423