Rare event likelihood estimation and conditioning in risk analysis

This document presents the development of a formal and rigorous methodology, titled Rare Event Likelihood Estimation and Conditioning (RELEC), which was established to deal with the quantification of the rare event, making use of "close call accident" information. The approach illustrates the application of fuzzy set theory and simulation techniques to maximize the knowledge gained from such data. A new way of viewing subjective probability, within the framework of fuzzy set theory, is illustrated. This work successfully demonstrates the estimation of likelihood of the rare event using RELEC, the technique's ability to systematically capture the information contained in close call accidents, the utility of the technique to formulate process improvement recommendations, and its ability to reduce the level of subjectivity associated with the quantification of the rare event. Essentially, there are two types of probability recognized by classical set theory, objective and subjective, the later of which is the basis of expert opinion analysis. Objective probability is based upon either a discrete set of outcomes or data obtained from reasonable, empirical experience. As is the case with the rare event, subjective probability must be utilized when all of the outcomes are not known, or are fuzzy, and when even the frequency of those outcomes recognized cannot be estimated with any certainty. Taking a frequentist view of fuzzy set theory, however, allows the analyst to evaluate data that do not clearly belong, or not belong to the set of events representing the fault state of interest. There may be intermediate grades of membership. This idea is the concept of a fuzzy set, which is a "class" with a continuum of grades of membership. Viewing "close call accidents" as a fuzzy set allows for the systematic inclusion of these events in the analysis process and greatly reduces the degree of subjectivity. Application of RELEC is a four phase process. First, a Possibility Logic Tree (PLT) is developed by experts using physical knowledge and experience of the operational environment. Essentially, this phase captures the knowledge of the experts and allows for a more systematic and repeatable analysis of the "close call accident" information. Once the PLT has been fully developed, the risk analyst then performs a possibility logic tree analysis (PLTA) using an accident history database. Discrete accidents are assigned to possibility states by meeting the predetermined criteria established in the PLT. The results of this analysis, in turn, feed directly into the development of the fuzzy set conditioning module of the RELEC simulation model. The fourth and final phase of the application of RELEC is to run the simulation and analyze the model output, thus facilitating the quantification of the rare event. In addition, by plotting the possibility spectrum derived from the simulation, the analyst, using Pareto principles in conjunction with the possibility logic tree, may make and test direct process improvement recommendations. Risk reduction should not be viewed as an add on, but as another design objective, on par with operability, security, and maintainability.