Fuzzy representations of statistical uncertainty for risk assessment



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Texas Tech University


When insufficient data is available, the use of probability theory for risk assessment may be both difficult and highly inaccurate. In such cases, subjective expert experience may be a viable alternative. Experts can give their degree of belief that a parameter's value would fall within a given range. These parameters are interpreted as fuzzy variables.

Hazardous material transportation is one topic in which the constraints and consequences of possible actions/events are not known precisely, with no means to acquire enough statistical data. This motivates our investigation using fuzzy set theory.

We use a fuzzy fault tree to assess the risk of failure associated with transportation of hazardous material. The fault tree describes the sequence/combination of events that may lead to a failure. Such events may be due to human errors, severe weather conditions, intelligence leaks, etc. The top event of the tree is a catastrophic failure, such as environmental contamination or cross of material.

Each event in the fault tree has its own membership function in which the fuzzy variable is the probability that this even may occur. The membership grade is the degree of belief that this probability may take on a certain value. Our work is inspired by PHASER (Probabilistic Hybrid Analytical System Evaluation Routine), implemented at Sandia National Laboratories by R.J. Roginski and J.A. Cooper. PHASER calculates the top event probability of failure for a fault.