A Fuzzy Probability Algorithm for Evaluating the AP1000 Long Term Cooling System to Mitigate Large Break LOCA

Abstract

Components of nuclear power plants do not always have historical failure data to probabilistically evaluate their reliability characteristics. To overcome this drawback, an alternative approach has been proposed by involving experts to qualitatively justify basic event likelihood occurences. However, expert judgments always involve epistemic uncertainty and this uncertainty needs to be quantified. Existing fault tree analysis quantifies uncertainty using Monte Carlo simulation, which is based on probability distributions. Since expert judgments are not described in probability distributions, Monte Carlo simulation is not appropriate for evaluating epistemic uncertainty. Therefore, a new approach needs to be developed to overcome this limitation. This study proposes a fuzzy probability algorithm to evaluate epistemic uncertainties in fault tree analysis. In the proposed algorithm, fuzzy probabilities are used to represent epistemic uncertainties of basic events, intermediate events, and the top event. To propagate and quantify epistemic uncertainty in fault tree analysis, a fuzzy multiplication rule and a fuzzy complementation rule are applied to substitute the AND Boolean and OR Boolean gates, respectively. To see the feasibility and applicability of the proposed algorithm, a case-based experiment on uncertainty evaluation of the AP1000 long term cooling system to mitigate the large break loss of coolant accident is discussed. The result shows that the best estimate probability to describe the failure of AP1000 long term cooling system generated by the proposed algorithmis 3.15×10-11 , which is very closed to the reference value of 1.11×10-11. This result confirms that the proposed algorithm offers a good alternative approach to quantify uncertainties in probabilistic safety assessment by fault tree analysis.

Fuzzy probability and α‐cut based‐fault tree analysis approach to evaluate the reliability and safety of complex engineering systems

“…For the sake of benchmarking, this case study applies data published in Purba 72 . The details of the experts’ subjective justifications for the LTCS can be read in Purba 72 .…”

“…72 The details of the experts' subjective justifications for the LTCS can be read in Purba. 72 It can be read in this reference that 26 basic events of the LTCS FT need to be evaluated. Using Equation (11), those basic events can be denoted as in Equation (31).…”

“…For the sake of benchmarking, this case study applies data published in Purba. 72 The details of the experts' subjective justifications for the LTCS can be read in Purba. 72 Those data are then used to generate the 26-by-7 matrix of failure possibilities (F) in Equation (12).…”

“…72 The details of the experts' subjective justifications for the LTCS can be read in Purba. 72 Those data are then used to generate the 26-by-7 matrix of failure possibilities (F) in Equation (12). For example, the fifth basic event in Equation (31), which can be denoted as V 15 , are characterized as RL, M, M, RL, RL, RL, and M, which are subjectively justified by the seven selected experts.…”

The Implementation of Importance Measure Approaches for Criticality Analysis in Fault Tree Analysis: A Review

“…Furthermore, Hadavi [2] developed accident scenarios and evaluated the performance of safety related systems of a typical WWER-1000 nuclear reactor also using FTA. FTA was also applied to evaluate the reliability of the Indian Prototype Fast Breeder Reactor [3], the failure probability of the containment spray injection system [4] and the reactor protection system [5] of a typical PWR, and the reliability of the AP1000 passive safety systems [6][7][8][9].…”