A Method for Temporal Fault Tree Analysis Using Intuitionistic Fuzzy Set and Expert Elicitation

Temporal fault trees (TFTs), an extension of classical Boolean fault trees, can model time-dependent failure behaviour of dynamic systems. The methodologies used for quantitative analysis of TFTs include algebraic solutions, Petri nets (PN), and Bayesian networks (BN). In these approaches, precise failure data of components are usually used to calculate the probability of the top event of a TFT. However, it can be problematic to obtain these precise data due to the imprecise and incomplete information about the components of a system. In this paper, we propose a framework that combines intuitionistic fuzzy set theory and expert elicitation to enable quantitative analysis of TFTs of dynamic systems with uncertain data. Experts' opinions are taken into account to compute the failure probability of the basic events of the TFT as intuitionistic fuzzy numbers. Subsequently, for the algebraic approach, the intuitionistic fuzzy operators for the logic gates of TFT are defined to quantify the TFT. On the other hand, for the quantification of TFTs via PN and BN-based approaches, the intuitionistic fuzzy numbers are defuzzified to be used in these approaches. As a result, the framework can be used with all the currently available TFT analysis approaches. The effectiveness of the proposed framework is illustrated via application to a practical system and through a comparison of the results of each approach.