Fuzzy Reliability Based Bow Tie Analysis of Coal Mine Water Inrush Risks

"Water inrush is a serious geological accident in underground coal mines. This paper focuses on the method of the bow tie analysis based on fuzzy reliability to assess the risk of water inrush in coal mines. First, post failure probability and repair probability of initiating events are divided into 5 levels. Then triangular fuzzy numbers are adopted to quantify experts’ language and to acquire the reliability rate which close to the actual values by defuzzification and calculation. According to dynamic bow-tie analysis model, using the method of moments to fit the reliability time of events by Weibull distribution and offering the random sampling rule of failure and repair time for illustrating the feasibility of fuzzy reliability evaluation. To demonstrate the effectiveness of the proposed assessment approach, bow tie analysis model of water inrush in coal mines is taken as an example.Introduction Dynamic bow tie (DBT) analysis is composed of dynamic fault tree and dynamic event tree analysis, and considers the impact of the time factor upon risk assessment of a system. There are many algorithms applied to calculation of the probabilities of node accident and accident consequence of dynamic bow tie analysis: Hidden Markov Model, Bayesian Network (Khakzad et al 2013), Integral Algorithm (Amari et al 2003) and Monte Carlo Simulation (Kim et al 2016). In terms of simulated time and practicability, the Monte Carlo Simulation has an advantage over other methods. DBT requires mass data in quantitative analysis, including the failure rates and the repair rates of the basic events of the Fault Tree (FT) and the subsequent events of the Event Tree (ET) at different time points, i.e., the distribution of failure time and repair time. In practical analysis, it is hard to obtain a large amount of exact historical statistical data, which is a major problem of risk assessment. Due to the difficulty of obtaining the exact data and historical failure data of the basic events and the subsequent events, the FT and ET analysis is stuck with the study of minimal cut sets, minimal diameter sets, structural importance and qualitative analysis (Liu and Zhang 2010, Yan et al 2012, Wang et al 2009, Li and Wang 2011). This paper will use fuzzy numbers and the defuzzification method to transform the experts’ language into the failure rates and repair rates of basic events and subsequent events, solving the problem that it is difficult to obtain a large amount of historical statistical data, and will use the method of moment to conduct Weibull fitting of the reliability time to provide the random sampling criteria of event failure and repair time in Monte Carlo simulation."