## 1 Introduction  
Many engineering systems have such characters as high technology, high investment and high risk. During the operation process, the complex system is enormously affected by the internal and external loads, such as vibration, fatigue, temperature and human operation factors, even subjected to various hazards including natural disasters, terrorist and criminal acts [1; 2; 3]. Once an accident occurs,it will cause a series of problems such as transport accidents, explosions, casualties, fires and chemical and biological emission. Especially equipment storing inflammable and explosive materials such as chemical fuels, aviation equipment that is extremely hazardous in the event of an accident, and facilities that transport oil and gas energy have negative effects on environment, economy, society and life if an accident happened. Therefore, good judgments should be made on the risk, reliability, availability and uncertainty of such facilities. A series of analysis methods were proposed over the years for reliability and risk evaluation, such as fault tree, bowtie, event tree, Petri nets, Markov models, Bayesian networks and so on. Though these methods can model potential faults, they have limited capabilities to handle insufficient data of failure probabilities, therefore resulting in an inaccurate risk assessment result [4]. To resolve this issue, expert evaluation and fuzzy theory were adopted to calculate fuzzy failure probabilities of risk factors. The method can characterize the uncertain parameters involved in a risk analysis process [2; 5]. The method has been extensively used in engineering fields, such as aerospace, subsea facilities, energy, transport, etc. [PERSON] introduced it into fault tree to calculate probabilities of base events of spread mooring systems [6]. [PERSON] [7] proposed a Bayesian network-based model for well plugging and abandonment in uncertain conditions with limited data. In addition, researchers such as [PERSON] [8], [PERSON] [9], [PERSON] [10], [PERSON] [11], [PERSON] [12] and [PERSON] [13] all made related research works. According to previous studies, the \"Failure Cause Probability\" and \"Failure Effect Severity\" play vital roles in the reliability and safety of the system. Thus, the \"Failure Cause Probability\" and \"Failure Effect Severity\" of risk factors should be considered. Considering the weight coefficient of every expert, the comprehensive risk value of the failure event can be obtained. After sufficient data are available, an accurate analysis of system reliability and availability can be performed. The assessment of the availability and reliability of a multi-state degraded system with repairs and preventive maintenance usually uses a Markov process [14]. The availability of subsea Blowout Preventers in the Gulf of Mexico Outer Continental Shelf was investigated using a Markov method by [PERSON] [15]. [PERSON] [16] presented a Markov method to analyze the reliability of the electrical control system of a subsea blowout preventer stack. [PERSON] used Markov processes to model the reliability for the electrical control system of the subsea control module [17] and enhanced the reliability within the given space [18]. Fuzzy theory and Markov technology have been increasingly used in reliability and risk analysis studies. However, due to the increasing complexity of engineering systems and the inherent limitations of each technology, many scholars [19; 20; 21] have used a combination of multiple analysis methods to evaluate the system performance; the use of hybrid models is a general trend. In addition, because the risk of the engineering system abounds with uncertainty, uncontrollability and randomness, it is necessary to use the uncertainty analysis method to evaluate the operation of the system. [PERSON] proposed a probabilistic approach to account for the uncertainty of shallow landslide assessment. This method can evaluate the location and time of the possibility of soil failure plane by calculating the joint probability [22].