تجزیه و تحلیل ایمنی در تجهیزات فرآیند: مقایسه درخت خطا و روش شبکه های بیزی

Safety analysis in gas process facilities is necessary to prevent unwanted events that may cause catastrophic accidents. Accident scenario analysis with probability updating is the key to dynamic safety analysis. Although conventional failure assessment techniques such as fault tree (FT) have been used effectively for this purpose, they suffer severe limitations of static structure and uncertainty handling, which are of great significance in process safety analysis. Bayesian network (BN) is an alternative technique with ample potential for application in safety analysis. BNs have a strong similarity to FTs in many respects; however, the distinct advantages making them more suitable than FTs are their ability in explicitly representing the dependencies of events, updating probabilities, and coping with uncertainties. The objective of this paper is to demonstrate the application of BNs in safety analysis of process systems. The first part of the paper shows those modeling aspects that are common between FT and BN, giving preference to BN due to its ability to update probabilities. The second part is devoted to various modeling features of BN, helping to incorporate multi-state variables, dependent failures, functional uncertainty, and expert opinion which are frequently encountered in safety analysis, but cannot be considered by FT. The paper concludes that BN is a superior technique in safety analysis because of its flexible structure, allowing it to fit a wide variety of accident scenarios.

Safety analysis is very important in gas process facilities as they deal with a large amount of flammable chemicals; also, process areas are congested with complex piping, high-pressure compressors, and separators of which malfunctions and mishaps may lead to catastrophic accidents [1] and [2]. There have been many fatal explosions and fires imposing major capital loss and considerable death toll in the past two decades. On 23 March 2005, the BP refinery explosion in Texas City caused 15 deaths and more than 170 injuries [3]. According to the final report issued by BP [4], a lack of process safety measures and insufficient risk reduction measures were entirely to blame for the accident. On 7 February 2010, the Kleen Energy power plant exploded in Middletown, Connecticut, U.S., killing 6 and injuring at least 12. The explosion was one of the worst industrial disasters in the U.S. in recent years [5]. Most recently, on 20 April 2010, explosion and fire on Transocean Ltd’s drilling rig killed 11 and injured 17 in the Gulf of Mexico. The failure of a blowout preventer has been determined as the primary cause of the accident [6]. It is important to broaden the risk analysis scope by considering accident scenario and real-time safety analysis in order to predict and continuously update the likelihood of catastrophic accidents and to take actions to prevent them. Forecasting likely accident scenarios is the most important step in safety analysis. Khan [7] proposed a “maximum credible accident scenario” approach that short-lists the important scenarios based on both their consequences and the likelihood of accident occurrence. Delvosalle et al. [8] used two methodologies: MIMAH for the identification of major accident hazards, in which no safety system was considered, and MIRAS for the identification of reference accident scenarios, in which all the actual safety functions and barriers were included in the analysis. The next step in safety analysis is to quantify the occurrence probability of the selected accident scenarios. For this, there are many techniques available, among which fault tree (FT) is very popular. Although having some limitations, FTs are extensively used in the field of risk analysis of process systems [1], [9] and [10] and fault diagnosis [11], [12] and [13]. Standard FTs are not suitable for analyzing large systems, particularly if the system presents redundant failures, common cause failures, or mutually exclusive primary events. More importantly, events in a FT are assumed independent, which is not usually a valid assumption [2], [14] and [15]. In recent years, a Bayesian network (BN) methodology has begun to be used in engineering applications. A BN is a graphical inference technique used to express the causal relationships among variables. BNs are used either to predict the probability of unknown variables or to update the probability of known variables given the certain state of other variables (evidence) through the process of probability propagation or reasoning. The reasoning is based on Bayes’ theorem. Due to this ability, BNs have provided a promising framework for system safety analysis and risk management [16]. BNs are increasingly used in reliability assessment [2], [16], [17] and [18], fault diagnosis [19] and [20], and updating the failure probability of safety systems [21] and [22] have examined the parallels between BNs and FTs and have shown the obvious superiority of BNs over FTs in terms of modeling and analysis capabilities. Bobbio et al. [14] showed that the limitations of FTs can be relaxed to a great extent by relying on BNs. Other relevant works have been done by either mapping static FTs to BNs [15], [23] and [24] or mapping dynamic FTs into the corresponding dynamic BNs [22], [25] and [26]. Many authors have investigated different techniques in accident scenario analysis, very few of whom have used BNs in their work. Sklet [27] qualitatively compared some commonly used methods such as FT analysis, event tree analysis, and barrier analysis for accident analysis. The comparison was made based on criteria such as graphical representation and the ability to support safety barriers. Nivolianitou et al. [28] used FT, event tree, and Petri nets for a qualitative accident scenario analysis in an ammonia storage plant, concluding that Petri nets are able to incorporate the evidence through scenario analysis and thus are more appropriate for dynamic accident analysis. Zheng and Liu [29] made a comparison among some widely used methods for accident forecasting. Although FT as a scenario analysis method and BN were briefly discussed, the main focus in their research was devoted to methods such as regression models, time-series methods, and neural networks. Most recently, Weber et al. [30] gave an exhaustive statistical review of BN application in different areas such as risk and maintenance analysis, in which BN was qualitatively compared with other methods such as FTs, Markov chains, and Petri nets. The present work is aimed at showing the parallels between FTs and BNs in the specific area of accident modeling and process safety analysis, which have not been studied thus far. The paper also discusses the modeling potential offered by BNs, making them a superior method compared to FTs for dynamic safety analysis. A brief description of the fundamentals of FTs, BNs, and the mapping algorithm are presented in Section 2. The comparison of the two methods is done in Section 3, where a simple accident scenario is modeled using both methods. Section 4 is devoted to the application of BN to more complicated scenarios which cannot be modeled using FTs. The conclusions and recommendations for future work are presented in Section 5.

The present study has illustrated the use of BNs in both accident occurrence probability estimation and updating in the light of new information. It also focused on various modeling techniques to capture some types of uncertainty that are common in accident analysis and risk assessment. The first half of the paper was devoted to common features of FT and BN, where a FT was used to construct a corresponding BN. Although both methods resulted in similar estimations for accident occurrence probability, it was the BN that was able to update the prior beliefs about the accident by taking new information into account and by taking advantage of probability updating. The second half of the paper discussed those aspects and modeling issues of BN which FT is incapable of handling, such as multi-state variables, dependent failures and uncertainty. The main conclusions of this study can be summarized as follows: 1. By propagation of new observations through the network, BN updates the prior probabilities, yielding posterior probabilities. These posteriors, unlike priors that are based mainly on generic data and expert knowledge, are more specific to the accident studied and better reflect its characteristics. 2. The calculation of CPTs requires a comprehensive study of causal relationships and a huge amount of data usually provided by domain experts. However, the current study has shown that a BN is a superior technique to a traditional FT even if its CPTs are developed deterministically (Fig. 3). This may be helpful in situations where there is not enough information to estimate the CPT values probabilistically. 3. Considering minimal cut-set importance, it is observed that BN produces a more reliable measure of such importance by providing the most probable configuration of primary events leading to an accident. Unlike minimal cut-sets, the most probable configuration provides information about both occurrence and non-occurrence of primary events. 4. Each FT can be mapped to its corresponding BN, while a BN does not necessarily have an equivalent FT due to multi-state variables, different causal relationships rather than simple Boolean functions such as OR-gate and AND-gate, and sequentially dependent failures. BNs are also able to handle uncertainty without coupling by other methods, i.e., by simply modifying their structure. In general, BN has a much more flexible structure than FT, fitting to a wide range of accident scenarios. Its ability for abductive reasoning and uncertainty handling makes it a more suitable technique for real-time accident analysis and more importantly, for design and evaluation of safety measures. However, before BNs can be used in a comprehensive accident risk assessment, their applicability in accident consequence analysis, safety barrier implementation, and decision making must be examined thoroughly.