Failure Probability Of Top Event Research Articles

An intuitionistic fuzzy probabilistic Petri net method for risk assessment on submarine pipeline leakage failure

Under the influence of various factors, the submarine pipelines will be damaged, resulting in oil and gas leakage accidents. It is essential to perform risk assessments to prevent accidents. However, accurate and sufficient historical data usually can not be obtained. To solve this problem, this study proposes a probabilistic Petri net (PPN) method based on intuitionistic fuzzy evidential reasoning (IFER), which can determine the failure probability of basic events through domain expert experience, and quantitatively evaluate the probability of submarine pipeline leakage failure. The main contributes include: according to DNV-RP-F107, a group of intuitionistic fuzzy numbers is defined and an improved probability conversion method is proposed for defuzzification; an IFER approach is proposed, which uses belief structures as expert linguistic terms and transforms them into IFNs to deal with the uncertainty of expert evaluation; a probabilistic Petri net method is proposed to quantitatively calculate the failure probability of top event and identify the critical events. Finally, the proposed intuitionistic fuzzy probabilistic Petri net (IFPPN) method is illustrated by a case study. By comparing with the existing methods, the feasibility of this method is validated, and the evaluation results can provide a reference for the safe operation of the pipeline system.

Risk Assessment of Water Treatment Plants Using Fuzzy Fault Tree Analysis and Monte Carlo Simulation

Urban water supply, transmission, and distribution systems are considered as the basic infrastructures of each community. Deficiency of water resources in system leads to lack of some subscribers’ access to safe water at any time. The water treatment units have a high potential for massive crisis and importance of sustainable performance in water treatment plants, due to their special role in high quantity and quality water supply even in critical situations, requires a comprehensive approach in assessing and increasing the reliability. A comprehensive approach in assessing the performance of water treatment plants and reducing their vulnerability can lead to cost reduction of inappropriate performance in critical situations and also a focus on the most important vulnerable parts of water treatment plants to decrease their vulnerability, as well as cost-effective budgeting in recovery programs. In this research, due to the uncertainties in the input information, two methods of fuzzy fault tree analysis (FFTA) and fault tree analysis (FTA) based on Monte Carlo simulation were evaluated in Jalaliyeh water treatment plant in Tehran, and results of both approaches were compared in terms of uncertainty analysis. The results indicate the low to moderate failure risk in the treatment plant in both approaches and a small difference between results in both cases. Failure probability of top event for FFTA and Monte Carlo-based FTA methods is 0.194 and 0.27, respectively. In the basic event rating, it was found that threats such as inappropriate reservoir design, power equipment failure, transfer pipe failure, and inappropriate maintenance of the pumps play the major role in treatment plant failure.

A Stochastic Approach for the Analysis of Fault Trees With Priority AND Gates

Dynamic fault tree (DFT) analysis has been used to account for dynamic behaviors such as the sequence-dependent, functional-dependent, and priority relationships among the failures of basic events. Various methodologies have been developed to analyze a DFT; however, most methods require a complex analytical procedure or a significant simulation time for an accurate analysis. In this paper, a stochastic computational approach is proposed for an efficient analysis of the top event's failure probability in a DFT with priority AND (PAND) gates. A stochastic model is initially proposed for a two-input PAND gate, and a successive cascading model is then presented for a general multiple-input PAND gate. A stochastic approach using the proposed models provides an efficient analysis of a DFT compared to an accurate analysis or algebraic approach. The accuracy of a stochastic analysis increases with the length of random binary bit streams in stochastic computation. The use of non-Bernoulli sequences of random permutations of fixed counts of 1s and 0s as initial input events' probabilities makes the stochastic approach more efficient, and more accurate than Monte Carlo simulation. Non-exponential failure distributions and repeated events are readily handled by the stochastic approach. The accuracy, efficiency, and scalability of the stochastic approach are shown by several case studies of DFT analysis.

Reliability Analysis of Ventilation System Based on Fuzzy Fault Tree

The fuzzy Fault Tree Analysis (FTA) of mine ventilation system is set up based on thorough composition of the system, with triangular fuzzy number being used as probability of elementary event and “mine ventilation system fault” being deemed as top event. In this paper, the reliability of FTA has been analyzed and applied to a mine in Gansu Province. The result shows that the minimum cut set of fault tree is 549 and the main reason why it has a huge number of minimum cut set is Level 1，Event 7，“Monitoring feedback system failure”. The reliability of top event and Level 1 event is low, and fuzzy failure probability of top event is (0.009, 0.014, 0.009), the maximum of which is 2.3% of it. The degree of fuzzy importance of elementary event is the highest in Level 1，Event 7. The maximum of fuzzy importance is 0.0843 by the normalization and the rest vary from 0.0050 to 0.0100 mostly.

Estimation of failure probability of oil and gas transmission pipelines by fuzzy fault tree analysis

Abstract Failure of oil and gas transmission pipelines was analyzed by fault tree analysis in this paper. According to failure modes of pipeline: leakage and rupture, a fault tree of the pipeline was constructed. Fifty-five minimal cut sets of the fault tree had been achieved by qualitative analysis, while the failure probability of top event and the important analyses of basic events were evaluated by quantitative analysis. In conventional fault tree analysis, probabilities of the basic events were treated as precise values, which could not reflect real situation of system because of ambiguity and imprecision of some basic events. In order to overcome this disadvantage, a new method was proposed which combined expert elicitation with fuzzy set theories to evaluate probability of the events. As an example, failure probability of pipeline installation was assessed by using the proposed method, achieving its fuzzy failure probability of 6.4603×10 −3 . The method given in this article is effective to treat fuzzy events of FTA.

Uncertainty in fault tree analysis: A fuzzy approach

In fault tree analysis, the uncertainties in the failure probability and/or failure rate of system components or basic events can be propagated to find the uncertainty in the overall system failure probability. The conventional approach is Monte-Carlo simulation by assuming a probability distribution for the failure probability. In addition, a new methodology based on fuzzy set theory is also being used in the fault tree analysis for quantifying the basic event uncertainty and for propagating it. However, identification of the components which contribute maximum to the system failure probability is also important in fault tree analysis. Similarly, ranking the components based on their contribution of uncertainty to the uncertainty of the system failure probability is also very important. This paper presents a comparative study of probabilistic and fuzzy methodologies for top event uncertainty evaluation. Further, it explains a new approach to rank the system components or basic events depending on (1) their contribution to the top event failure probability and (2) their uncertainty contribution to the uncertainty of the top event based on fuzzy set theory.

A simple method of determining moments of a top event

Describes a simple algorithm which has been developed for determining exact moments of top event failure probability from the moments of the basic events in a fault tree. This method requires neither Taylor series expansion of top event failure probability function nor its partial derivates to find these moments. This method has subsequently extended to systems with multistate components. Describes a general algorithm for the purpose. Provides several illustrations to highlight its usefulness.

A general method dealing with correlations in uncertainty propagation in fault trees

Abstract This paper deals with the correlations among the failure probabilities (frequencies) of not only the identical basic events but also other basic events in a fault tree. It presents a general and simple method to include these correlations in uncertainty propagation. Two examples illustrate this method and show that neglecting these correlations results in large underestimation of the top event failure probability (frequency).

Fault tree truncation error bounds

The solution of large fault trees can only performed if cut sets of a high order or low probability are neglected. This procedure is non-pessimistic since possible contributions to the top gate failure probability are ignored. Since the number of cut sets neglected is generally large, it is possible that their total contribution is significant compared to the total probability of those cut sets included in the evaluation of the top gate failure probability. In this paper a practical method for the estimation of upper bounds on the total failure probability of cuts sets of a given order is presented. This allows bounds on the contribution of all the cut sets neglected through cut-off procedures in fault tree solutions to be calculated, and so validate the top event failure probability. The method given here is much superior to that suggested by Modarres and Dezfuli in that it produces much lower and hence more useful bounds. The method of Modarres and Dezfuli can be refined, but for realistic fault tree examples the method given here always gives the least pessimistic and most practical bounds.

Uncertainty analysis of reactor safety systems with statistically correlated failure data

The probability of occurrence of the top event of a fault tree is estimated from failure probability of components that constitute the fault tree. Component failure probabilities are subject to statistical uncertainties. In addition, there are cases where the failure data are statistically correlated. Most fault tree evaluations have so far been based on uncorrelated component failure data. The subject of this paper is the description of a method of assessing the probability intervals for the top event failure probability of fault trees when component failure data are statistically correlated. To estimate the mean and variance of the top event, a second-order system moment method is presented through Taylor series expansion, which provides an alternative to the normally used Monte-Carlo method. For cases where component failure probabilities are statistically correlated, the Taylor expansion terms are treated properly. A moment matching technique is used to obtain the probability distribution function (pdf) of the top event through fitting a Johnson S B distribution. The computer program (CORRELATE) was developed to perform the calculations necessary for the implementation of the method developed. The CORRELATE code is very efficient and consumes minimal computer time. This is primarily because it does not employ the time-consuming Monte-Carlo method.