A Stochastic Computational Approach for the Analysis of Fuzzy Systems

Uncertainty in fault tree analysis: A fuzzy approach

The traditional Fault Tree Analysis (FTA) has limitations in its capacity to process imprecise, incomplete, and subjective failure data that is usually found in railway door safety systems. To overcome this weakness, this paper proposed a new Fuzzy Fault Tree Analysis (FFTA) model based on Interval Type-2 Fuzzy Sets (IT2FS). A two-parameter Weibull distribution is used to model failure probabilities of basic events in a realistic way for the representation of time-dependent failure behaviour based on expert elicitation and maintenance data. Fuzzy logic gates are used to construct the fault tree, and fuzzy probability propagation is carried out through α-cut decomposition, which is backed by a convexity theorem that guarantees valid interval behaviour in the decomposition. To prioritize critical events, an Adapted Wasserstein Distance (AWD) based Fuzzy Importance Index (FII) is proposed, along with a convergence theorem proving the stability of fuzzy failure estimates with the increase in expert information. The actionable numerical values are derived through the Weighted Divided Search Enhanced Karnik-Mendel (WDEKM) algorithm to transform system-level fuzzy risk outputs into actionable numerical values. The framework is implemented in Python 3.11, using standard scientific libraries. Findings indicate the proposed method’s high performance with a Fuzzy Priority Index of 0.0214, Fuzzy Criticality Index of 0.0186, and better sensitivity values (SI = 0.69, NSC = 0.63, RCR = 16.8) than the existing models. These results prove that the proposed framework provides more informative uncertainty-aware risk estimates and sensitivity indicators for safety and maintenance prioritization in railway door systems.

Improvement of the Reliability Graph with General Gates to Analyze the Reliability of Dynamic Systems That Have Various Operation Modes

In modern science, computer models are often used to understand complex phenomena and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models—providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.

Fuzzy set theory is investigated as a tool for the diagnostics of systems described by means of a fault tree. The objective is to diagnose component failures from the observation of fuzzy symptoms using the information contained in a fault tree. A two-step procedure is used to solve the problem. In this first step, causal reasoning is used to diagnose failure modes, consisting of minimal cut-sets of basic events, from the observation of triggered gates treated as symptoms. In the second step, the authors identify the particular components which have failed based on the diagnosed failure modes. To perform this second step, the solution of a fuzzy relational equation a= V-product (S/sup T/ alpha x) connecting failure mode a to basic events x is derived. With this method, the diagnostics equations can be symmetrically generated and solved in terms of the tree's basic events. The systematic nature with which a diagnosis can be generated from a fault tree lends this method to potential application of object-based programming techniques. >

There are many available techniques which are widely used for failure probability analysis. Fault tree analysis (FTA) is a well-known method to identify the basic events (BEs) to reach top event. However, the FTA method in real circumstances is limited because of the many unknown and the vagueness of the situations. Thus, fuzzy set theory with respect to subjective expert opinion is employed to cope with the uncertain knowledge of BEs including randomness, ignorance, and shortages of data. In addition, to gain this purpose, much subjectivity may appear; as an example, the main one is the expert weighting. This study highlights the utility of fuzzy set theory and analytic hierarchy process to failure probability analysis in a case study. A chemical process plant has been selected to illustrate the application of proposed model with a comparison of the results with conventional model.

Current reliability approaches were designed to assess and quantify the reliability associated with complex systems such as nuclear power plants (NPPs). These approaches are generally based on classical Boolean logic structures such as event trees (ETs) and fault trees (FTs) [Rausand, 2020]. The outcome obtained by combining FTs and ETs is the set of minimal cuts sets (MCSs), with each MCS representing a unique combination of BEs that leads to an undesired outcome (e.g., core damage). Probabilistic evaluation of a MCS is performed by evaluating the product of the probability values associated with each BE. A relevant factor here is that the probability values associated with BEs used in the plant models are updated at least every 4 years based on past operational experience and through the use of a Bayesian statistical process [Siu, 1998]. Hence, the probability value of a BE associated with a physical asset (e.g., a centrifugal pump or motor-operated valve) in no way reflects that asset’s actual condition and performance.
 This fact plays a major role in the application of plant reliability models to support risk-informed decisions. With the particular goal of reducing operation and maintenance costs, existing NPPs are moving from corrective and periodic maintenance toward new types of predictive maintenance strategies [Agarwal, 2021]. This transition is designed such that maintenance is conducted only when the asset requires it (i.e., prior to undergoing imminent failure). And though these benefits cannot be achieved through actual reliability modelling methods and currently employed reliability data, they can be achieved by employing asset-monitoring sensors, automated data acquisition systems, data analysis methods, and improved decision-making processes. Combined, these resources can provide precise information on the health of an asset, track its degradation trends, and estimate its expected failure time. Based on such information, maintenance operations can be scheduled and performed for each asset on an as-needed basis. This dynamic context of predictive maintenance operations requires new methods of data analysis, the propagation of asset health information from the asset level to the system level, and the optimization of plant resources.
 This paper provides an alternative reliability approach designed for a predictive maintenance context in which a direct link is created between monitoring data and decision-making. Rather than thinking of reliability in terms of system/asset probability of failure, we propose a reliability mindset based on the concept of margin [Mandelli, 2023]. An asset’s health is quantified by determining its margin, based on the asset’s current and historical monitoring data. The margin values of the monitored asset are then propagated through system reliability models (e.g., FTs or reliability block diagrams) to identify the assets that are more critical to guarantee system operation. We show how a margin-based approach can be used assess asset health, based solely on current and historic monitoring data (e.g., condition-based, anomaly detection, diagnostic, and prognostic data) [Xingang, 2021]. A margin-based approach directly addresses the limitations of classical reliability modelling approaches and provides a snapshot of system health—given the availability of monitoring data. These two different approaches are designed to address different types of decisions: classical reliability models support static decisions (e.g., a set frequency of periodic maintenance or surveillance operations) based on past operational experience, whereas a margin-based approach directly supports dynamic decisions involving maintenance operations that should only be performed when necessary, based on monitoring data (i.e., a predictive maintenance context).

The article deals with the modelling the complex engineering systems in Aerospace on pre-conceptual design stage. It has been established that the analytical dependence for the modelling do not fully satisfy the modern requirements for the accuracy of calculations and can lead to large errors. This suggests a lack of methodological security of modelling in the preconceptual design. The developed software LANE is a sequential process of iterative procedures of the modelling, decomposition, analysis and synthesis new complex engineering systems in Aerospace.

Nuclear power plants play a significant role in the contribution of electricity generation on a global scale. Various reactor designs have advantages over others in different aspects. APR-1400 is a pressurized water reactor that is deemed safe due to the redundancy and independence of the multiple safety systems. Probabilistic safety assessment (PSA) is well known for its effectiveness in the representation of risk and safety analysis of the systems in a nuclear power plant. It provides different scenarios of system failure and accident progression via fault tree analysis. A loss of feedwater (LOFW) accident may occur due to numerous reasons such as spurious closure of valves, component failure of heaters, pumps, tanks, or a loss of offsite power (LOOP) event. In the present research, a methodology has been developed that aims to investigate different factors contributing to the loss of feedwater. This research also aims to analyze LOFW accidents by developing fault tree models for the main feedwater system of the APR-1400 to identify the basic events, which may lead to a loss of feedwater accidents. The results of the top event probabilities, risk decrease factor (RDF), risk increase factor (RIF), minimal cut sets (MCS), basic event probabilities, and sensitivity analysis were compared with the WASH-1400 database. It has been found that the control valve (V04) and main feedwater isolation valve (V05) have more contribution to the LOFW accident. The common cause failure (CCF) analysis has been carried out, and it was found that the flow toward the check valve and steam generator are most critical for CCF.

In this paper, the authors demonstrate how fault tree analysis could be used to perform reliability analysis of hardware-software systems. The functional dependency of the hardware components on the interfacing software components is appropriately modeled using fault trees. The MIT (Massachusetts Institute of Technology)-CSR's (Center for Space Research) ACIS (Advanced X-ray Astrophysics Facility Imaging Charge Couple Device Imaging Spectrometer) system is used to illustrate the fault tree analysis method in reliability analysis of complex hardware-software systems. The ACIS science instrument system is a space borne system to acquire and process X-ray images over the sky, and sends them to earth. It has hardware and software components with interfaces between them making it a very good example of a complex hardware software system. This approach could be used in analyzing other complex systems being designed today and in identifying the critical components to make the system safe and more reliable.

A reliability analysis method for fuzzy multi-state system with common cause failure based on improved the weakest T-norm

The aim of this paper is introducing a method based on Fuzzy Time-To Failure (FTTF) to improve reliability analysis of complex engineering systems based on fault tree analysis. This method focuses on the quantitative part of fault trees (either static or dynamic) analysis and will compute failure probabilities. FTTF model is developed to estimate the reliability of system and solve aforetime methods problems. The presented FTTF model is able to figure out any construction consist of static and dynamic gates with FTTF distributions integrated on Fuzzy Monte Carlo Simulation (FMCS) techniques to analyzing Possibilistic functions associated with the fuzzy probability distributions for each basic event. Using fuzzy algorithm, gates FTTF are generated, and Top-event TTF evaluated. Some case studies are used to demonstrate the priority of this method in exact evaluation in compared with other solving methods (like: BN, Analytical solution, Markov chain and traditional fuzzy fault tree modeling), but has much less effort while having higher accuracy. Finally, this model is implemented in an Emergency Detection System (EDS) which is a useful system in aerospace and space applications.

In systems engineering (SE) activity in System of Systems (SoS), Enterprise Systems Engineering (ESE), and Complex Systems Engineering (CSE) continues to increase. There is controversy as to how well conventional methods of SE are able to handle our most difficult complex systems problems, and whether new ways of systems thinking will help. This tutorial will: 1) explain and give examples of complex systems and CSE; 2) review related definitions and terminology; 3) present CSE principles to create mindsets that will accelerate progress in your application domains; 4) provide tools for characterizing SE environments and what is being doing about it; and 5) suggest a methodology for CSE. Teamed class exercises will stimulate creative thought and interactions among participants. The presentation materials and accompanying discussions should deepen our understanding of SE and better prepare us for future SE endeavors.

During the modeling of uncertain and imprecise systems, the intelligent approach, based on the use of so-called Fuzzy Cognitive Maps (FCM) is often used. Constructors of the FCM models usually use a technique, in which fuzzy quantities are converted to their crisp equivalents (e.g. in a model learning phase). Such a procedure converts the fuzzy model in a crisp model, which may be a problem in systems with uncertainty. This risk can be avoided by building a model based on fuzzy numbers, fuzzy relations and fuzzy arithmetic operations, but then the new problem — of technical nature — arises, related to the specifics of operations on fuzzy numbers — manifested in the support deformations. The paper proposes a solution to this problem, consisting in a new look at the interpretation of the results of arithmetic operations on fuzzy numbers. New mechanism, that allows overcoming the negative effects of such deformations, is presented. The use of the proposed approach enables maintaining the fuzzy nature of the model at each stage of its operation. The results of simulations for different variants of the proposed method are also shown.

Fault tree analysis is regarded as a powerful technique for assessing system reliability. The conventional approach of solving fault trees is based on applying probability theory by assigning probability distributions to basic events and propagating the probabilities to calculate the overall probability of the top event. However, applying this technique, especially in construction projects, entails several difficulties attributed to the lack of sufficient data to estimate the probability distributions for basic events. Thus, risk analysts tend to assume probability distributions of basic events, which adds further uncertainty to the analysis. To overcome these difficulties, this paper presents a simplified approach in which basic events are represented by a possibility distribution, and the possibility distribution of the top event probability is calculated by applying fuzzy arithmetic operations. The method presented herein is demonstrated using a case study to quantify the probability of failure of horizontal directional drilling (HDD). The proposed approach is able to overcome the difficulties of using the conventional approach by relying on linguistic terms rather than assuming probability distributions for basic events.